%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: eprint.dvi %%Pages: 25 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMR8 CMR6 CMR9 CMSS9 CMSY9 CMBX9 CMMI9 %%+ CMTI9 CMBX10 CMTI10 CMMI10 CMTT10 MSBM10 CMMI8 CMSS10 CMMIB10 CMBX8 %%+ CMSL9 CMMI6 CMSY10 CMSS8 CMSY8 CMBXTI10 CMSSI10 CMEX10 CMSSBX10 %%+ CMCSC10 MSBM7 CMTT9 CMSY6 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips eprint.dvi -o eprint.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.03.19:2224 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: f7b6d320.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10 % cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8 % cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10 % cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10 % /TeXf7b6d320Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /exclamdown /equal /questiondown /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: bbad153f.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9 % /TeXbbad153fEncoding [ /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast /arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup /arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional /prime /infinity /element /owner /triangle /triangleinv /negationslash /mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur /latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection /unionmulti /logicaland /logicalor /turnstileleft /turnstileright /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright /angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv /backslash /wreathproduct /radical /coproduct /nabla /integral /unionsq /intersectionsq /subsetsqequal /supersetsqequal /section /dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: aae443f0.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10 % /TeXaae443f0Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf /arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft /arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle /twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle /sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash /greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow /slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector /tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 74afc74c.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmbxti10 cmff10 cmfi10 cmfib8 cmti10 cmti12 cmti7 cmti8cmti9 cmu10 % /TeX74afc74cEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /sterling /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /exclamdown /equal /questiondown /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 09fbbfac.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsltt10 cmtt10 cmtt12 cmtt8 cmtt9 /TeX09fbbfacEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /dieresis /visiblespace /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 0ef0afca.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmr5 % /TeX0ef0afcaEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT9 %!PS-AdobeFont-1.1: CMTT9 1.0 %%CreationDate: 1991 Aug 20 16:46:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-6 -233 542 698}readonly def /UniqueID 5000831 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS8 %!PS-AdobeFont-1.1: CMSS8 1.0 %%CreationDate: 1991 Aug 20 17:34:12 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-65 -250 1062 761}readonly def /UniqueID 5000801 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 70 /F put dup 71 /G put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSSBX10 %!PS-AdobeFont-1.1: CMSSBX10 1.0 %%CreationDate: 1991 Aug 20 16:43:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSSBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSSBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-71 -250 1099 780}readonly def /UniqueID 5000806 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 80 /summationtext put dup 88 /summationdisplay put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSSI10 %!PS-AdobeFont-1.1: CMSSI10 1.0 %%CreationDate: 1991 Aug 20 17:34:37 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSSI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -12 def /isFixedPitch false def end readonly def /FontName /CMSSI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-97 -250 1077 759}readonly def /UniqueID 5000810 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBXTI10 %!PS-AdobeFont-1.1: CMBXTI10 1.0 %%CreationDate: 1991 Aug 18 17:46:30 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBXTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMBXTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1274 754}readonly def /UniqueID 5000771 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 5087392 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 4391C9DF440285B8FC159D0E98D4258FC57892DDF0342CA1080743A076089583 6AD6FB2DC4C13F077F17789476E48402796E685107AF60A63FB0DE0266D55CF1 8D0AD65B9342CB686E564758C96164FFA711B11C1CE8C726F3C7BB1044BBD283 9AA4675747DF61E130A55E297CA5F0182A3F12F9085AF2F503481071724077A9 387E27879A9649AD5F186F33500FAC8F7FA26634BDCE1221EC0ED0E359E5EA5E 6166526FEB90C30D30099FBDC1BC2F9B62EFEEC48345160804AA98F8D0AA54B7 A480E715426651865C8E444EDB798C7E11040AF6E5A7ED1888653C6DBF5E6169 70BCD9C063B63B561EF165BF3AF11F8E519F37C6FDA2827685739DE2C48B5ADE EE84F067D704D4511DBFA49E166D543CFD9ECD7417055D8A827F51E087CD2927 BAFC7E6CFBD70B0FE969F890A11149D3D44D422C3370495DA9951AEE7253A49F 3A9444C8CD9158D84117299F7F2332FEB0F94E6ED8BC7AA789A3219BC2F227D3 3B5BC75FB53B55D72AF4A6A7BB613FA235B11BB37D059FD87127CEF73D5B3FBF 9F91ABAD78BD9240BD9525EBA78095EA0BDB25D1A19E876F292882EAD5619D46 D201BA9D4ACCA53A0E4EF0228A39E444F3D674B9BEB0C09BF8FED1922BB97AF0 2CE842A8610A95C6BAF7DACADC32E2D7CBB3F9D263AF03E4B0914CCF9AA55C94 130C7A4AFF8E02ED4BF3E9095DD125E1B31525964367D478A2DDA733AC3B6D51 A1340303F392D802CF23D89D1C2F0FFAB150DB006F94B31AC442F81E84BDE9AF 8CDB1EAEF4C4B22F65104F6D0CF41B88E4322854AE339D9218D212E212342659 207726BC743D5CC43D649F4556F67DCA3C288BB52B1EBC92D2081DBDE279C145 69C5172A5DEA353B13CB41E290D797B3D3B74F933044E6A0621E8824CD89431D 80F453FE409614C0FE8FA8065CE860A1898C40600C1C53FA6B111E053D722BE2 15BA89B04D49A9D06E59850CD9EDE50C7154433DFF792C0E5F176F54144C8305 912AADB683F5BE0C21EC3432EB57C9D16D3246DE9A447BBDADE349E622618A78 992C82D7F7BD91A0BAF396C27C3D8A205C88076E0456CFF799FB46F01877A7A3 6DADD521EE53B501C9C109E9C8410EF3B3BCD37CA68D0CFD50CDB8DF54E61F4C 08B37A649ADC860DA206779D188117F970750D25998BB163F332012A23683333 8A768C3C43D7EDEDF91B0EA1F6C8325A5BFFEADB43FE7716B838CB6B614AC248 237641AA191021089D92D58BE3D39933E718CE0FA12D92D432FDBA85BC31F7F0 D820C5BA212CC81C00B88FE3B5B9AADEB126653F63B64A567202709361E42CD8 49DA24CD269F9567B280D3BE291664F6FD206374DFFA835215F3B8DA26294A7A 41974D58F7DD734B0472204E82C181FF33B082D1A35CB8DE139E338ED7B28F2B 5E35BA90890B61ACE06E3CBF8210D56F709EC5982B10367937548FE909562A2E 6DC758A4B4B8B8D146DFB7B000CAA519FE7512A61DF8E9B65F2F00126A7299A7 FCE34057A20C8FCAFD84BF3EA10D24B7D3ABFD4FD1FA0BBAC43C93710F129431 59E49CD3BEFC389AEC27B82E09B2CB57863F6D405A1CC5C3981A60C939DB15E9 DF1CA71ACBD5B3D3DEBA54C1C22BF214DA6C594CCBB615FCFF224F3FA60C4CA6 785D6DC66E0023F4700FD924D4ED15E453F06B99BE4ABEB082BA220C6991FBBE AEE1D237B0577405ECC68DBDCBC7875F9B2209092E42D76CECE476E3EBA97BFF 90133686B991DF66FD487993724A23D3933AF15E2CBF09AF8833FACE368C96F6 EA7F21B6F2D43C89D646E79BF0BC88E616769A209B4EDF2A36399EDE68FCBA1B 7EAD75C6EF7050044E2EE6027C3CA360055C35E89C89825C0FB992AB0D5AC2AC 2F14DAE7A87611A8A864EEF936F5BCA1212BF16BB1904676425D845180005127 315F6B2E164A005998AA306D42868E8BF837B3F8B40CB11CF9C7FC5098059A52 E6C1C2D0925E50862ADC200AC1E9439E6BAF016866B122870D9DDC9903D5964E FA396DAD6C8BE6FCED13E80331AF785EC57BAFFC798147466A9545E975FBB920 6D1E70ED5E7BA99B737FBB95219EBBDC4405888782A55B6223B435FAD3B4D349 7EC68985528D97EA64BBD0B578C4F89223D25C1D3E74D469F76E7B214F12E76D 5E0FA4BC6E66C14C1090B9F974D75E07834406E842FEB4DB1BC3C6F3AC78AE07 410E40A90802E1FA2AE38C01B2B267B7E7CC5100A0B5C569E8F8882795ED935D B2A2E58D1D903FD4DC112C07D2536749B20ECC1755B5755864B9E18625A7ED5D 596EE41E31708AA7F4B021BDF8A14043B912A6D20DED0B2465068259CE3A9EB9 5F3DE8AAFE11AFFCB26808913220E53C07C8BCFDF81B45BC20F2549E98CC7A20 1F159A4E25AAD45EF304760A2D1E74D430C6BC97EEFB886AFDC0CC536E84592C 8C19C7B571E1B70272DF63147FF8869215703E0739C936A04075DC86390B3D24 1CD8923B7770E413A56DDFBD4C7158D52FA07D131F28F57F55A9762D5E8687CE 53E2A5018EC7F077121D77714A2156C05BEB18772FC7071DC85B38F9A96CDB5F 0F9AD399162520DBA77C23BEF6775170819C3734603C8565F7884F26D373E541 1523F5E0C2C487ED68A478CE6F9D288DCF492F6BAD43975AD3C6F78DEF6C520D 0E047CAD1CCC375CF6828875C71D95C1E1C372452C375B97CC12A3EF087AA893 6C69D111E878AF74ABFF48AAB04F0ADA5F699367E3F4B4C1DD47036803466DA2 AAC4190F211E1C40B6C13544F1EF69543DC17940C62ED33C35D005B07B823434 9709335776BD2AAFEA8182022574BEB444E38D8C9ED8A14CC53A68885960F40E 709E83F6A6811AC6A7A2A3A51394F678AB1A06783D946FF3F234B8FEB953DA4E 2356A54899978515BD2B1AABC710245F2411770AB388C5714972479B4432DBFA 3FCD790890B8F9D0632F46BF7550868154BB378C8A28D3236D7BDA135A56420F 725140B5F4E60659C8350D8846BE775A163D37C827AC2DB0B8C379C1A0614D58 F61B217166C635DA6C135718E9792D1B44389ACF2C1FAB5369D2202A799031C2 AE5251AADBAAAE77A7DBD888966F62C34322B9089BC85D9BE0D50F032701D470 22B659BC5AD6F5FE8C0B8305F4C7BFBEF97F1BD999BED89C0E05865CC34E7C86 00E9E38104F0D86CC3A7204459C53985E01BCC4107CF3558A1DE3636B238F8A7 88C478F10C7FDE2B7AF031D652390EDA9EA8DCCBA70DB8B46603EFC2863B2F1A 50C8CE4F2682BC72056C40E0B1BB79FC12200FB6A81B7A1AE2327B9DF03EBE55 88273F21C8F164B25D6B957127676318F911BC5321311BD9FAF041E012293AE6 AB215A1D2EDA17C85865DF3B7AAE8BC8E0C511C1432A2AFB7534D515173E1074 0DF67CF0984D368DE6664A8483FFB7527F52CC72448EF54025B2B226AEC59E2F 7054A04CCF550505CBBC78B8472F40BC63DD0BC4746D18F5A4446F191943C1C2 C4A05D07AEC7793FA7F70BC75E1146FDCE3DEC1CFAF3D44E6C83E038F9E94D12 7D2344DB515F5154D47BF75B157A1F85740F1585FE949C54E286B1BA50AFEB09 29115813526A2F9703CFB6298A8677BE43BEE985BB275D9FB6F2EE5A2A854A79 E8C5C7CC3891D5003A03372EF6EF87574F4B81D64B98F097A9C984E1625448A2 BD7CAA0A7B236CC1C366F9D21899632EA2DD415079BF711C4577F8E40981F759 72CC2034B01C9B8713AE17B5B587C32EDC0CB081AFCA3040016E7BAF31CF5195 4ECB49568497AE7B5F6F4A78D1A460586209D763201BEA95413B2997D670466A 19D5174680B10FF52B6D6D4B49019D9465F4EF63C9AE240676A2BE38AABD1474 0AE4BBF36B6FD2D0F0C240D53EC4C5D513F5E833FE986E544B943C882A0019DE 7F67071A8CA8AF6852CBBACE3A3C8458941F34D7FFB15FC276216097211821F7 D2B4B0C10AC837A7099B1730500AF256A171AC34217C8092F67E5F6FE036710E E7D2112FA607A40A2E3BFC5B8E1B49A8AEFE8816BD8C461332B968D2F375AD53 93DB73BB426E8C16EA663F62B2F5C780904386AC3627925C82B1D6514DB99EA8 64C20ED850869C2E3647DCAC5E8821F0505A0A66C8CB16C61DD4774163E830D0 E4CC28283BA2DFD8F2B43DF67EEEAF7D9154BE9C5C0160ACD18AD9840E16B6F2 76857331DE5A5526141E3EA125B414649E1B31656F932416CC07D5B601CE9A7C F716B217C49BCE66803009029B8723B59F24C3FCFDB720D9BF39B1A97598791F FB3E244F7C7261CCC8A7B8DB059653AFE880857B0488B4516E6609783C65ACE3 57072BA5FEF9B8103C04FE6172FA7FAE5920D913A3EA5C0B8CD55224B045369C 436EB51B20ADAE7A1B73AE6C18CBAE92EFC2D8D2DECEBEBD661735740DDAF2F0 09D06ED0F2388FCE75D502401DD10866799437CD8F4334300387CA2B630C27BB 7F50048A2B2995FCB9DDAC6D7904A89BE17E07279A57F734A846B031986865BF 09FB6CD8EC9159A91C551363A8F148314EDFFA805EFC892C6EFBA61B3DD2F96B 064DA472D1F0C99DF62FEAA7F85BD6549D746733AF75992EBC058E7A17B197D4 23B1ED8A26CBC6EFA0B996E005D77F74DDAB8F27CB73C5B918AAC11216AB98B9 8CD2D3F8A0E2ABFD48144A2D4447596AE5E8193BC672431B1CEDC1E7040A55CA 440E86C683EF352ABA1518BB0050780CECCADE3D7B9DA3438469D1A5E176C012 E77F8017C4B173EF5F2748AF2D89EF6CA6ACF8A7FAF78C920C9F4A8C38668605 E4D5D1966664B40829917CA3C0523BEF08D678BDF4B1BD2558752CE93BD177B1 4106D755BFEC7CEFD402A1FE0FD21F8B49EB9F0D0E9F864E4B4DD9581D9FF702 8D5926006E832E9C7EE0951E851EEB67BAD9098A092A8351F058976AAA42FD34 7C506C5217151347B3F365E46BB3629876C94582F666E74B2A932CEECD9179E9 E896385FA659A863C5DB623C748CF0DAD3A9995CC2E74DCF5A53C594E734BBE1 3C85110230E567DB91DD59CCDB65FE7AC21B7E0FD7D7E74BADA5B9A4FAC21822 7A6A44178850E8659F130EB4FF887CC7171DDAD850F1C9211390A7CFBB669BAF A42B565905AD250B5AC94FB914A321BC2D69A564BA371FDEDD60AA205BFFFE5D 7A4C3B1558DDA902681D5088A764B3C3D6E837035359FDA0962307AB680461A4 99D2E40CBE113938942FF84BD91533660632C901890E89E3023D000E389C4B23 A8101F1714CB890BC05D7AEF832EB017F8D7EDE46F3FBFFD1BBC0F0DDF65AEA7 FD59D1C7A24401199642CB0D4DBF88BEE4448B97A8746E3700F0557EAFC888DB CB5AC6A36A209A22CD825C0110E599A9E031C8838E8614D62FC81CE526E02792 F59BBFCC96B5793AB7B58ACED7417C8FF3175785D991A98058AB32A3883E1C7C 7E29B7FF43594FE97376A3A28BFA632FC7C0E6FF0D7FB7F05F360F0FFD7DC8D4 B5DF7808574F52E78E0764641914014C89111AB5029A9BAD5AC2CECDAF918800 B75107E206C68EC01758ABCFBCBF2C71D5A7667DD1A730DF4CCF700AD01FF7BE A1C01B58FCDFBE7723EC6A829587EFD734FB4986802E9D1035A721903650495C 170CF841DB880B6025BDD1D6FF5C80CAAF83E70F2733C9D8E5A0684120275FB2 3589A5595D8D21867B34051903D55CB5FB5827199864B5B96A7F7362A86A1D09 AB49212CC695228D8BA3523D8361A9165B7D39873C1962A64E688025BA6E81F2 F01E2D4DA5F1EC121027DBCEEBB66AEE231B4DC42A3120D5FFD67B7225BEF2EC 8A52C2942C14C01B5D76A6594A6BF33042E9DD1F6BEA89D902A93ED6660F8270 13E4DE7A53FDAC825DE408807789D76D9397ABEA4CFB748C397B36FF7168CF9A 3B1ABA64E4C91A4B540CB46A1FA16D898B29C12CD6BA1AE2766B7CEF96426CAC D1C28685BF1870D899640831EEF6BAEA35F1877442E1E9CD62EA6CAE181E20F3 1D9A0353F586946AACDCF19CDA7246D6F2F744333FE53C60845C72B5D6E218A6 01D5C38D634AB11487CC387ACCFBD2EE9EF01B0D82B680EB82E14FFC3FC37760 B5DB8546C4FD4CEA2E6B2F5DF62C6FCCBC9637A1BD005C91433EF014D1E2995A 57E2C764A863E04E8E9C7734B6DBA12F5A383707759DFD682BDB48524C166478 D922A6E5C7ADC2B9C86B958EEA18C3237B37E8996C089074C53100569108FA0E 924758ECCD9CB6E0EFC61E568D346612C211007E110014B829EFB5319CF042EE 16888DCCA8CD469F7E19D2CDE4C757E20A9DB4E15A281CB82B58A0C20E130DD7 82F4213B82E23F65652FE50230E117718931CE771F00E15D9487EA069A0BE290 7E0CAB9A42E92A31A23D77F52FA1B07C3CB404424759BB2315C898D3FC021BCE 1356B9CA608B866C2C4038E3B9F88A7F741B8631A347F6C11AF5B2A9C0580FD9 3FA4FA4590640EE719ADC595CC30E36FF473C6C25A96B368E5D81DDDAE5BC7AF F9294C63D86F502AFEE88EF8152B9C2C44DFDEDA721288D98DC5FAE0374F7459 B041792BE39C157459031CCBCA0196E555611F39E992992D2155AD2E168048B0 24CD97012F4DBB58E2BFC4D8A2DE1825ABBCAE72D5C15FDC79C26F40280AA480 C0E9085FD3B7152A1FEA77CCC0210BA8B9E031C586D3CB231F3872CDCA9A581C 7C060F4FE6211EE940ACAC1B301086B30AD5C578F083072378AEF9D3632C93DD C2894254D0CF584B7374136D685685F1204355F66DBDF24DACC6D666F1875FD0 B25CF458A33AF4ABEA028A88DBC867DF1D2646B0EBAF9401817F326575B51462 97263802F1BB6933B82860C100AEC384C33BD252EE6836B372DCF2B96B7C91BD DBC70C5366AC14373E456A4EAD53618AD89F69EE2BF65995892653DE4731B070 52AF020A0C7EDBAA661865251F79B49F7E2840F9AA049429F78CF339D6B05DD5 54E74A4606D1E8A9A7F700090CA12E4E9B6F5CF840ACB0719400287F1379CAA9 EE477AE5663A49C21E55C293E205AC4BC36CB1E38C67BA35100BA78BF46A934E 19EDC8D86AA4361A2C371045EB7B38A04A15C26B20B9C40B36142B069548B389 B7616D6FEEE4412B411B57B35912C5710E28567F9DB2CAE680DBB62D328980BB 9F65647367EB7713FF154EBA7CC850BF11541164E5ECE29EECB58753F7BB8407 ECD211236FB6F160741E8599E3C4B9F67EFFE4605C23137FBE1EE2033A4A12FA E263EFBE709909B413A1EEED720EB8B3725A890BABF681B9C664524841225B8C 87E1DB22BA3020C7EC2808F80501D85F5E8DFEE322E11A1CF8 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 69 /E put dup 70 /F put dup 71 /G put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 1D432B0D064B56C598F4338C319309181D78E1629A31ECA5DD8536379B03C383 D10F04E2C2822D3E73F25B81C424627D3D9A158EAB554233A25D3C6849ABA86F 1F25C1667CB57D2E79B7803083CB7CC0616467F68450D9A3FEAB534EB9721003 DBFEEFD050F3AC3492F5C74162A9A531ECEC0F47610B4940E946D21CAA771D30 A6C27ECBA11708CC46C62396BF9D1990D579D0C394899D24FE7A4382EA18E7E1 160E7283AF5BE17254790628E79FCC206F28B5566075B3A5697D5209062544FF D85FD89D6F43D6588B242AB2666B5D2861CD38A8CE676503EDFAE84D12A71E77 8405E468FE391F4F3F50D2C57ED55512036B0DB8E76A7EF413ED08673E56DE2C 16A3B65CD478433C0D2F9FEC4E662D54DAA43CFA6957D2A9AF8979BE06F70B68 ED4C8C493D6DAC4971A3F1D010A7726D084EC1074FECD7D12D72AE16C26194AF 21AF5774D9B860EEE8608D34F150092F09C19959BAA670022B9A9F263CD391E3 74DD1D1B4CD4D75273CAA4E37F68C631723E08FA35AD34C0AFB4621AE6689861 854D16CE1C375FD159A337E221A6FF1CFFB5693A0623E7EBB58C2969F590D081 AD92DD9E5322E26D6A15023664AC73A355998BCC48ADD0E7A4BC79790519606F A1FEF6075033BCD1A610B409D8FE658964CE1CA8A64EF177C95360CE69C73F35 E07A9E86CF83F8120AC0534065D4297B398A16D89C66320A79C68168F27257A0 BB947425E16659ECC4344E7575286F420E2AA3BE7E89FE249B51F44544D70446 CFD36D3F7ED241D48F5D838F5A21A9C16B463727A8AE10C4768713AA51BA7342 A795AD4EEA4CFC7D3546B182974856D3100372E73B524700CCC455A521EFDAB1 1378FA57CAB556A179A14CD8774E8F939210B54393F55E3880C1D4A04518248C 6E80E617710006DC9620F12013C029B4D299C662F932D9ACE5DB35BEA759F586 AD85B5803ECAADBFCF366596F5E3DC4BEC30136B8BBA28491112D2A1FBFBE9BB E4EAE017EB8B74B21B7E220F0B3E499C6ACA9F4931E9F31DF645F043EAE098F6 BEAE4CF5C7FCCD1905B7EA8C6949E54B28EDF710102B8C086088A445C03E3400 59B4CE55B77E83A5E42EECF17C1F3E2C76D4C1D811925ABA1B1AB36FB918337E F24B30C85C55487B0F2F2FA8BCE1BF3BAAE7EEFE910BCB48A6B3619FBDAEDCE6 D7853F1309AF47A83A2C231C92A18F2C37AA00E652C168D48926906253DB1D2B C421709D7899DB09F42BAD7C0233EC19C7A056830110B4A11A4343D0DBF42412 4E7D702C012A0DB5E13CCE6856686BB113CAA6BC29A4EB4AAD2FB3B38B62F820 10D412B7F67B6DF12595AA8CECBD0CFEF3487F3DFD2090BA191519C6E18A0E71 C515897AC64DADCD65FBC840B4C44F035A0EAE433D67FE80B00E979FAD716CAD A31CB3B37FD6D6D34BE89B75C9CEECE3F901ADCE873873333EC484B832723A1B D6180727A7510F46516A39F38026ACA0A9F853796A20ED61BA3CE2175675D1FB 7B717F83A18A8354AA0EB09DA8F4A570FB758B9F77E2093D59643A87B4489608 75D95F71790E6BAA63E9F3D08CBACFEB0BE73EA80378E810CDE44538593C46A7 3F2A03D718716A6F81FB6309192C9E6E121167E1944ED597A5BB020B5A2E9563 6D65F5E3E309E158B5819BDBA2318D5AFF56AF87497C4BD237D56DEC481DFA9C FF8D8ED8FBC282CB8B028A1A03E4EA76D682C3FA3BC7938E4D4E52235FCFA2CB C5D41BB6AE55525CB7D41C2B5188A73DB037D180FC093CDAD652B29CEED5974D 2C72651E9B2AE355E469B485206837AFF2E0C8A3DFF1A409F14DC5E20595D1AC BBA2CB707919565D36D5579833D09A03B22306C0B7FE129D5C9255E38B80AC54 471CA23CCB2658C9A6CD2EE792A0D8E1925930F7CB172D6E81602691E4B76350 FCA1E0351AE036298407A441F499E30711D0911C03854D0825F34A8C974B755A 6628FD94E69129F2BFE3E5180CFC9158518BD102265685FFAC8DE88315827889 1502AA8944091AB76D8C73F662D9EBA256BA5FB14D8302D1D2D761994F1A6344 5FC8E5DF5BBA5488D313CC81B9A50D39F071AD1AE3AB6F31532B1374C09B6005 9998B655A503C341A8DB22C93387D5F736AC5E7668E84FEBCA65A3CABB8A0F37 999A4618C188983AA5C060E7A936D906819ACFD40B506970BA12CB25EC2A6E88 BAB696C02001E57E0205FBE96EAD9CFE8BBB9D2667ECA9BD1E49EAE0BA258247 075AA70745B0F374E2E38524725A8640F95B3937532E3D5E8DCA3E96D76EA2D9 C5447D32F85AB12ACC12320EF9B50AB159F4CCF91CDA14EB8EE1C43437D2C597 A55EFB1F8414A16DB5B5957E9E01BF55199F565BF5600A41EF5C2C7F5F077B26 4DA4A018E6BFB775A603294DA69D9FBE99F51373356ACEBA3AE8E937A14070C3 70D6AC6BFC451CC50D9C39BA8DF8A4ECA94D4CA21C7A58856537C03B0847A126 A8E2758EF8428EF6A94043D5831C3C60C293DB01E7F4AA68AEE205181DB43EE7 28951EB54E70987765C449E77031FA4B358AEBFF5934A268E15384A0F8B5DCDD 1ACFD67B43A606389C62550122CA93C3CEAC849D93019F00E5190A7731B1D6ED 81E6F1D7342081719E61D0394DA207FEADB207FD5BF07E3EB3CC70A266D96087 2D68FF05297B142AC97D6954F18D8F1EC6DF7652588FAD946E62F62E48172EDE 98D108A8487C360C7C11DE346B263F91363515374C532121A66D3B99A9E02C49 BCBE098AD75D78CA6CC6930A54A7C85888DC6D01E6560E381E041C6E9716C871 8E6E84B284BF50FBA1297AF8D3E02D3E907361BBBAB2439314A456CDA65546BF 66EA4D2CA039172770911EA53DD6C05CBEDFD25CF853E5302DBF8D91BC74D4F3 8943B7E754C22A2EC71FDB54F76D0129B75510F144DA203645D2828B6CF23160 94 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSL9 %!PS-AdobeFont-1.1: CMSL9 1.0 %%CreationDate: 1991 Aug 20 16:41:23 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-61 -250 1150 750}readonly def /UniqueID 5000797 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS10 %!PS-AdobeFont-1.1: CMSS10 1.0 %%CreationDate: 1991 Aug 20 17:33:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC27E4A7E07D09FB08355F6EA74E530B0743143F2A871732D62D80F35B19FD2 C7FDF08105847F13D50934419AC647CBA71DF74F4531DC02BBDA22AEEA3FBBBB 407E0ACC52BDC60D01A29407CC4F93EB8BF6D4813E9BA858D54F38918AC82720 4956D50291F0546E50FCAFA6DBD0099123F5ECD4AB338DB310DB4CAE11337A89 8ED99B6F483940C97544F888EAF0CBEB11094A13C073D0061808662A04A82BA0 AD35E8782F854AF66C20C0FEF18D0ECDD1646321B93D327E53D88CA0E825FA95 05AA57BD77B4E4C5AE617269154084CCE82545C6478B4F3326DA5BBD9C0DB288 BA4F95700C82BF60B8B201DFB375317AFF1468525A6058D1BD5315FE96F55BF4 97BEFD7BF65EB09B65C15DBAE9A2EA5968656151398E551A635F3BBC2CC10300 22F4D32DB4DB81E88BDF244C8C4F981D3813FB9EDD367AF2007355E327E8A77B 8EE2D3C71EE02E5D40DF4FC25C1BC973B19C0D82AE0F828E0A24EFCF57A95172 841739CC8E2419013DBBD4CE5BAA1D796ED098994357F0B792E04C73D68214B7 3FC6D55108EFE3B040AB7138CCDCE0295623164052B2BDED2B39FA6D6105C9F3 C8DC28EA88B1FDB84FEE360BB0DFF1D2AAF8F382F820811841384A40B60089BE 62E6ECBA7E71AA9618EDC13233B15BD2B51AEF65D3319F071887353AE60E4765 02DA1E6BEDB93C78E32774E1C6F37F29768B03E5A3AE8791329CE15793FEB2DE 507F9975BD3DE976047C2D854A2EF317DBAD7DB134F8FC47FFD7B781ED1C2E20 D059D3415E17D66DBEE9EB11BD14CFB85180461358B84BC9660A863CE381CA5F B387528183B067AA053544E3D8F2891F8C0C4BDE4192998197280ED0A1CD2C46 36615425CD99338C6E93553742CC67DBEEF31F8917BC9BD77604B962B7E2ED03 2D11421CC01360AF4CE1D9D02EEA67402DB5996C713F9276A694527B86DA3047 6BC1F5523555C8821A2C08DDB8B19E7E0C83D6E2F12B866075DE7856296405A7 76E313277DD2BF5627C025DDC2CBA78616B432185BA4CE2206BC93F82D4F63CD E44CC0D33360BD186D6C341996B06C971B1BBA69A4594A7CF9075626E5F8C444 65D05DF685687AA84E105FB1F599B41F6B086ABACD4CB0D3305CCEA9C4A2BB37 59AF25134510395DA406C77967CF09EFDDE94E475A1637B3A4C8C7DA733B708E 3DDE70208F6A4DAEA70C5B6BF8D94B5811C257B11310A88DDE48D0F71A96DA95 6CEB32ED2B6D7D616A520431A16A60AA7ADF316D61F906C6C5731947236CC3E0 CAE5DC5A34D9FD599EC4E8EDC4EF7011D4BBCC44278055CA657B01B86EAD3CFF 73086065945466AA6452BD3E893E0E6F423608FF18BC88C06127B3B250D92AC9 A547DF5B257C5A116DB00EA7AA4AE0FA2CE4B350E0A4932BB15483A685423FE0 2CB6EEF264CD581D319255BC2CA932131DEE79AD6CD1F8E44ECAEED5ED4C576F 70F6F2FE0D1389E43BBABC443B0210515BF1B18F1C548099BA8A9488A6A015DC FB8CEADAFB395837F06D19D253C089CDA55581E82DBA1E1297FEC38C01F75FA6 99A1932A0DB36F3D1D215BD366295CBBF1320D3B70799C3E79AF833B43616177 6E6788B80B9CE9C2576B53794308D63D80B30F8D1D72FC80ABD217A5B7D23ECB 7568A21BFB06EF402711EBD63CB3BC0BB425F0B24F7BDB5EEC35353114F46EDD DCF3898B3997EB8AA4EEDF80702D8AAB4BC1A281D200259681AF21DEEDD21E37 511308E3767433388AA9C44E191F0087B3495880F0A09FFF59B435FDE8ED0F7A 8A3ECBE511C90CD56A9947B00109D7F53205A6F0571B9D6E5DD6D9D829F95B10 800084856734A783416985266B902B46A2C8D639EFCC8DB2F2802E9123539F8E E356DCF088DCB7FC98BA99F6B500B7B752BD5A9E29F80D16D9FEF55F0BFF7377 C2CB183694A388110B64998FBCF71F931BCB48B09C313D4B64F93B1FA80302B9 0A889EE8B5AA8BC999A5CA86E3BBB329408BF1D0F702FEB92C7D6F495A33A769 8694D727A64E4008AE1E71C821297AC3E127F714EF55E9207EE1FCBF08DE150F 25832C7E90351B542C50A2B79CD452D09A917EED3130CD0944F091E38BE062F5 FEC6E921B3FE995482CE58F131CF8F0EB951B5A0CF405697E90C5845350ECE86 D845792FCBEB24AB3C17FD04E5CDEE80A99AF789AD281D9EF477B27BB3E48BE7 BDCC336D49B8AECCCF3BD89E11A79A5D4D931D8F2D80BFBFE7E3A0A99820611D 380AEE2A09250B08051B6B22C205DD969212BA1651CB32DBE01F58F26CCF7EF0 765F79D2D2AD9F68FB0485F84E236A52FEA35591DBEB2F4469504D9EEB533690 D080F30723695237F7B924E70CD030FCDBEAF9D933A5CBDDD3F738374416887A E3AE13ED48103AF1029C4A8FB1C0CC82E41AE420F57B51B4991F1925B6463B91 8C1C077E0456B04BE51476E183A5F2AA481FCCF2EF57752BA6B580621D6C2A64 F92F5FA09A4857AF5EB646A1E770C77E606EE543BC721B5863225E8CE421804C 841C9102BC4CD6537CAB0D5032F1CA4B8BAEBF497F13B819DC9F421CDFA8F5C0 8D8298BC9F66BBBDB211A36B9E2BCAE03589E918A7008118E8DA22B90C0060DB ECCFD46758CFAC91C76059B38E1435145B64D4AFCE26A79461B80977557B66FE 2464AA767F84BB733F4A99D43475948D86E5521B14EBFCA4BC923CFE3EA00C8A 04B16B3361B4C7CC861BC44713C4C20070B7D2CEFD758BE9B03992B5503DF1F2 5E59B9DDF9DAE957D938089713417FD834DB69B9C3499845DC4B6257AA8B53F6 4002D92A47FB161BC30D653D4B5DB4945AD101C7051632B09C34C7A887BF4EE8 A0B23F13A26B958448568D0C93A1C4E60D1C650DBC17614BE4EC20AF450980F3 7113197394046EEADC3A0F740262BEF76E1850DAD371DE28D8252719E73051A2 D67DC5B245CD620AE75685F158BEBC7E914165253417478DBD28D3138468D804 2041F6E6F108399D316926F51ECC862654661339685C4F0D2E110107D4F0F0DB 74AF4F818336E6CA09CB0BA569167EC0D102E9D5AE95E1FDBFBEB0ED64EA35A7 8D1FA1721EA6C82AD87E7B789318153D4339173FD869E9839F22E0078281561B 486F30386292A17AF0DD9F51BD12F8F00FEE65922CA288C3F93AEB6AC1A45C1E 33AAF2E76967426748E89174ED6F4B5762FA979156C4050458B9D8319519D2A2 CEDCAE605450B660E6840667AE318C4979F46601F66A5097C4C406665AC23AB5 9FCC34BF041CE7FFDA4C123323BAA8625733A3715B439114D96A55ECBB046AFB FEBD3809630DF624DCF1DA54E714660207DABD5D110B78BE9D043D93EA9B15AB D6B36573E1C62F64AEA845581F9A433E24D3C1B43FB7ADC4A9A5C8C4F7002A89 1C7A3BE6529C9A96CC06FFD107DFDEB5C6271EA3909ED8F7A29B6C5F8D6BF766 D60A92DE74337F5C1B9AC0E13B6275C076C3C8966670C724B3FCCBE677E4BDD7 A1836827CC6582280C6978BCED3A4AF8A34AB9781F7ECB957F3603FCACC58317 B5EE68A2D28167C2F91D9E10503956F146DE151F1B3392CDAEC5A4EFCDE6692C 5D96BCE1C93C58676448DB29977C1144EF98A54B4702596224D9265D18A8385B 6235EE59E00E9AC1701BD2AF893D0FBD30079CC68D14F75641C0BD53C7FA9F73 D7B9BF525A4A087B098C1F0A1F1A4914563A89AA4C35C8FC987AA63134193CC5 948DCE989C9D9364A6B84F6F8C6A27B7344755FB258CB609805FA74236157C13 8A27C0C583406AFD3715547209BCD12C132684117B257B145A881BA146DA2E1B 9025DC84CFFABA78053085334CD520BD9545D396F3CC04175FB4B267CC00C5F4 F68685FAAC965ED778F23ED5E9A94F06ACA8C1F6C632A03B7EA22B221DDC7091 EF0893E5651145B198531C2BB2B905C7E6EDC672692F69BB689A2C03F7B0867D E82AFFA0F2C999AB17E7967E2E203A12D75112B04B4205B2577DAA9068A2B841 025B1A25E4FE0AF6F2D09DF2F60368E98EE9EA914B4DCD6234AFFE702987E773 CE2E0FDE94B54759A99B9F81397130BC8BEEF47E2962D4BF769CBC952178E9AF DD28A2844746810F62BF89DA3976A96F756DC13B6AAABFEAD959717B35327164 74EE9F28F8D48BDBD3C260369A10E6E4D92A3CA4422B2A7212A80CCB24D45133 500BB236550FF3FE97E7B0A056C6EEB5A2E534CAE765F414A216C24DD4340FE5 553DA617249C89AE284214C6E22C0D3519E04009E5A9EDF8EBCE44B373211810 CB9B407B5ED2D2FBED33610DDE84B5AB60857481C77F36C86DAC97D5B04297EF 7D3643633C6C12518AC69A109D9C9026AD98B141F174A2B7496F0BA3909ADE29 50353460FFC0BF3E09AC5154B8506ACE72A75A1C8B66FCD81CAA36FC0BEEF8C6 0B2312A09D2FA68EB277E1B59ED77D52CB29F4A3B529857043D34CF51C8B6EFC 9B5314C06899F36940B7E99C5D3874311CDE29E4D68451E83E2E0F1B2108FAB8 95A05CD96F5592E8989840872AC1574F047E17FCBE2B606F990BCCC5EF77D595 688184AE8AE50C171E2DF2E20B258F3EB91540BF46B8EA36774CCCDA938240EC D423A45C82A0C28E341A9EBEE787B6274603D9CB313CACA38B47EDCC41595770 4CBC5E7EB643D2EA019B6632B3B73790D06389FDC62EF2630D7DFCBAB78FDB3E 78F487039EE5198445A02745786CF11B086F010E056845AEC38B704BCF24DEE6 F5A061EDEDBA2F02F8614245C310684FAEBC37F4F7C97F784EC225FBC3ECCFE9 EC41E262031D1F1F2960872F7B5B91FD73DA5F10C32444F24A5FDC02B55586E0 B2153A4DED4A326D0DF4BF0B657384BB49CE909CE439683E218A4777272761C5 E722475DFD9F0B32C0F71220ACFAFC47E2123040F23680CE71D12AF879D575D2 210731C6723A90573399C57F9A700A5AA4BCF17DEB5440D008838A2186E343E7 E3665EA369E53C5A21BE7CAEF5DE48BB83B3C77E1139C28D625201DC5DCB1858 3913074D3F8BE819A0FF713C14EE1D57F180FF7081EA689E7FEDAB16EABFCA90 29AE01908DE109D3D392046C5F2C026BB7AC7631C5C357E7391E29E9D2DF2849 8B8CADDB320800A075E3D4F939A9001F668EFDBEA46A8F5349CFCCFF797434CC 56C2F1F1D45884CD5B4A621B169FCA33D271F23F6E144057A149EA6654876733 E33F0412E4D52F64444FC84EF5FA8666468FD7A5C48614284C55F9B09CDF4733 863F7552A3F8B215C2B9B718C9676BC86AFC4FBC28B379B270E9DA92B146141F 601B74AB1EBE0CC6925310261EBE3871556FBFAFF9CF0F44A1E4A3BEB8FAAE8E 4492B7C70748E054B73180B7C4B109525C8D20F590ADF1945ABCEA1D14BA31B9 CBAE584E51BEDEB767ED5107E80C1CA5BD3769156076CCAAA98A59146471B672 55A6C4C8CFA996C47D08173C2FC06C2733D12B049C8D90567EEF415770B7D521 2E3C73E163AFC06C385F8216F957453E298267EC48A71AF656601C7FDC34C9AC BD7524E89E47430E98BE3CEA03D951E9D8CAE9E8CE6522A82FC906AEAE08EA1C 250014C708BDAC9466E56EE0DC35449D9574FD8D36F7494621C6674A0BE6F953 53E3D385337ABF0AA5E1F97990D2433197122834E46984263486DEC32A48F105 EAED3C94C81CB75BBCD8DED7DB0B4A5AC18BE4F2584B0B70E23D7E067A4F8A1B 295169106D77715446D9363FBC7836F05140CC0CD8E56A25C309A6F4E58E1D2E AFAD1F742CC2A9C46F705F94754E1207108F58FEA34DCD3E86D9B8DDACBEB6EE 215F57FE09EEF3F2FAFD01AAC388D532820A7DF692763EB33BC79F12E23D6980 D3E8780CF18C31E352227AB301CCA43D524E0A8436F28D304B0E07C48885C234 4A2A74489DE673476B62869783889FA9699394DA009FC25344F46A5549E06F1D 06FBE55466A3982C9EF1D22A78BB8DFAB412AFF2C6E62978F4F9DE553F691BD4 8C2E0729F22461C903FCF65260B91FBAE238458CFDE5C3BE327A40061FAAC8B8 387F9F29C21C813E13FB78422E0AE7EFCF2A2C74BD033148B4D0345D768CCE1F B234EF858D5D4098ADC22677A82F1134C2FC7D873D1C3F1DF8424117C040F515 F003E09FE44DBFB41AA72AA7CC617201BE41DD7BE39D590E08932E982C58F5AC 6D94B51B4CEC22CF108E9A3B6AE4154ADD9F279FB8F05A7F55DA01B2E82C4DD1 621C67DBE7CE6542FD8FB509ABAEB889F83B3C8D1F0644490CEC2FB16B902716 17F71F2ACE843B06AA0948FCB898621063510F10C2311224BC4016800D736470 6275B9F2E989462964B5DF9A382181C1255AE89399983F2698C8F87488F54597 30A33B1F55843B7A43044B594F671B24E2E976375BA1D8DCEE91FC46FF175336 A20D1FD4D992C37C4E33FD1A526AC0271CD1C4DD0372644962E90198773A2ED1 2EC1B1C712390EEC24D4A359E853BA2817F757312D2CB048C3123BF2381B421B B6ED4DE2014F577EE8B060D619566A731381445B90F70EA8058899D08988E7AD E509A7E1AC16B9A10C99CCF667E6BA83E95B7710CC363564BFAA77947E3A405F 454B65FB73C7C81FC4C53683B8E6D31BE14127BCE480493F2887A21EC27B7177 115FFE3DD62C76A2EB6434B91804E91C928681808A3B0301E885716057A134B5 2EE92F753DDC6BC26A5588A0D6A6A1543F9570254FF9891B692ACAE9A9EDF787 B380BAE90B0A88B9E695C80BBC03A0413DE822B9A01885C062E7937D71951E70 C26FFCA50BB54293F7009725771317F356AAD0276E59845DFB4C10D00E6983BD D1F8C35C40045C1F245AF1BC14A24A0B50A93940FC802E20B0AA22D33BFD10C9 AB79A38CB74FAE34CE8B6C0133A388FFF04915A8F3F5DCCDE5049656E8609B63 A20C0A7D7F353066E33CA53B47F2DD5600A16EA543FFC71481AF731F7F57060A EFA6309BCB961EE68D9C144B4FDA7CB2C771E88DFAF1F4C3EB9DC3F0B1ED7C9D 52796E0EA2E01F4845A4BCB20DEC682B58C2C57972752230F0854D053AB72769 F6AA71E63CABD279E7B4E541307C1AFD61050DF7A7AD1250D290B4C4C3461C77 C1FA074DB37FF16524909516258B2AF7A1A05F75E8F2DAE2F1604B53E6080A6A DE99FF40E168B2F4988DAE2880EF0B28109F8771E8241425D36C134AC6C5FC23 2C88BC0440F5F6D9C4D7DE5F4E939CAA15DEA625D0D415A8E2B4400BA7BE1E21 26700AC9BECBA5C70725D5F2E767DDCC0023925C549BCECAB83D6215FA54CC50 73F36D528C5EBE9261CEF843EECEE4A92A26F7CEDDFA437B50ED72E733307629 30026021A423ED97EFC0A686E375D5FFE144C63DD536D604BD75561A1F6BD3FE 585665F05FEAE29B8EE95256841B988C6D2F5D6771616EDFEF6337450D5C3DD4 34AF71A39A675F490EE613466F559C401C93DC407EC6994AE109114CFFEE0424 F8F22FCF9D7244298F11F2032C3A3095C78D281943813C61FAE4C2FED4C8F5CB 568655B43D9A57AA1A83010A4B442F6906C36E2EE94593B752046B33DF7A805A D8A5F9C7A3753747A971E775498D91408E0414DD952799C2DAAE8B302E441A99 829095C58A97AEE63B723F78676EE9D891BE5D0396C5A715A1D54D0E86134917 CB3A792FD9CFBC2422F01E126351CED366BF920E2438A8F1D99B98FC497ED9E0 E50AEA94CC09223E7E5AF1894FF87F05DFF716E5AB18C5E2C2E5F51EF46F0496 1AFDDAC3FDBCDD961F065D2129317023A9E6D42290ADEA236F8365AAD2407995 5D7102AB22BDFA576050DD7393699DB0F9C6921776976C7BD02B0E229B255DA3 01359F56F2972CE1E0A82D4D0CDFB9FCB82C99FB5722A1668E3C3CCE68CEC731 88C8B56F163EF49EAAD6A7200CC8B9BD7B4D122096373BD7D5FBC33EE1381C55 B58568CD948FDE389F5D4AB03BB40DC7933EEAF146246DEF1A352F143184DB50 3D289BE66A58A738B900503D5DF757716889F9AFF813A7A5ACED8D3108D0E2E4 BF4F11093788B2D40B3336670D099E646E5DC629F21AB6104EF089B9C93BFE8D 8CFCE9A8D841FC967A098FDC1017B867E40CA3BB99ABF26149F2B4B13997E717 D849F511A253B26866E47F62DFBC4EE020D21FD4731D9925A6489584B4B5512E 44E2B1CEF5065AA85E4FF064D9929C576DE104F80E0800B55C1F361FFA0A78CC 5A87698929A998E638669D245B0435FD9038D3F4D8690160D217AB18DC66E10E 84088A4E107F62AB7BE50448B3B87EA83038F051BA448516B534B4AB6C8314DD AC9D5B6C0B40A7642EDFE2CCDCA51F9063CEE0302F54DE64A16033BDC12C5A22 B54A85F1449BA150D43A252C00FB07FF56A4C76238B58BA22B9BE1E464DF88C7 759A4C6C9FF9C0993691CB1E66170236763A5E8947FF652877611A22FC62AAED 1B2766E89F370A954EE8BA2AE2EC9735C193743C6525FEF0BA5B0C7F3268B113 5FE5B1D20C62E2DF64FC62E67D5C78DDCDFCFA2B57705679BEA44BFF953815FF B554FF8B00108E0D7017708CE475F95FA5215B1CD5AC4364D90CEFEA215E642C C4ED4573811E6D82AC97B10CF33A69FFA957728EE136FA6393FD71067AD30872 AA7A17CD4EC15B84722692040FB132206896B4A09F5FCFC16A031E1130CDEEB8 00D96672B02D9E15C6A0EF28D7080D057B5B2A674A5667F41F1DC00B43408F1A EF52B9EA361871E8691082CA36DD7776905EC54E66608C9357EEB4ECE682CA9E 72C30C7538B1DE0AEE28B773F8A89988E6074EDC984CED6C4DC630E4B80B41F5 C895A3FE41F0833FD685922C5B2F0CE35560F271E22D6479DC6AE9E152AD096D FE10977D68ED6752F89480753AF328112E7DDD1AF6C9E602801B86F8FCF4E48A BF9C485CE3A0AEE997B123C2236B23206EC68C77209564C2E9584488EE6533F5 2860463184CB7629C7DF717354E157714A81D2223F5FDFE6086D0BD037F4A25C C4F4FAE2AAFB8D4DA00719EC7BEF7C155FDAF71A0FC0B87BC305892E8EBA0E0C 2699A67742618C8D66736AC2AEEAD6E4A311EFA24419173889A6DE57B80DB827 C48A316918A4E283F44E7F8D80BEFE593028D33C7319302BD2AA0F474F3533DC 1B5D50C8CDF43BD000D7EC3E725526007FAAB5369F6DA412FFDE0F4241246044 B48BB3125A59A4B753E3D213F5E47202FF17F8CF4323BAC476AD2F7CA9FE1D6E 3FEA48DB845872BF1BA4E432D40878C7EE674847FF74F43CFE4689ADD3B735C6 859A8EAB496E026A431341850408B332C61A9BE8F7627C9EA302FCF505AF8701 477548177C2BA0BAD6F7F418A024092CAFAD2622572B4DF47E490C75490C71D7 257852C85234D685636CE67C874B6E8A1BAB6E664FBC3F27D43EE8D1EB050087 6E46070213F4FACD092E89DD2C302E03AC716CCE0115F0F2581E001404367099 9F4D5362CB9A30EFF154C5F9C8F795371F6D260BA68271A9FD5FA2B40566164E 1A6AA2A9D72460D9A7E6A361F9DD24EEF0A2DAEF00E5D2F6BD3D7560C35BB4A2 B351CFDB8F4DFDA6A68402079133FED1BFE69DDE8A80280A6711C6A55ABF8D61 46146AEFDF7E27A7A8A7B53098CDA6062AAB5F0014E4A55EEC94FC927BE16D93 ADF3E2CEDABA5D831E813112CA883C030E0BBAA809A81459DAB7A4128AC32807 80A649AB9962D82A15903E18B11286CBF39FB75E42ED6915BCBC0DC7AE80B474 3FF4F52809D8FB719AC4CC7701888E0DC9234BB17FA62A29D77C031983E43883 1C5318E752A8B5336294DA8B7FD9003D00D5390213862CCE9285DCE54D39D8BB 6F0099ED844D1AE1F682D7205E03D8CF1AE566D1929C707F70B51D38EF32585E C2438B71673732B05C89EA962DC6FB210D4C58064F8F1BC7295BA16DE3ECC171 266C69F7B00125422B06178D9A9D05AA3E7F6E2D6521260860F3BE4EFBD74CF3 2E3CF06A07DCA0C075B504983120EC720574442B812E26B87AFD6EE265E628B2 FDFAF073AE87C859FC8BBC713E6F5F549BCD7425806B436399E418786F97DF7C 9A00AB1B1FF034DB12C3075713F043F6BF0D47D6A482CB73E658AD0D8A4B4632 AD91160C70F7B035ACE49F5964927C1E1B75725D9B68D799756136D8C3ABB474 0ABC1AAA422C792D276B05AC0CAC933FFCD69CA0CE6FC91C39A4292F94AE8AF2 5516948FA0EDEB815B16EDDAB437916308CC4F912879595272A4F7FE261B57C5 218DE5BA283B6F0D8AD82049AE6C54E8690FDB76879F5987835D7FF305180BAC 7FDC4D91972E3A5E8EC54B71C299DC6D3F1374C131A54DDB3FFFCC4FA576A911 0D02A494694CC6FF5A7D96329561EA5C8E73207369FC7E3CE97DA493877CF1C5 02EB98678DB111D9989BB869969BE2C13C878FB281003318D299738CC6106D60 B7618573194648311A2589604DF373D8C757DE5306E26BF942D94CA536CB1C54 BE7A8F150C67048123FDABB3AB0B0745E1C58CA83738076B68A86A1366E9ECCA ED89C0DB7EA0FB155AAD5911B9BA7450B70E52B30EC0A673F1E9BF7D8D8C178A 9E9B0B06BBE7C584E5879D2BCDDB0E2D4EC9E98AEBCBF3D21B176DC87367CE5A CF69BAB40D5FE5C49BBB9B23A10A358723B13C6F9EAE265DFBAEF0418FCDEBA7 67E0FACBB2CBF020898AFBE649651CEB91E030D4535FB3A17B85FB4EA573CD87 A67D470B705BD8CCA39A46D11F9CE4661964845AB1D1795FCB95457ED6A485F8 4C8A3C0E10BFB6BC33B78990D67CFBE66C11A84B076A940411FCFE07CEA51B7E B13A10984660AD1935F8962D13A3727599734F0EF77B7338FF0EA645831063ED EA1F1DE6A454836EAB90309AFD5211FECC38C9DF5C6B3C582089FDCA2516F749 51EE6DD5B4AFCBB6A05D4E90A1A15D62A055CD6D265486D4767F9B8E1BD415BD 360AC916FD8921EE83E54D954A225C5E286C27610EA84696D98DE057B14C6D1C BEE4BE8FCF025CC25FEFC10EE321746E9F5613653F3FB3B018010CBE34848F93 3B23CAACA94001A4339F7A91F30AC442CE9A1096AE4D0316B96B8A4885D40025 3D2ABB42196903CE9EC68D54183D65531599A2907DB2E9F935B52D9C218B9DA2 49B0AD308EBFD19C96B8A772EC8AE7DC7B2DF3B503CE5EAAFBF273B475E02973 61A1996AB8752158EEF696F4BFBE21BC1B021EBB173B8993E863E5EC91692209 3CF5870AA11E3E77FD29A24BD69AA64D4DB10AC0057AF7A8E99A26775D9B3E92 6AAE2498DE8418A05CA61D723DD12206BB7D299558B227219F1685E21F0FDCE1 258301459019C1A79C233DEB084F9B8132F8258A67B57A17EE86F6D5525953F2 0CA179A36D6B122BCBED22A773D3227D8A404A789EB7A6C047604AC9BFCC3978 5BED87B7CA5E6FBBF1311EF20966107956EC7D653B881172D3480DD07C58C959 7DC17810730EE2DFAD137CD0B99D31CED0932957AFE88DCBE21E8DFF3655DACA AF5272D4C3A03C51479CD6DA8ED77D9F7A2BD97CF40A502A58DB79469A7B8A58 41CD1607318FE113A15E8CCF9400F13E8259995833B796E971719CFC6C72A51B 7B1D60FE6CE38C162F66CACC83F89CBDC6670D1915FE405A0817F77D666CB566 483CA83990AD6B9F96315C606B59A8CFB25C6F5ABD344E9F6834BF4BFC020E92 4D56CB81AA55257EF279D96D2D10C1F469DC16ACC77095693D8D53A9F69C6D10 DFC11723D2E37D7FD5481CE29913D7754D0D67171D17C77648700B5A884852DA 92F1362A522AF682C1EBDFF7A1CCD1E4088CB7F966A51AC84A56B8C782F10504 19DE0A98FE200F6DDD313A16C2FA3DF1DD6D3A3AC08B4B86C231DE28B2FA7E92 169CD88BA2D3D784BBCA208E39B5D292BD616D2A4B8A54E90B20EB19084ECEEF FC3B3A8D433F07B4E755256DE204DC298E6BB2E920732635B3EEABCE1641226A 025007833476B198AC19734F2D0E0FD02D2D50709FD9E04226788C52F4042594 5A71AD9EB2EC7F45B3B010D94468BB06E965F9216980B3FF97717B8675CC1F86 337BB3D7B466FC290F9E0D0D6C9B4F43874293DCC3D2CA6FAC536EC678475F59 D6718E7FD522D1B33BD31FE80C7F45C9FF0C8990C968BD301BFE216F3762342D B1D7B4727CACD9579AFF3E7080778018A7E41A006442C847C0958826BD08961A EF375E0CFBBC9A0EE6FA9D0428F4DF13FAEADFC609E55BF8404359D596AA4CFF 0DD45151BC05BABA2334FBE73AC34A3E9F3870C948AB2E1F0212DE0F53525DAB 539A2FF65499393F8F97C0E5BE7E6CD4993910F90F71B78557192D4766D5545C 738ECE92B5FC58FB688A3380E397ED60BDB49AE6FD22BBF37DBB59241C67F5F0 56D14CF821DD8703992103588420EC0F23945E0964500905914CCF4D9A499D31 592BFA7FB80DB794656E968D0E30183F4A99F5E35C1292F14055B9FB5B90E0E6 DB0FF6C846FBE990FA352A3B2C69DEB49AE752E3CC359881FB6A59ED7778A2E1 90D735072B16C5BB08C028211012750078684B6A52241DCF7E928B25A76C9450 8BB25386CFE7DF77B2AEC4884BEA7FA132D0AE4149124F7B4593BFC373A442F8 13D72D254EF7865B6D0607A9FDC7C0620697FEF27F571683F4789D28DABC69A4 3DDDD69D5B9C614B27E62FE7E36827B40DD2844B58FE59EBEFAAED156ECC3A1B 3A35AFC0F479E7CC32AF36D7306DF6988C139E8AABEEA4E55D3B9E7C9C917AF8 B4FD66C014DB436B453C3DC05555AD6F093E9D99D3B67AB5AC5CE3F579C9EDA3 B1663A741CF8CF77A0FC381A94EBED4F2CA789885BBA7C09B7E1F383B988B2E6 2BB537C955431CD7563DAE421AB127E2FACFF54FE1DBD681ADF22DDB476F6E43 2CF9DA7F5694DF50454FBD2A5B469B43199EBB80938AD0F6CF44FC5515236E0B 816486F641EA4729A436F4C4D5E508826BCB8E5EC35386B46E8F9601BC6295EC 94FBB0AC46405DA7D8463B984FEA8C79078B97A27A398AE801C5040789656726 C09ADAB4A4E6C942B9A5A10F64BFC2CC8FB9943AF26D2D39C1F336CDEBF396E8 5B3D60C6CACBA792F937108948A3E84879CC7D02B845E439C75EA1B7110673C7 7DD2EF887C4827DFA2FCEEFA145FBDA99AD2DAA5822D2FB538DA477B81ADD4E2 09366B895FDBF1F13C35C99884F120A414FD99F107304810FEC2B0FF6958D887 A13B0854D651302E49AA1246A2C96ED3E57AC62CF2CE68040004995677817599 F453A834B4BDB18E1BB9AB6E765D4BB0204B88F738249A29E80E55360C179A56 7369275F6085E947197A7EED478BFA4EEC741CE622753A23AE1E6447E0D37376 54D5E80A5CDAAF42CD5C4A3953781733AD19B8BE50F1973B099BB44402F35C60 A90AE7C0EEBA22F833A18E38EF5BEF660B728FD29F50D1FE6CEBA78C0C594314 88126274A8EC071DDAAD2CE5C5A68086A9796869FCEB1095A9E653B04B5333A9 E444458F37EC26E059D341A89F8242B69AC4B9E9BB02285ED05B3246184C0808 7F69762F43813EFC0D571FBB402253ED361FC63605A8B37B70543ABADEAB0C93 6EEDD792DC4F918F5FBFCB76753B1CB0E49A960C6388A9A3527B1D824BFE0632 C91AD352C885D4B7994F3AD67413A9373C88C66D762FFC36EC0AA677E8C776D6 13A047371F502927D489B30FFAE7D7F00CD4BB235E49E82484190398DC8983F0 2FE919898DC017A1CC55E47438EA87BCEA49EDBC71D35BF259ACEB05C60223C5 3059F6750017C62DAAA29ABEBEF139AAD05A3D343DFA1D24A6AB06132A0FAE2A 51551060B804FC8DCC6D4DD33A11AE83D1876D3686DE2E742642B457CCE7676C 2ECCF4FC39E0E420A6805A7719DA845109163E03D0FAADE6400A343010F41411 26AF74F08DE142471714F63FF0EEAA9B76FE2EF6DDC01AE3CC58E269A8209058 0D46A929F95DD0D328A862045E1CAA627B81B215754643DA6B044774E09004E0 D49CF5CDE39D332B0E5A6D3F2FC375BD82A08583E04204A011CC35624BC26FE6 854FCD292E9D2CD242DA8C5AD9F9C2766C3272D2FC4E3D794DB99ED3AB177B68 D19E61C80FC9EEF2F3E27E7514979B689BADC6177C3671FECF50A8C21DD1FE6B BA420A72413F7329BE92DEFCA2CEB06DD3C43DD9F83FAF94B02C21D44104F0BB E185C395DEEE99EC0AC5B8B24DF5FB73126C74FBFCF0DC7ED13E73D99A474B1B 6CB2D1A46514C6B885B3A89E3C3EA518B80E04C1ECC581EC019ACB2714E78C07 2B7AE4470A5E9666CF63348B57E5426BAB102BF06DD4A61F6F80B783FF1ABD7B 377CA116BAC379702AF2D3DDFCC2A1B7D6954E1608F4E386420BC2FE4300397A 796D30066E721841F94271B763C75852948933C5C4A6B1762E5607B7358E96C9 120707B185FB809A394891044DF0830E9A8882EAD3CF92922821080ED97B2740 DF35206543971C391A6EF4FEA702E7F8BAAA9CAFE21213C105EC9C57B6C97BA7 35373FDE9479EB577CE19431B48AF03459AF7849493CAA46C737DEA73FB4E8CE 3732315CFB718133F284C6036D019012E721890F4352D0F8205AC710E1BB6F95 BCCB40226AFB8FFFEB8CB10D726575D370F1671971618B208D399C945801AD04 6CCB8A66E71FDEA07A8AF2D2339F81B9DB6A09E72A0F517D39E50DFBF9455683 4C14C706335B067E64070F05A6CEE92D7C31B1E3CF60DB27E3443D2BD1049556 0830E30ECFE91E9FE794CF8D4096666DE7A93B764F9DAC4F742619C9859781E8 DBFB31CB3F05435D8169DCF2504AB888683F02419A56342540F7F0E66796D0B3 D465CEF29E426E81217B85BAD25112057ACB65F3C335F9E13507EA21C81769E9 1EC71CD34BD5AA4F1AB39164CB845A3C3A5206FEE5BCDB5FAF1550BD2D0D1F76 5FD72DEF819A5FA16471ECC9836511929D32E249640432C3E687CE2A8160B16A F7698625979FA0DD8BF00A1B1E26608A1982688049E07E773870A1898F0155AA 3BC5522EDBE94EFE2BDCF95A8ABEDEF458A3A4EE901B4822E3D97A0DCFFBD10B A138FC13BA6A16BDEA23AA8C7A09AA521E5D0CF94ACE4224E0006A84494573ED D389605E61C76E7E10093A015F21F0336513008E07457D0AE2515DB2355C1D73 8ED4344518E1681D234D75CC662FC9733549DEB363F09EFC5E080E6199930D11 492470E73D09B68216E2FD4B1655DB97BD0E70C38381323F0235AC1AEB191D68 C93881ADFBBB316B559C81E0F5AC510FDAD020952662AE0C261E1987EA538752 E743C3F9DB21F2D774DA171E2DDCCDE4C4D5CD1A77198F448322F23F7D32B640 EE3D1CD45711DF7E054BC6AE4185C247AEFD04DDCE6A328D4491EADCA68940AA 9AE2100E0B3C63778B485B70E2A3A49A9729F6B858C6865BBD85FD2F99A10C09 E300088F8846BB370763296C021270A6B57F5E77539818F42C9E7E38A32BC716 0A595926A7AABE5D8DC62E7E1D964555DB66660B5E0226F15EA06F995E8172F2 94025416449E6BFD5DCB29CC619F5336443A5CA08C0D25A3B4EB1C9477A921AE 053BB180DBA88D479D691548E32CAB775F53A7EB901916F827CEC45237555FF2 79845E6F27202E480BAE725962FE1D9A0403F8D7423C6A46DB415AFD2C4C53C8 6131F1EB61A470360C48FBB364F9557B48E60225D731384BAF9F1A30285AB6FD F9716BA371D2766042E3DAFEA1206CFC3B5C0AEA5F2988C196394F1E554DAE1E CE70BD0A153AC12157DEDABB7A571C4853DB665E01D6B2CA3B0B66A764080694 ACF58358BC215FC57F004F7DC1ECE8ABD0DE410F036516267A2F32C1E93665B2 8793C6209218FA4E089F1D5AF0750A7A2FFE50C550AC5ABAF8868E4B15B3BAD8 C7B4BE44261A8515878A8A930DD5DFEDE389C1B3FC0632722B651EA6BF942DCC 5E72C112900D536BEE4A8963534DD116A726977542ECCAC7ECBC724D7D81C01E 952B34ABBEC68D6A8D8EC86C3529CD6AEA8B94A3DCB7F7FEC8AD225DEABBA9FA C05A7C4CB5EEC3BE353162602E29F48E64E93C2BCF908A1000912D60D0D9C44F 00138160262CCBB953510777CBF2165732E438C75CAD9CA2433D7C4872E42AFF 1C7EEE4645884BF5756AC2D6028C94C90969AE2CAC7A9DFE42C9877E9E66E2D0 2369D9CAC9E0C65F197C964CB302E7640B2680C1431A7FB3314229261EBC16AD 8CDE9429E1CBD10D53887C034CA2A711A308EA4523AF494E3406FBE7B54DB39D E705828A286CE53AA1745F880C8BB49B31E16205A8032BF7BEC0B23DE96FB38E 9B166B9599810BD22A5233E58F264D8402A62149C6AAB77305824F2B63493DFF 841B62E9C786FB468EC26BCEFDED8D83583485002C5D8CA864828D05CEA22BFE 05F1EBA3B5B91F37A8079674CCFC8874B89A3B1934781999715CDBC2AA344BBB 31787F52E450CE750DA237E522DA1430DD4228BB877C52DB3970E4FFACAFAAB8 1D38CAF02C73B572265569CB8FEA15D0CD18B3351D277CA8E9658CFBC127D30A 51FFF97B89C37129216217521B89B790CCAFD2C0FDE2C00F98E1969F31F9DD75 F1B4E47DECFAFD9F6BDB114BE00AF895F1BBF6BBD7A22F89EB75EE8A5D8994BD A324E793402460C9A3764558FC1A6B1354565859389393FED925EA40000F7D75 98AE 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI9 %!PS-AdobeFont-1.1: CMTI9 1.0 %%CreationDate: 1991 Aug 18 21:08:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-35 -250 1148 750}readonly def /UniqueID 5000827 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB3DF7BFF10C9BDA4EFE5F68A8CB1526990D1357AE6D2F7C2D2EF8496 4E47B39E6712EB8908A3265E5FAB40567E866C244814449F1E993AAB422C3F1D DFA8C7118584F2E5197FD4BFA3A8AE9E953C6CD4672C0FF51E41C3A919749C1A F06650DF4C5E17492164BDBCDF22609A74BFA7F69960A64B9F949FFC2A807458 8579366C4F41BDE1FDFBCC4845FA19BBB6963D65EE8532549274BAEBDFF24FA6 03235D1BE37C06B1938AF369DA75BF38DDBC87A1FF445EAA16E1895ABE9506B9 211955753E447865D33CEF007391D2666A046277A30A49804FFCED3FEA5EB2C3 E52EE14A9F75241EA10C91974CDA6236EB840FD44D6DDE4D9B3266C3B99BD38B D835BCA8CB819C073480FB972CC028D218F6A1D344CE1B63F4FBF2C826F412E1 6E0B05A26125865A14FD7B7030B478BB8BC6BC395335C3BA940E1C348267F4F9 0AF97BBEE253511940F1048E175D3569F7D05A28851B6F50765FEB6C9654FEDC 1BF52F535DB5BB90C1BD5D2EBF75E0AEBE82B20507F3C28A03746781018D4EB2 298E4F2C27ACF73FA73EBE43F014BB575AAD516C0407B29E1653375135ECB74D C91372F06FA8EF37C31AF3FA48AE65318EAA6C34830A5377ABB2DFA5DA53A574 4266FD34C25C8025FD7DD45F44301DCF03F51335198F9EE71CBD72BB906F445D EE6AFBA2FA06A0A045D56CDE98A6F0DE807D81F26D017B74D1C7A5AE254B7705 7D96CFB3C342DD38DB5730ED913639C2BF3CEBFA6F3D493DCE5F8218F8BD8035 9E6CDFB95628F7198CFA2EBDE1905F051BFC4F835C5A787E3B43EAD947EC893D 9D1B04A9A7EE7CF3E02A58BB0867AA7C77F30CFEBCB4B3E6EC68F6B234FB6B26 7A9D88A3CBF7A2992F28241517BD818BE5D2EF432378FC3280CD8AC8F6130F7F F58EE9656321EB9EA3E97A65A10F6D020A37523F371201D0DC024CBC48D86491 115B8505577A237065B314CBEAF959CE55AC6F7BD54CC476C2C8BAF40CDE5596 59E15A12A0BDC070CD6621C8923437F1735D03AA0CA5FFC0602291CFEFF420DC B81EB420CB4074893F5351992E99265A9E3B8E93763E1DB22BF39DA381035A26 69637F2A5F4A353C86754EA7B1478F05E86F2C265C0E5003165480C0BB8DD8CB 3841FE66C66499362CFB611CFFE827BF06D4DA6A3624860EB0645EFC015D6FBF D7863C9627F6F0B8F43F537ABD3D9935B2BD0644011C5A0225C93D981DF4AF9B 3087A652B777BEA145D6D8C8064BE6E46D50492AAB15328BAF9E345A2E204E1E 20CA4953FEE4F5AD5834665FB199300E7A87C209B13A0349B19A88ABB1973024 D2A28F21430B4ED96F3877C4B61E531D933B26781159A7FA8766AD40F2B26607 A40E3D6E73D08F19A0B9E5655EA85BE44F483B28F81A6FC291C23D9D322A001C C380FF38905847C0D85A7287B11274B593E662D10894601DD44A28A3F21A95D0 71F28D43EF15D6731444284CA5117927F53947FD3FB358E8D3ED234F2C513BEF 65C9D143845EC349AEF10B0AD8953388A5114C083DEEFE8C5030299B7A3D1AE0 041C9ED2E9EE6C7A7B4796879D716787D2FC401F06734BFCEBC60311B1CD039D A3F22B9393F59B76649D7D65966C86B4AC36F32445EB7DE8CDEF1D3BFB1396A6 2AB2E65EB14275CC809D8FDDC4CFB9C4EF16EDFA6FA4C4D7AD240014B2B24B4E 7D3DF45D42006A8183077A2E87AAE1BF7607AF6ED174803A51D9B6E1977E112D CD05068D8FEC1340F590FDB057DFD7D32712A34B7A4938C84A776ADB72725CF1 E85919AB181154E97746DE52D9151196E579D44EF96313C6696F1D4198DE2DB7 041AC7FC4BBE6B4873EA8F82CFC81F849F7A142AC75121290F42EB7E4533FD3B B3BE610198733A33F213661A641E6C2A1E88FECB54642E277A23F3D491503A87 B4F85CC44B304F2EBE55655DD969B6CDCC8E25C52C0FFA1D450648199B0FC93A F774755EC3CFAD283CAA82D3C498AD5801B39B98BC2E331C12D48FE53B05C1B2 B329AC8A0ADE8F5CF0D3FDC2C52CB2222B6DB1A3342C5994B5FCBD58BACCCA99 ED4CFA419BC7CB0552EB405988236CD9442C3106CE1B0F567A6CF7B321BEEE50 8BBBBA440426BA35D01F5327BF2BF7D280BA292E0CFC9D1CE6B21FBF9CFE14F6 6605AF67B0EA0B9175FD92EF4CC445405DB2CF1DA67288507040EB5F047A2F0D E7B3A9AA0C6E9362A2BC0CEB76670C4C5110C6FB1029D1855F916984E382FFD2 5BA9155800E8FB84F1E2AA473F5376AD55E2E7AA9E43F282F405AD60B411B0E2 612410AE6A4F32740D62C45280AB8877601B82982A6DCD12A82777C7A19A4188 DB28487CE1B7D92DABDC92BDB09C60586AB632323DF67DD2B42612259DD2B8B1 A560875298112F5C608B5CA498782C204625B11ED0F5BF7170CC5539501A7C5E B9FD33E6B84AFE0851D5BC586DF85BF9199BBD3F25EA0FD2F923E2761044FF1D F54089BD5A74AF43F6C43D80B76EECC59ADD7AE3D24F857C9FFBC18C5FE1C853 084F4040A599EF0372B1CE3446AB4CC6D0F841869E3AE3269337ABA379BAD54B 662C02ED01322281533A5578C3F7E0EC15E2CADA4D677CC4784707F577288A70 7B71E310F3FD6F9613BFE0BF1F72D2196E6D68B4B4FA8EB66BDC98976545FF6C 33838C8A021810C3ABB2E46DBC3B0B3B5250F38523C5BCB99682A3EB2EC195A3 ED9AA36168D967C876287DC7A9013DC9AC2293C608EA28C227A3DBD001268FB7 5122B3B168155E5D76BCAEEADBF47BD019DC7C1848FD0DDB5BEDD47FF67C048A AD78ECC7D39300855C945933B61982C16223A97F1CEC3268B77EC60B7AAFED9B 109B384E1A1B18877BC195D70DD9640F857E406DAA3ED5D5C9EA5C7534AABA3C B22FEF657FA04BCCE89D621E97DAD69832E0C6A1B029E7D29947856731D2DB32 4BDE638DFD63A6896394F27EC29C4C762BE3C73C53905D0421DA2ED8669F92EB 389921625CAE20B587EEE0EFD8AC0CB6068AEDCE6B111F6EE7A082941C1C9E56 BF07E5E1FC640D3F5FEBB9AFF1944CEE705C1AB1D6B87F73CEDFB261333488D2 589E40D863463A55661A42EA3CDFDCF09686EF72B1AACB41D490CEF66FC35C06 DA07C8B50E86EDFD6459D11F003F27E116B196C544DA6E9609FAF1CAFD508013 8007CDDBA53CE75B68E84C4C329C187CC7154FD5486D23D2F870BDEC6AFEDCBE A0B7CFC62D68AB81A65103C2CF00504870B919DCE81757F8AA49952C35379593 69305BBD94B43F6912E54797236A7A65F6197C94C74E69184C60C47251947F1D 789E14479F2B7C2319B97C9B464A984707E3C250F12606C4C27C85EBC2062CAE 72EB4F777C7B10180B177396ACDCF33A95B1BCB28F5B53B871F2729B82A91355 8AE2342BA1C75EF74A5225D62ED9ED0F48A3E69979EA2FB597313DC2F7FB80F4 026C12D4DAC0819A720C8D2E953A45A2179449303359C63E38F993581B8EF48A B56033971C8998086279BD8E16E19AA773DF24DDB03420F08EE5AE134B5E6792 C6E1ED754C22FF774B03597CC31DE527EECD52B09E3456F33DEAD6C32F342164 4B2212019A3DD2F4DE00C0D33318093787577EC998A7E9F67FA3A01552653C3E AF15D70D2AD3BC5590AFABFFFD8154F224A1C69749CDBA863A96ABC70E0A5D13 55535CA7C3700C0F8D15A012C5B41FA0DD38CF7FD7F471C672E1D8144BD35848 9B91EA282B40793AE4C821A0F0865D2F7700C0727D6C986ED8FCF8C3C1353B3A 4DC1C84EE43145DCEA867722388A5AFE5DEC31116F7F7FEA0B3357E5383FABE9 AA5CD3F9D15720A73265E9E0AFA64DBF41287038302360115907CAAB4C07FB40 75D8E573516A7288C4E4BB99DBDA736534ED344E10D801E1E4A7776D432A3805 DF596E0C16B23BB770C130506B5E6710FB0FDC725843E3996A0A25FF3F0FF841 19D03C94CA04B1565307DB194FF85B46F3891BA172662B008BAEAB1BF71AEE19 B777C3F11985446545FB0A48F00EC5F339865D1A1EE79F3F3DEAA0161695E0C5 B2AD90EC600EA56F7D0E3035965A9F5EB8BC9AA84D690E666BB30A3B67CC6FB4 63C3D4981F6F80F06827183D1CC2E31F9BC149E992056D11F751F433A18E644F 50F383AB92A5E32240F6BA1378D2245323FCEB7FD3CA54CDFFE67C1C0AB2D891 43CD96A15249F0DFA17073763B9B877F607A1294655AFC862287DB69C5F09EE4 D9038B0F3D5E8C5B04DD1D092DCB2252B7602EB8A52A74EA43589734CE66C96F F63DB52618E8BE1D964087F93CF33C6AC55E2509B04B1131F6658CFA9EF7B3F5 9A966EF4FD717628A1E4F96D7B81CA8C528C1AE47B0706EE63B1C55275317C0E 02F1711619A4FA8BC05F817A24132735E86389E468BAE040EB59763CEDA136F3 CDF6C3D6E5B9DE2B5B001DFAA481271BCDCF0DD52C26FD33092D364B8E6D3AC8 218FF17B2A9C014B9726BA1FCE273C929530A6D1AC5642362BB51D7F34442212 54B04DB87A6B439B875FEE00FF1FA7D1A9FC91BEF657EDE9E01F303E6F42B004 33B09E7098F1613761F7536E1E4643BC3DE802DAAE08AA8D7C04DABCEA2A6835 86714C40144F0C2DB625C5B5047BF90806915958FB0AB96711DA7AE79FAE1851 DA10DE1FF0611F30BA2F52CA00AEE321DEDA6F25B838EA69F763CFBF4E4419EF F9251D2E0CD50DFA8469F6848E9DF8DA7AB6323BC295AA744D5870D0CCF56A71 640F06702BB5B1D0396571675EF43223ACAECB2CE6D6B24DD5B461AC1571211F 6F76FB159632D1000FD6AD5979FC9C950C31D3EF2F41D699DFC4110BD08CBF04 560BABE10023AC92E336AD18079AE0FF99AD0A120CA25DAB66183566A63C14E4 D5D9702AD98EFF1B32A45E3ED67443E7EEB776B6C875B69615E9BA0BCE50DEDE CC2D7428DA61771497031E7D132F1014A632EB621DCE4C714D2D5CDAE3B6F0FA 04187D5E60A5B152FC11A7B087E9A349784C3FECB4158098DEB8B88B3AAD0B8C EEEFE352801CCD5FDAD3B8AA936BFA0BD2F2358955C8441671BF1499D1572B00 6429781D1E4789B1578BD7649B3C1B341A1D6DE8D2D008032B6A2C66110E6922 C72923946871C2EEDB536EDDA2939D3092CD4978A539848C2D02F5A5F128015D E64AB42C6B0318A72A190CB66F111207507259331EC25B8A98D39EFDE2683790 C0D9F5526ED6E1FB598CAC1947CE4AED32C6BF41F65BA464CECBE12084536FD1 2911DEB0CB8FA58453242AB0A65B24E644733006904F13A0F7E2EC957C2AF40C 0812B166D23895A813CEA9D84B8B16A5D1B4E9263EAE1AF17EA533C20E4453E7 D6A1B9C053FC004E2C8AFFEE1A8F286D742F51370DD8404602E16FD83AFED8F9 9485EA6AD6142BE3634FBB78B1FCCF08FD0C1FA05E564A565B0DE7B6CBCC5F8F 7EB310D8FEE0DA1BD9136EEACB594EF8C06C5903286D7E832C3CC8C866BD1A33 730F0791284BA5C9D20A25A4165BDE144C130896BB6A94AC58C1707E29B6B63B F91D826D72D1D455EE19B8E11FAA93BCB5E5B1C74282FF4A421A469CF5E54130 FDD6B9F0CCBD17F6C0B7CF19F8B0A1DE0DED07BCF178245F941A960B84DBC11E AD82F31DFC8B58F2403B6DE19E577D71D4DCA20C2FFC31CC8B1257E1D081A834 85B3963D76B6DC70745C2FFE780B3C84B67411132218D02CFE35E9D68309AB68 FAF556B654E0FC1099828D6403209F6ECFE799124A365FB8EC60E5973BD12A4C 302ACDF0F53834A86152C107CB16973E9D138A00763E00AD94C496786748A35A C755BCFF070505A598ED60D2B0435AA64EE9BB26604CA34D2D82BC7A5205AA6C 8C04FB2294AD21A0970240AFF9EBD54A7BE786874B5CE555B40AF4BC9449869A BEA8A587B9E6B36C77E19A9149092BD356C711EA364CD6D8540FB4C7F24DD146 B1F27CA0B4CDB5A71DE077DA75EC0FA6A3477422838ABB04C79D49CE50978D6C 120A649B9569123F67F74B8FB5A3425FE5C5AEBF19B0F87EE2490DAC446BDF92 513C2B9F57BE4973926F62749C1C9C2E2F96E83031599C41D1D238CC9C498583 57BFA8E07C94ECFA7A987E2502731D9A0732DAD6FD169B6309D1ADFC55945BD6 884839AE84B9E580F9B39A658B3233297E1A7E15CA96C059BD7F1759A11BDF0F CFA42109B8649BF5221B0785E147DF75921987723DB1994784E56D7F74EEF437 712B696DEFA3E0C0426B0790353F869FDD27CA4A596C11802F17766FDA38A54C F440765D44F4F4A694B5DE495F475D69552B3A04A9EC64B26718293B5B494742 34A25A25E3E736E806CC35B6DAFB28416B3B0499B4DFA2E2BD22073D561988C5 E5B341F52A35F9224C91298C5E59CC9DAE33C8DAA2D17D77EA8749E61B709644 891C4116C9E8D996376272773FBADACBF0F88A518DFF2442EF93E758866E8BA6 A80A71DA8E54CCEF32374F797E9D06DDF126C5C140758362FED7D279709F5C83 0841DD5E56F86C010EA10CB6F27B7C8B3D8B4C821A88B8C2478FD62F99983C14 FFCD457EE209889EB7E30A7FBDFEF8CD3C8541A31A77DA2769A4AC16EEBED5DB 30324F5067FCDDF4B049CD67BC0A8E34BA718A6957686BA13D0AA29E7C79626B B5797E96968A503033ECF1E5AB4BCC887A628199205182BECF023F58765B62C0 84A164E48496A144E674207B1385D791C581FD3E789C0305E029FF26E365C671 8C77C1490A2731B1479BFE67435B06F4A00F931D87818BA8A2D1305CDCE3D5D2 7A8E1F426DB4E37FD3620E1574D3EF572733B170F8D2620C1472445EFCE51B8E DB2A0DB919016A42DC8C181A0E781B231092B0D36B1CDD46292BD3382B114511 93982392FEBC61F8609445908BE97A7D0BD3507DEA7C4EC1C15F9AD30E34AE0B BCA474D6B370CD5463C0291BF6BF92C1E0E8E6BC1D95ECE08413AFE7EC112388 15DB4877C33723FA9A2F7CE9BA9201A82D148C6877B09D268BAF9DDA918D799B 8D35994DE2FCD75126A76D5476F0941967A8B28CA935E42B64F19C639DE54FD4 FF61B738C7BA276D90837F0342D71328395097BB27FE6C923B8260FA0CA3602B 48522464A80C3D0DDCAB79189A2C6703810ECE08A6D40C7C447801019D3BC27B F028465A194A208EC879037B749731E9CFA0ADB29A4F1F29EABC07586BE9476C 462FDCF3A6EDC4BA83DBC67A60A26CD29F7AFF62C485E8F0A1A0F24B24926EEB 8BF598B8D73910A02E78F900C4D91241DEB8DB4E690763E2519A553058B16828 97621172535B1ADE0586A47B3698DB2F45628BB575881CD8B114D0C048BAD0EC 9FE6445378ACFF769344E0FA3EEB5794FA44A857D371220A018C28D9B6E2D412 DAC1E0FB33B4CA0AED2CCAEFFD9E6B4C0AE47CF1AA806D5D3C918BBBC317A2F3 F0B65B2FC35E69693882DACFDBD802E748A3ADDFE1AA939934F6AA32DB482766 BD89263B438EF74987E31E0FC5646EEE26C40F2299035A765C839DE019431D82 2619C384CC9092936032867E0A79F8D33B294F0C9C7367FC219B92CE9F5E7941 D347D34A1EF2EDF982FCF3C5BDCA08732866BA984A62EBEA765C93522A59BA4C 39368E69DA8276975F734CD94E6F50860ADDF843B7F066478097EB9EA9932A41 FDE89894BADEDA0B2D166ED7FE25EBA46B660950428F37FBD2F0D4B195ACB48A 532DCF7F6787674087AA9C76785A35E9108D9C5379C352E91D507431B684F776 9A3344CB6D655FDC516D2BD43B521E1756500B1B071F418A47A4A30322A9A442 A6D46A6FD52C2738EBD9255412B79740B64BC731886E6840B5680E31315B1E69 83523123C5F15789969D9AF35BAECD529DEFDD9CE2AD244F0ECA53EA3296C28D B1E55DCF8AAD792253B37D4A4A23561399826682E9DE14ED402A0F297CC8E97F C948A75938D02364E5AE471AC663C26E92015B2DC96216FE20359FCB2E8EA8AE A5EC0345E40759CDD20AF977EB1CB2EC0B8F78B46DAB1B498C1462B51442319E 4AFFC7EBD3F338133337CA67467DD091DD64649EA74007A80F57F9E8AD473655 D3B5F189292E18502DE681F415EF24AEA6633D1DC17F8449F94069A94F9979D5 8676D78CBE3E389A92829B3472725DBBC9E74DA10DC0E0D41F042795BE33BFA8 8BA200024298E97A92C015B72EDC68FC92546BCE622EBFB231F4C06158DB1631 B40EA0C90E7B0CDC4782AA7304071265041472FDC7AEA766A7E840584EFA7247 DF5EFCA3AC9A6EFB21F9F3F6ADF9F50BC8481D78D0BF4973B9A1F558B5925B91 944AAC01DBB25DD448C5F98CBA9CEFA6F5E3CB8609BCCFD8AC778F84D5BABBA0 6E7061937F0A3147A1AE134C2B0CA96F59D4D6633A14CDFE288888863066DB01 496B8A3246634B933768F9659647C07F35E7F2113C01EE78026C2FF54CA5A0AA E118A5DF0A5FE4913EF069A2615784FC340557D79704088EE755D5D33C930F14 20AB25B58387B9BE326302791449C3114E8E41DC10E29DBCF0CD46C6F63145B0 FF10FC7C7A57950BA595C294B4D190F1D224CD70AD4A2487BB37E3DE5E08784F 36C12980F671C420E93DAE90289FF825E4FA1B537DFA1C19DF73356E45B661BB 8217F5A0EF4660327BC78495147FE666D5C271217CA91A090EE83CCEEA958074 9492B8CB4CAF8EF1FD1A0809AAC7AC98E3EDAEB7C86C6E323DE2AFF4233283E4 959F8130B4C204364B52B294BB0A0763E9948E3E1FDDB56FCAAB4F2F2CDB7B23 CD05898D07E0442A82770578DD81117BF36E52518329373F66D8B74C6A9ECC0E 4CBC0A04A4BF3E4C03B80B1878E4124284D66C64A0658AB5BFB6A38AA9AEFA34 421B504032CB483B4223DF303886D7BE90840A7CF1AFEC8C12374E9AACB9E6B8 45773C13B575FB92B96430E7B4E120FEDB6A73485C2679C4D2A5BD90DB56B7A1 44263BBEC6CF8E6F35231C619894D0D3F4DE26F2871EE9C0B74428548CE6620A E4D6791B494C056210414FBE81FAE035A79ECFB9C9DB7EA364E2D1D21CC4A95D 913CBFC2854A1DE158D373A6A926A064119DD4C6CF326315BD79D8D9FE808A00 1AA4B8E8576189F8AA5EDB9B227484C9E0C7F7E1E0C6DB5DD22CFD0FEFBA5AB8 F875181EC4FBA5F397825B7DAE488C416A6D323C7E74CE3D3D1CFA8DC8DB1007 66D93B9FCD48341E6CD8458E966731F0904B59F41AE69192F67EB6989776F793 3F8F088835D383662AB1A24B9E12F8F2C25705557938225A66127713C4FB5270 12F48B37295AF00AF05104DC43C705164342615137DDBFA060E0F6EE2566394A 7A7D3B4343CA47D00E3629E2CAB4DAA099BADDAC0EDEFD22B86BCE2760F16AED 92924E52B34D977A53EA10090FA48F82CAA37BA4C2CCF29FB273E1589581A75F 427B60EA51CC00716512F773FF9189FEB85E663B8343C7AA3AE1F3263D84F730 FF31F29D8EA0998EEC82AD1A3217D6707D036BD93014E50E55D6969AAFC6DBE6 2033ECCABC8E3EFAB62EA6734C91366E793A5B6554C00A0023B0F83141AC30A1 E6EFA7004DA123842CA635BDF34B519F70817292CC1992916D2BB4CF21691A65 5160D254836259FE6C0723B165871C5D5F0BCFC973120A8048A4DD82BF0249BE 48E4B10C4A618436C700D34372C4FCD234992A143E38C25170E9263335E68926 83ECEBE88962C485586DB65F604F8CA6B705981329476B3C24FC4FC88CB5065F 7FFC93B0A97D5D45283568E28BB5ECEEF89D2A09E4982975AF00B22EA9772A8B 00369B58A08F41558B76E5C8AC2F8E62AC27977A39341450394E2748A2982E18 D4A63C5127B3E73CE65D53FC52E400390C5A08C18F74E1DB89B63D8BEC626BAA 9343471925A3F77E8E8BDBF7EC1ABC4B16A9EDA5F86705585187497DB64AADEE B967AFEE48F60B189DD83D573696698E63EB2D1E749E8D450BCE63C32E77F857 87269CCE01CEF400C4DC63E6A79E5E3D263939B80BE7638E4EE4DE4C6F82624F 032ECAEBE6988D922B532FE6DA3CE6D5ADB3BAE45E8EDB53DB62A6A0C5433B02 ADAC74B27E43508A6EFA3BE60A785D95D91633790DAD3654C0D00D20A3A52B2D B63C6C5DE1A422771C481A7D0306864E54DF680AF7049D62111A010F18FC3DC4 8614A784120DD46159E59C3AA081B2C81DF5DFD64D57441537B0B3440A263FC0 02DDF62A38C2EA7472050E49603300F521909F5F535CFA8D8235B7C7E251DCBD 6DFC7E3C4CCC04E6C492F911FE860B52FB962044DD452B18C82175230C48FA39 1B6253BB73724CDF59DB98890B7126337EF2335337CBE0624385B7844E71519B CAF88860C76C5327537AD486084405243210B45BE1EE7E435E2621EC006E41CA BC737F0E8A03E16A7731CA45E51FCAEF0B6E94DD71C6380C51EE416B09F49E18 E602767B704F3CB80C801D202A1858B1E13B5C6FB67120C882333DF1E35F55D7 74AAA2A8FC965C4E63483B2C4922B6630F92B81C28CCCE86947948FA1EEC8B41 CD4D59CBF130F95C0A294321283FB363A3F82713310A2316829B2F42C256F526 DC6D327CF738A6C9721DC96C697F965FB3A73E73A745E92A391E18D5F0093B3E 21829D91DA299212B2953EF1123C817957A3CCF4265C19C28448ADC3A4E62941 B9AE24D1239A5FD93A34FCB329957A9912E1E82DD075A262ED9278EDFE08210D 8E0F4402F7E7C72E47C0120209FBE30F891709C6F1D8A403F5E805C491120FD7 F14BEB378CD61A2D64A8F78D105A45445D772D3E38BA465DCD4670E24E803DFD 43C7BBBFAD3DF34AFFF7B67C9C8B47B968339100BD95CF4277F265DD35D1D750 E4F6D0811A54F96A5471E0CF4965E29F4760ED24C47AD78129112F9A7ACEE5AC 3C99079B283989600A1CAC43145492237306327C8F20553D4E79BACEA22E7841 53895131BE36C4D331DC628228FAC86D35761CE9A70D639CCE589CB851B0DC70 3E82956B57E3CC97A5C430E0BC906AC184E06442DFCFEC1E3EA58A845A815C08 6C668488C07D065210558C06A3F5DCB3369A76A113F513914FA865EFB89A7FD8 F608D5309BA9DC19CFC2E165079ADAA6134533EC71EC69183122660451E146D7 4E11ADD284105B005C4D4C6366556E2884E5FD2CDDA28E5F64D15464E8375FAB 3F990268B659E3229F984FC8766FF4893C6455935834808BB71711A072157CD7 CC4EF7F484315C74B5A55F71E99E2EEAF76EDA667609FB95A214E27BAEDF9AA8 01D96FB8AD38AA61CD845395B5A0EEABE6CD33559BBEC71F5961209E235C2A42 2D6517426CDA236BA637466ECA79B012EBFC481FC98CC850E820FBC31E2AA47B 3300AB73EE1842B59756680E2DB0C00845EE3D7692189B03D8D06869FF8A140B 5F7356C70368D5C3B289BF285E9586C4B863932A380CBD9A67C0D7A0D46C816F 45B605C22C27CF5FCC72260A0F9E6CC61B4078426CD47C5ECBE54B53D91FC209 AEE5CFE04D1E69AC6D5AC8652425159D73533137CED9FFCC75BF6BE4716CB7BA 692830025C6B57C6033A342457B2EB723D69DA1C503E14EBDB7E875604743BE6 4E212905E67F2029368277D72B4D70B44CC4513A8E281F38E7E1808E2E6DA508 73327F28BF0B64BE13E062DE2989DB535F703F75A6ED0171A02BAFCFD64DB582 0F74587A97BF272C3F4419009A16C67DC25A9DCB14DE077AF44B4C6F0170160A 6EE056B17603104BB61888C65407886EC95CD62A77D3E91E0B1A9C66BB868C4F 6344D8178D3B4D98D9007A99EE6F4713C791E6B59FF24C16FE551753718BAFE2 AEFFA5A789F91C2AECA8363DE6CFA4116060A9D153B4BE3F12119A43A672530B D717B3FCFD5CE04FF01825DC32EB2C9F6094E3237170304AF59FB4B00C2C143F 999346407F69E3E1F47D9146CD0E728DE412B55F91657B2E239A035E2B582F38 E12296A59516EC285E9E85AC181BC24C5CC7D7656FFE0040D80534A618F2D0D5 E35C82B9137F4FED997A2D098E474DC70DD2FC66D245AED7FD5695526F73D0EC CF6138BFAD509B3BCA8E577FEA5BF6956D6251B8B1E4E97E2C1A0229769C8C81 AE59DAD680B2AEB37594CC4618832B0FB41C2D85A79D63406907FB89DB966625 3033F3A264A99998701F9B691C3CF98BE022BB8A18CA1534C527073BC042E433 DCE82840DFE72EE041D77098BCAA81FFE4B03189BCD607D8779726CE2F993BFC C41781B3A90EA107C48C5F36AB8678B4BD1F19100686467BD3A1902E61789318 7916960782E9DD66F5AE5DAE41DFB1C5E095EC44B6743143F294D1EF204BC352 FC192EB9AAD0219614DAA7CAAE7625F58BAC1E5CBD816AEC695EAD4B206274E7 3CAA8ECC688071E9F0160B9B96D7E3BD1EDCE1E89337AAE1E6EA479D2796998B 513ABFAC005DDE550106D14FBE41E31542D701CF632CAD724C7D60730D622D65 B54BE815F2C330B6FA9556B202DAE41109B59FA12A8E9D0F624597D43B06EEE8 3DA263296EE6E9B83289BFFED2377B5B6ED54EDAF42360EAA1CAC70825EE5BB0 E2943919C1ED1246C87697FB2E0E5693D4B4DBD7CA63FAF9E80A8543D1C66179 85C7DD019D1FDCF3DB4C8FF3E45CCE55AF4D1703FAA49D415D2BCC8A2CECD7E9 346EB3977FA297EF6CD531F79F9CBED10D99F60B741E14B73DB7A78A72F740EF C7B3FCE04D04E1EB30DF78FA54731D91F5D2D46F2ED64837CCF0C522914BF3E1 61FCC0AA7CA7BC03379E20375AB48B5BF198F11C15C574E48E9FA856B2D29F23 D332BD3DD274F481E00F844713142BF24DCB6B087B2981B03A110B25DCF32A1A 7CD8079EFA8147121D496CA40107A880490F023732EB32C55DB1604FF93ABE8E BB86C5F45F9937749A662B4FF2A1FFFF6597C905BFC6F37F58E4627BB20DDAB2 662832540E55895F3F836DA71FB2CF061A05290C2E985FEBE98C365DD177B246 7902BE2C5643140969D9DDDEC09196167894BEA2281DAF426F132E92EA3EEC0A 1A7D08B3746C28EBAD7D6555D89D19EE6283819F2D1035A91FB41F1CF55BB4CD AE7E1EDB87D969679537219106FFA292D1942AA392321DB59A11F14EFC3B0756 D7FDB6C52EA04C6774675B3009C142B3F56992DE36B0CB2EA025C2E2723BDB92 FC0E0461B856651C74CC3300E436E404C5D3D16FBCECFEC4D1B9E59E3DDEEAAE 55EF52E5E09B8B81091F5866C179D64EA8E02635606CC635CC27AB61001FD07B 25B155EEF6FF1DFC155F34FDB78FD4EB1D904C7A3B43A04A955CEEEB80984F01 DEC46EB719216E67C1C0D56D6C4CC517A40EC2B7F00A2BE8BE663B06193F13D0 ADDFC8252E49477D8657E23A930B2817767B57F888E8977431898D68A05735C9 FFA543DE6922AF3BBD5FDD4F54A5AD03E4C060EC1A5736952184F9D366C0F344 9F79E0FC163619C7A30F0F17C249F6871EC8584FA84A0751D9852731A21171E0 6D2CAB8FF5255B304C7FDD22CB79E06F3F9F2BCB2B3CA95A5F9D1D3EE5F11400 C965CEA250F484B0D399339C1C8E8F6FB5460791FBE8F8F0FFE6D497C63689E9 946EA0E18E5C70857773FAB8026F48080C0AFF50A90300B374F2C45013A9B18F A8EAFDA180DF920E19DDB209D0D0682C60178C5F6953B6FF0A6BCCD18B8FC359 1919F7F02237C16F1E7BAC987FCC0B4EE1681E4DCABFB5334526CC8735179C16 5D6ABC7A26C9CF596C483C0AFEDF0C968248FAB0F587B6F9F1D3C08ED25F2F24 701142341E3E092732A738B5DDFE40228F383FAB152931DE295A81B28A23D240 E00440B83C445FF08E137ECA3A691D4C5CD26D6268687A4C45AAE7D10E2F02BC 62B5AAEB4C8ABB02865E2445B14C18FA5DB08002B916B4F128B0A56E560F931D A1F0F1490DC278C97410FE19D7FED94374A6664D68AAC9F33E7BFF4E6ADC0EFC 6982D96C160D3A216967CE799BD238FB64C415B15FABAFF0422D15A9E573E783 358E6FD273ACCBBEBADAFF3B5875ED629AC4A5A286BE165A4E71347DC5525AED CA1EF6CF6C6E409F9CA868D4DC3A121B917C71E47F74C092069ED3944424AB3C A53B2BDE47E043782B074D3B967602148A59B2E6984101B159A3A699DD5DC543 28325905C387B68B8D2F930553836E280EBF42552720DC389477982384EF9A11 3E08BDAFB2AE84F51141F4991059AEB92AFE61E08B62F66CC43DC4960A600EE4 8E8B6ACABB12DDF666066CAB5BA053323B13E8F0E75F9DB02C8EB63A1160CCA2 B321644311EFB7EB956D0456E806D90DFED2BE425A08310477C2522499AA261D 3F2CDE5205E221E589E4E06BCF922E966393B6983F75111240484DAF9BCE3CD8 E8042CD651BED624A4737D889174FBA121AA1A74FFE91ED71B9AB45077F3F9E1 D9D365CA9685CB6563C9818F5D142B387AB197E0AA3E79FFE4F29FCEDABE86B4 8E3DDA7DA9CB1060F7F3ABE39D256AC53EAE9DC0188017F5446234A444C652E1 0223A720A5A74C471DE8E03BB894E1C0FA3F220E5DC7EED28495C6F42E1212E4 0AC40C62D076DC01381E4D3A654135E6187714692F652D2546C8C53A61868F32 A4B257EC00948FB7F23128263FA6699B7E40235CD6550886CC2CE98EB5626F3B 6F809799D2D7FD58EC83DC72033E28E15C65BB2D3BF7B106338723C4695424A7 F13D1B5CB6BA743E505F2E6F29DE3435C376A4D53E80788FD06EA8AE1EBCDD4C 3F7363D3D6F5BD7B86D4AB00BEE5090923BA4CE5F238E7EC0DA67AE14F3CCC62 E75CD03FCC27A3F869DA8808FF5255DBB7D1DACDDFA1AF7C955D564918533502 8E1D05E3F9CAD34FC778AF102937A3DDC8BDB6F59AB17F9640909B1D44777833 271F2C1ECAEBC4C94CC5B901A6BA895CCC65016A8C8596000C77A955E82F8667 0750F81D3AE9C072D00FE41E84EEEB260B454688F749E3AECDF087D0D7F06955 D546AB0891DFFDF50FA9573820552E2FFFD7093FCB11CA45F3C4EB9945DCC5D1 5AB4D46425C9ADB7E355D457E0F6AB193DED5432B9B39BFB968DA50B53A11597 C15773FD5CC1761CDEEB4DD23912778E6677F782B82141F7385C1F57B1A1E3D7 5253B9CB60DB59674E8E9B856D89A6303DB94E6C680D0A8EE37839FAAFC187C4 F25A421E3F8706ECB8BA756C7B55C4C8BE31F30B181C3543AB023E14595C748F 17A14F8848EB428890A1030A76B0E46081839359BFE99C53ACE0B1125FF74F1B B592DE855B8F4DF502E668C6A31BD0840B766F5F744ADF60A8C1910052639E4A 41233C99B870F63FAB6F4ACDAD876790140DA85B79FD0B698F4291961A8806DB 43C2E22AD846C8C8D75309FB8B3FE66D03A43B3EF2B7EC0C8A688EC05D49CAA0 71C0BA09A671972664C3E89BC4A928D5EA7BD337608C72E610C14BD2CE7D4BAA 873E5317B0A00D4DEDC06FE2718496E4BAD41D1E62DAE561B6190A8CADEBDC5A D24B6030F302F19C4678E48E39A5EDEC78B503992B769F3E4709E621187806E4 345686F029AF9DD143B3284EC828273A79827E3FCFB55B6FD918E5EEBC2D17C1 EA5482AB80AE4A5CEB9DAE610523E161F9306DEFCA3E4672A4814637BB7C9ECC 90E069AB8AC7969A3673105FBF89391E4565FCF0182FD52F77C768C693420695 2C4A25B0D8DBA10784914B562E9158736DE89F6DD23E5A0168B7C9F96465ED0A 83A3236C0FBD2E7FAB9ABE1FBD4B6C9703869FF44DF65E806624301B0CB57AC5 2F00ECFD6F532AC59BF7CD60A01A5915A0175288C29AACA0D843BD649A142589 049C0734D901CACED026BCB23E4441F47F24EE499F0BD7737C39753E69307CA5 5AB2AAC9445DAF546AB29601AE1E92F917182E732A68C3DCD88DCD88C7A8C915 48C5A59AE3B8FA325B17A63B7F50D277535C24390640A74AB06ABE59B1CAC7E7 55AF122DCF10EC4EE842F13819236D04392004868B563D1D4A44FD0DB719D52C 33291DB74DA7D8CF0E9AE27798576A5ADE16490B2C528B76342E92E39C4BBEFB 335AEB6F21388EC307972BCE467E89A2E1B53D805D291C70AC6A8A17F35F74B5 639D5358A01838EF79F1EADE9A00AEA31DE3F0BA9A44C5AB81E7769891F91E21 D631C40DBBF3CEED2A1ECF43F2FAEF50AB7D70181526B23A98340D1370928A48 B12A38EC 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D0037D33F24E2FAC2B0009AD3C8350CDF8CC 65BCA87979C36D14CB552E9A985E48BE4E88ECA16DF418749AF04FDD2B0E1380 D281BB2476BB45FF30946B247DFD7F57305FA87E50CA338121C71CDFDF927A9C 77FF14CB4A1D6D80356FB1171ED38C37702350497B44E42CE31DB2F493807DAA 15B887C671199A54C4C1294BC520F5538C15556BC43C9F62342B121C6DCD6C5F 491DA47FF360201EE21C08A781ED0589A6DF91B99FE118B9B29E4F068672E52F 1A06C514D91C4C937D4E642503392B1CD1B54AC18027C6327AA3C947049B128F 7937DA2D0D2C89D06D39B582F24B9804B7F62A3C3B04792250831706883284A8 674BB3CDBB404B221B4D9B50E7A98518B52C50B03946FDB97C17EC1DE87D693D 00F79323823CE39752C702635EB5A5E6E9C8DD4126069370FEE874AEEFB833D2 A7D944EC49DB6B8BDF0BEED184C145778DEC68BA21C90ECD10C7F55BDD800C30 1ABD374E76F44F296D64AF28D2B52F16FC043D3DB24D5D452FA3A50FF2D7E412 6B492BE91D5D2C45679A41D7A443DDDAD6F21D2444967208927B56839685D399 A668F45BC4BD5BA0B47653376CE9F62B5DA4275A25E54671B0151DC8778401B7 7E720C4286CCFBBE21D143F8155B9A75C9D47697D28AD3FBBB6CF0843ABB3204 101D965A687C279E6496D378A685195547FCE8ABE661AE761B4E1454945999B5 2EA1DF7A38D0D54FA0E75A60A25C27257DA520E5F3E845364BE3E14F4FDC0A3A A8C2FB5185D4A6BB035879E6A06133EDA32C06303C82D241572EE617FDE56942 70028E0176451AF982A86708340335668121D6FF571C7B26D53F39CE307F436E D006E00C44B3741789BF6E6730880DB4AA9F25DF343D4EABAF9E918C929BA698 9C0CD332AEA9183F87394E4E2C3D97BFA9FD437E4110C86AB8B5DD5DC90A3B27 6F08340AED637FBA3A49C228B3F3BD92653CB77490BC88C3D2248B6E58AE26A3 947DE052E13A1CC5B02B98D413A9DD011AFF15520C4110D0C43DEBC4C836CE57 9CDD6B71A1AD4986AB14C9AEA45EC7355D51B8D92B40FC05706C0AC0848FEDBB BA20BB244842AE653461FD5DC7D666C4648AD8E4E410FC3FC36B6D1C1BD13D4F 2A5CB664E9DE9F73A0DC7F4774FA05E8BF2F375A20BF0E5B1B17D58ED7A10256 3270112F5FFBDE4EB74F79E9C95F3EB79C698B04FD213F6D27E222C040AEDAEA 3074F2025588DAA4A83E0BC1B0AE88F628D4317CF19BEEE0817133AC12FEFD0B 7815FF69AC3FAD72667B012841CF55D757FD6E14386DBA625FC50923CA7190B6 3307643D4C4AFD07651B0CA03DF005252CEE87DDA16404CCE9EB20BCDD263529 B2CB1A32A65DEE82F9A61162BE0F96615DFDAD06390E9E75C3601FF3F52150CA 71A2BBE81EBDA5B930F30CC55DF99336EA98E4AB347D80702351F0B8FBF7EE3C 577C323D8EC97F68EE4C2F2D7EE4020336E425399CE7D6EC50CA1EB36CC363E6 3B572552F6FD659174BF57342C36235769F2D0DBD27575FEF356F9908684B419 B65EB634C68A0C973C860AEBCABEF588208FB537508BA20B3056F938185F108B 25174972D04BE35305F22987787A34438E9AC50AB97899EE60B8C0305B433299 FCEC72A823B8D23B4E5534CAAC7E9966C7185A2BD91139FED7BFD9B76F461AAD E4272BDB9A74CA224BA7FC28FCD2F222522AD3BCF02BA4FB53615DE9E6C89259 1CDEC3AC5F3A64FCF0912B3ABCB27F08A1B1F78DFFFA6AFAB3219A75FB20AA6E 4A783C526C75AB9565E4360556083A6D9218A0C07B3AF1D7FC30E8DA232A0A5E D1907627C22E7367165B579EC5E7A8618E69D95D49E487AB3F1E7625D2615E25 A595214BEF09BC43E8ABA23A33177B3EE19579FE682A1DCBCB2949BD02A26ACE 860AAAC1BD527FB737CCEA00142A969DD758F151FA85B480F177BB193E8DE653 E2A60084693C327BD806FDDD348602EBD3A73136F7516C3716478A9A34311CD4 B2DF771FBE07C3E627EDAEC7 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSS9 %!PS-AdobeFont-1.1: CMSS9 1.0 %%CreationDate: 1991 Aug 20 17:34:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-63 -250 1027 760}readonly def /UniqueID 5000802 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F D1F017CE45884D76EF2CB9BC5821FD25365DDEA6E45F332B5F68A44AD8A530F0 92A36FADB679CF58BAFDD3E51DFDD314B91A605515D729EE20C42505FD4E0835 3C9D365B14C003BC6DD352F0228A8C161F172D2551CD1C67CD0B1B21DED53203 046FAFF9B1129167921DD82C5964F9DDDFE0D2686875BD075FC81831A941F20E C5CD90040A092E559F6D1D3B0E9BB71733595AE0EA6093F986377A96060BF12A A1B525CD9FA741FE051DD54A32BECD55A868DD63119A4370F8322CCBEC889BC2 A723CB4015FC4AA90AE873EA14DE13382CA9CF0D8DFB65F0ABEDFD9A64BB3F4D 731E2E1C9A1789228FF44116230A70C339C9819676022AB31B5C9C589AE9094B 09882051AD4637C1710D93E8DD117B4E7B478493B91EA6306FDB3FA6D738AAB1 49FBB21A00AC2A999C21445DE3177F21D8B6AAB33869C882613EA6B5EC56476B 5634181ECBF03BFEDB57F079EACE3B334F6F384BDF9D70AEBD592C8ECF21378B 54A8B5DBF7CB9282E16AA517E14843909339B5E7C55B038BF3BB493F3B884A1C C25F9E8FB912CBE23199AD9D2C3E573727701BA301526C66C3617B9514D6F11F 11930B1D97C17816C85B1BFD9B973A191B33CC3B391815AC46268691C741B2D4 48A840F1128D9B2F9CF07D0709FE796B23A836417BF7B5B12D67F74453C82F5F 25F7B30701D6F6D4F4DC623C0C27D6A6FBECC7312A3CD10932FC7C10851C3C52 24B75DEA8A648B7F34F5711DB0E843C914E25663C510185BC37BDB7593C1C259 21D8DDAD33982C336BF272BAB2F48E68217403FE9F54877B243614A87E64784D 2796EE4179FBF96123D1BEE3EF89D682B427BA4F12A1318A57F18BE5DD903815 261919C6C24454E652A8EE1835C79E7F020745D97E845D3B7682CE5630E64B69 C45C658C7A78D7D9DD832BF7527EFB82B88F85E13C6F6E0F45026FD39BE48879 4AB6AFE16D169BEBC3796BC8C6F87452B8AEA8670979A7D89F73C48DB8FD115E EC811E61B1ED68272FAF4B3D9B81590F5D0D76A066565A407D3ED1D37EABC5D3 36CBCF22C882E0C80FC6727039E8BF867C670A598E52953CB468AE614CF24E7E 2349FD7478FCE76FDD394ABE403B6CC12B4DC6C707C3FA8C649B7D6141EF48C5 AFA78B3FDA31597615F5070BA0569388B7E282253838DD3C76C35BB899F6364E C4F164D6EA9B685971A76A4720090AF32D1DC08A359A72DC4F4B5FD76A160FA6 D4B966B8E40A3E3CEB2F65A8BC5CC3F28EFA3C00F9C6AD9789400A4EB1A6D0D1 336DAC00326CABEE6181FA224C82D54D9199CD9B57127D55DF6BF3CA9F4404FC FDAFE3BCDDB845544A528B5319434C18618B89425057289FC39307F72041B635 42265372491364C711D89E7FECE311D6A885C3F32CE627FA3F2004E9E6D729AF E51E499F1371DC9AF4E857895CE4C295A41F85FF8A04186D3A6DA850471496CB 24C9FE34A91B16B0CD9B4F3FF6697FD04434979E785F5C6B032AAB929AC923E1 D50A70A40E95C40154A2807A352BC1C3CCEF325DBCC054D415F646826B6226A7 4AE4E68B94043114B6A6086005AB339CF86F7DF56141D3E85FC566FDE5C3609F 72C2A57B52FE5AB9CA1F67F06F1168F42BA29255BF5A1585CFEAB3B24B5E74D3 982915F104BFE9E1507C846A9442E5FE33645FD6FB4AD63D41EC78B0B50146A4 DDD75B89ACA8D5E4650C17CC39024CC46FE1B0EDF5DD0929C7761C5448076587 387C5EE4F47F01DA4E835495206B3FB1801DF098B3D31BDA1B95EEBC7D899889 ED3060BC41287DB8555A3459E60393D87BBD95AA39424A12FFE14476A9AED8FB CA5B4C39F66C5B33A0E93F783AB090A126CCB097ED5837A41D27DFFE130015AF A8E777E1B802CB70F1993D8A6C3E3FAEE17979129038E63B449D3665D396F562 B709D552392471AF5AA1AD8B96B6C6BBCBCFF8F0196366DA3A48864BDF5B8BF6 E522FD2C5078B24FEB2B18BA1CA194B2FA01D93321CE0D73CCEDAF291FD38215 6E91D9E6265AEEA7355BB6E500E7912C5B5B11B2C84151D80541CC29E6B0ACDC 07E4603B0BB8F8B073BFF0094A993620E9917E2C6A9F34FF2884DA3ADAE2F143 E1760CE296E1A6B3710046C7496CFAC9245B23497B97D8B5F2AAECF0E7B1A671 3EF3876FB807695BC140BCAF879BD8CDD07BED89A2A03A6D0B0776B1193C5AA8 065B03206C891BED13FBC0403DA193D31073A90F11D7B1F501991ECD0724040E 3B5C3004AA6828FF62ADA93D97D84A73057A391E2D77EB5FF3B11001FDAF1CFF 7E7F39C9453DB5110545D64705ECD0751B43A02437E2A1C17F0A7D7AC14AD5EA 451DF1B7FE186BB99DA05865C66C8F4FBED0C5639B987BD9D48A4F4AA2FC70BD 7A73CAFB7CD1C52FD81CDB3D863F24047509630AC4C33C525371CB90FEE4D56F 61142EB8DA426B2FF3373C287E814B57A63E0F47701A3C6C1F8E1C2329849503 38E060B16E9BF9F8CE160AE4438D59CD7E6D9F26317B728359B83A605343FF75 C9BA96498EAB76954D9EBA8B2746732BC2738E8475B44CBF14498B5DD5802BDB 93C041B917602A13626B759C16033B41A78FE7F7A3C1B10327F0291160A244CC 5CA5A0B064F77A648BD91E57D6D02E8FF4600380ADA8B4A495E5EF1C47879337 FEBEE21F2C91ABEECC66C526DCCD584531551BE97C7609F7EC7F47C81399F8B6 8EB717E41A0D36ECC458942726EA78ABA5CBCBA7C859DFC87842319AAF1C897A AAA52F6AB821664D798BBE9BC089A51C135FEF960D68C9E2B91FF93100592A7F D3F5107E1731F69934BAAF8C5A8DD689359F2749961B51D6E4EB10A1549D4DDE 5F7CC1C18CA2CD789EEC43B07A7AEDE1BD7365945A93261C747BCF62F8312EDB B1F42FDE9E3983F3B9FB32F1A6C0B24669A6A6F754E138793CF493369DF52071 C21740F59DD5F6B196ACC0A875219BC49F3D39BCE984A7C9D6BEA8898E7F6B8A 9598C46ED0007F98C8E5CA773FB198D3B571BB0B59E1748E67B96AE8FA188023 DABD20F6EC2DCD1547F20391A616BC546A583D3A755D10914BE6180F5535174C A5848F1DBF50F1C63544E678115FB2FEE8305BD764490C336BF66ABE39C5DF13 B1EC146A575AC5A62B2E61627ECB39BE057BC4AB7A46EB5A24C52059C92D0207 0C86D86855752AC08DB5C933D949C54C0E42E39C9B4732E9F0BDDA1C8283E3C7 D5616C9796D5F2BB8DA5EFEAA981A0926905CEAFAE049400C0985D84FFF9221E FDF00C92B004B65164FE4E68B64FF060BC59D1799D59C5EC8BD205D8148214C8 96800A4AE1F3DB5762FC67548EEB11A1EC352FB63045442328A8DA278B4EDF72 1CBA679DF60638B50B5898CBBB4C037E2AE40B9F6D8C6A322C1AD9FF080ED382 60067A591B0FB93CE2E883DD4D101A704E9084D31C7D321C6ECE2931DB501CE2 09501A5745DE2079EB04271D195B17ABBDB3D9F191C08B8BDEB6FE707A14D5C1 CCC80B47D8D6D8E54FB6042FB24C2BB2A063655D56E476682F357E441A4829D4 1FA585B0D57CD0795A3D6C221E57C177A8A751C7B36B3B9C88A9F9FC982E445C EE8D4E9C558DF4C21AF3876B571FE166A24BB8CB20496F0079CB2B290E65F979 BCBD7DED8711D4A7E3E454CD5390B99165E02F8DFF3117D6A7BDC789F6EEEBC1 7F7B5D4DDB169407820010351F3A8944C4F74AFC567A1515B7C6794652A1B4DA FFAACDD66118DA31B31116E564E133B1CDE120972620309F0CBDB2FCEC08842C E00E7C40E0F9D4A1B469A260E8964B4929A620A0EA7A1A45797BE5AA75C59680 EFA8A29B0DC9D39FE877D25E9F1A4D96EE9450FD2F2355816E205F595DC60D7D 599666297E697E4D4F74E0CBDE959C0D330C8565E3CA2DD2802BE4BA25F9EABE 292F3FD6AB78CF2A1B5C1AFAEB0A3305F1353EF41DED20CFD89F16834E2329ED 586AB90E0BD4555D0D9A0E32877249BBC7C9810441C339EDEB6943FF3918CF6C 930A07764E5707926A6DE193E39AB4CE543A44AA6D41D6D8F9F92689807039CB C6A29299C6E40310B8A94DCB5F8C838CFB103DEFD7EC92C09ACEA73A893410FD 9A999649E3C066679C7FD9FA769118547A4761FCCF7F9B431D811F1E3D81EE25 B7D2A5E6056E278B9EE1D8E45BA637404A275915536D3CA2A059241CEBF9FA6B 9A9A8278EF498CB63AC4D4C50EDE8B10EB5F8059F63EAF23B65D115EDD34143D 88ADD2584DCE9CEB8E5117B0060A41E1CCB1BB21C6C16647BB43E6AA70BCEE17 6915E475CE4AD23AE95990D2A814134ADDEA0DE4CF198B0D19FF4EE1574DC841 BB475B0A135EA6ADDBECEF4C693E45246B614B97DB1E5EEF5F7BB295EBE43A51 E54EB0BC90C823138D3B81623412FCCB8D38541FE3FACA975A1C6A925CBFC2B4 853E0E32391A8D0C71FD68329D9CD3E58751A81F54062B9BBC188562369B3E73 560BC3504A7A8ECBACFB3D70EA70068C8BCC9A6ADCB8A801AF6F208F8C8C1130 9FB9CA85EBE170889FDC453FED412A48A3E602D55277A1DC3757737DB11410B6 173A8C1DC9933BA943F166EE49B3B9FE5164CFD594635302276A66EDAB7ED6D1 56EA04AF47CEB3881C16DB21A18AC78469617C760B8AD69E1124860864BA31E8 61922FF7E29D69E2B6C034C01BCAAA56D6B813FC4599FB51841FD3CCDF36C26F F82C279E109FDA38130423C3E2CF0B03DB0115CE331497F39CBFD58A4EEFC94E 478F1CEA556C1D270799A3858F852ACBEC9CACC2C611BD936D52572A0497C7F0 3FF086737C5F7E8B7E491A63AD4769479CE29338AD67FE22BE5928AE68211225 8284294DA6FB3F9ADE2E4115D44226689221AFE6656D962EC72650485A4BEAF4 7576EAACF40C79DCCAF29477DD85BD94508DCC67D1ADB7DF569C5C1F4B8A8EF2 F58CA8112948E1581633CA3E2DE97DFD99DEED6BD23966559DE6F1EC47303D9E 4C71405FD598127F101802525186512B799C2600D22193ECA7DA990E3EA2D409 3C003467757D85A4748AA4FAD0FC9B2F27899B0F1C88AB67087DDEB85DA9B6F4 67E81120FED827C6CFF15F534830C4BDF37656136C831171B527279610F84F54 A75D9C0A2DF8C607CFB0E47336A15D5144C0F3560C37878F15ADF0FE61467E46 63946A18A304BC0E1165329DFF9088F6BE31CA96807643D49EA1640A31F6B2CC 4A55D61C60CB8B1CB5479CB6DE3EC0981102CEF8618884199DED9284C8EEE324 560AD5D7BC8ADFAAD56D355AF05F54C2A594E07C76E1A37EC844A01384B9B75A 43FAAF2DDBFE3CED0B4B872830A590AFFB7187647F1E5465FF4F24B7AA058494 46A786A152833CF4D45C0406C814494671286986C9E5124CBD4D098906046107 0BAE5C5889021D7F5F81A2C41CA3B9F719C702CE27A59D2BD8195429B600BB0A 91799F055F0DF9452D517F50AF7BA244E464E42B3E97E92B5422279EC14267FF DEE31141CB27AB3D9EC461E96650BB52AADED7A28E9620020B00E36097CC14E4 AF05D18578F317C336E483B164012C993D487530628D297C1B25EA7B94225A9D 5C60B412F1FF55D30B6EEEB03A0BF7B1C47DF32B77D00D77E0FF652FA096D57B B871CDE2BA1E54D7B423EFDFD62371EB272751C46C6E1798703AE5980D1DE566 1B8494BC281E4CB6E1445362B2145868595C64332769DD211F2CEA3A8CC81AC9 4541EBCC029BF92309E2B767B11193BD6967FE51307A74B2245FD482AC82CAE0 1D5AB48924EB4908DB3D06586692EFAD7EDCE14A1959BEB757FBAA5BFAB17B06 66A0883DEC705D62C33DB6749042EF0065C832EC02FC7A36E3BF177043993C00 01B66C074E7F05279927CAEA374E6778C7964BEA157C01C1BBDECA6559D2B8A9 DF74AC1BFDC918CC0B3E4A192DF81CC96B4F56A029C69428026D42EA9E07A185 98F6330D85FE1ECD32C65A101393DCA96B18121C09B79C2D7A3223CF0AA3515E 660534EB77F546D202D2F7A78365D8DB0B9EA055C076B263572D4934CBB42052 434D800C1FFEA5C26F32E2070C119D375096D1E18EF61C23A14FFB1EB8FA14E6 65566F6F52742578674F5639CDA63645325D5E016DF55E27BD7D1ECF354182AD 3B25AA38451FE31E41FAA8244476B35BC6E7C7CE7D30277F02E76F5E670BBFD5 1175219B1C2A43F51AFDBF648D9710D5F5AE90FDE9AEC12AA04BBA4426FB8D30 E8484F8A3D15DC14656BAF5A99E7945F1A007B86B6DF43F6322D117294F86F8C 5CAF0065F3E0B47CEDAA96E611F14E673AC04E650B542E318265A87308D4041E 0DD5F24954DC6D46F0EA4A3E4BDA4FA7AC1EE2E122BCEA8111A17F50B75948C9 F10CC38050C88C45F0EC96C3E576256F573EA8918D0EB1C0F97936870D9DB9CB F2A3D396817BBAC1011D08CD8A9850F540D7DACC745C16388CFB2B7F72050876 6C7035BC238AA52C048C4A96D75A6C68BDAA0215045565C3D6A549ACBF771137 B8B21AD5D0C71CA0D5F2A0A1B27AEAD5B93F56E8EB522C5EA512FB6A10B0A591 3577051F199F7515C62D8973336066DF7B203FFE694C7A2C3D6442465ABABAD1 F20ADC3C1B3F5638E2C462ECD8449885484A7F7273EC042E302F0388CAD8F805 BBAEF47ED1DB9336C1D3452876BFC4F5C668D4EDBDF029B1CD4080EB15DA7962 5C42D82BC9ADD90D209DD510EE80FEBABC9D0A3DA922BD2959F7C717A4DE15DE 9E0A589E7314A858D6A79F0A4383CF36FDD5350258634924CEF7E1AFE74CB076 8F03E4415E5CAF27AF6B640688DC221F02D859BF259AE764F545251CE2304400 DBBAE22877940F3C034F5C35E2D89C4B917E0A6E08FAE1E78213FD87D7865D75 69E67543C29906E2D7D6ED732F1A3C8876839E598B2DB83CD4CBD3E30A632434 9CABAF2731B70AA8EDB9FA29B83A0ADBCE4186FEE7A4110C0CFA16F96880426B A691A219073CB825D5D3A95F2D04590C8AC37CFA927A3BF1526AC242AC664E6B D65DC91C5FCE8E9D83FE9DDB5D7C39680708B7D19705A2728A29DCCCE8F23B74 919DFAAD08B0D702A598CB316236BC209F233AB69E09B136FD183DD4887847DD 3002967F56880B064021A66E619EDF41F8F023275E0054BBF8BC14607258F28D 231C26F3D3BEB412C217BF83729F11D9CCBBDCE8530E11F6968125F2306D038E 3F9DE958CAE2A388BAE0DC9D6C35BA95D90F2C749A5D33B3723482FFA1D3EF16 E25FFCC307A159C566436D9DCA18942ECF0F53BD3C80986F3AFAF5D8D4A89E61 57A4D01B1880D44F68CB025F073F288C795274E775A204829417D058BF2B1EEF 8B7FDD0AA168D5C7CED9C1C4AEC537255663A21D763D4D9DD98A9EA48865C9A7 A94F13AB955A9895FD69912E6746BB7E3A2C5A76668A0690AF7FD58088DA0DEC D7EAE38DFE56F93B438BFDD1DEBD6E8A0F6F9B4F14CC357561455DD756A47A51 A82D42DE4C987F334819DE6C460CBDAC6A6AB8CEC7F6C3ED69CB17D55758BF2A C4F571C31D24FCEC89C90DB71464D39F8B74A04C092A2E8265453854CB49AA00 9812CEAD394BCA9AE019943937C939AF2BF441A89080EB8CFDAF831AF9DD59F2 BD5F4C39ECA093F3993741F8B42E2DC68DA791D643FE105E78121237559212F5 DA6D77A07B2CB7170F22355CF0D4B9F06BA1044046B6C055E3924EBE895B35F0 FFA797CFA2B8D5CB98FFD2292042170CF1B1166DD886F1877B66C3B0397AABB4 D77B3D8685A5FD70C137809BA0545B8A967ADD76982D7E546F780C41D70B45D9 E162984FCA3F34CDC23DA596C7EAAAB56C838AF9ACC9EC3DF3C436EE70C27853 D5E61E9ACAEB27246AC5166FB532DF4DB97288EBB334F19277ECDDDA4F931485 E31A5117839CE910C1781A6E8451E8D3335EE43C048B4FBAA87D3889EBC1C32F 3A0A2925000FD1B2AF237D0C39ED2F9DDDDFC27F12FD6E8D90B73EF4C5EC8651 90C8C61DF880D9AD91D748D45A7A314F9A5E6DE5DC6B2CB2C07F71AA9967FEB8 24691C31167958349BEC7CD5A3AEE53756F2D894408287B5191DBBA858A30FD7 CCBFF46E6338B55960711BCC7871BB12C8334912C9E9BB2B508CBDBE417986CF 00A63860A6DFB3A0F4BAF4D212B65A7D627A86FC9571015C49C8BD1B5AE4384E 1752A550F6C4E04579F9A2AAFC5296DD1FD5947E412FA7DD6FF7817466264331 15812D2F87ABADE73AA09B19EB8A3E0A629284F3B9C2340EA48AA616FB4283E3 0F226E4FD38A763A49A4D866BB8E04EB2DAC3ED2988D88686605EA8C50E05EED 073AC4B6848C73198548103D7F137C0712309D35AC519AB9AC7EB2D8C4EC81D1 B28FF28FABC67E9A1CF45809C6506B551116C96D6D0BBF58976C97D8330364EC FFDCE625778C61F5679439B7B0E0D1C5B2DB429B30F516A4819D869669C62DF3 982EFFF5B6DC100976D27D0D09469142C1E676F68D4CF78F65F18091DEC01A6B EF74C1C66005AA126EAD8AAFA9D331907697E335E543F8920F0A743575E36585 3B7844A762633FDF81CB32E3D138D0235E72FEE05385D99B97E0DC927EB95CD6 B25E3D460610E69D8B98C148434C6597CF400B1959260F71BF510AE301B1B526 4B093DA9D58775F23EBC83097E9A49D6B2CADB4194D40543B11F75E9F93D49C2 9EC04CECBE3CCDDACFCD75D5D66B4D5319DF8BD99DE0FD8623B4D5130CE0F94F 0CD9A9EFEF8F7D54FACD9C1FA29F5EBA7B6394841AE2A923C669B3DB88B62BAA BDCCD66A95E8E9098A94F8BD161068228355CB4A24237EA06EB8C506B2F014F5 2D0E21E117C5092C23F6142603B95ACE790BB5601083774911DF8488D5FA5B01 B1588CCF23E72DA89C3A8BC9D1A26ABBEB7784CB5A44C5343D81E71C2A0ED122 5EB90285BA165EFE57F5F1DFB3AD53CEC1CA05210FB312D9220E489CCB5C255F 964AE1760F5DED67DF45A963B59C7944D62F5A0E53B9FC9070D12C49E5BB505E 06EAD3E08CDC6FFB6D5615EDD0F536EE3E5E4259B368B6032447D62565E486AF F7809FD16E931866D023D21D1451B8B64F8B11305692FD9990A49EEE2B89A3F1 05583761B3EA6B0D622E093D5245C35E360C8F1857D65218D6A2AE1A16BEF598 9C941992B74F161CF3555EEB1CF4AF373D98C73FB2351CE9ED950AF55F232858 C2B33152E27123ADCE76483AD7CF8B260C540D47EBF8F49D85697EEE6FEA4342 1AC56BD90E32D87ABD784531E983E4AFB598D6E5153B3EF2E0972BE1DEF8EF91 B841159F35133C64E5AB32C66D97FAEC07212AB9AE0F6E92DA19769A7C276F5B 69539D627575572723D7EDF00A948F57CED1209FE172F65E81FB96C4146FEF9E 975372F01A0D3E3A1FFDDA1C7D0515966B5F644A7EA02BD0D220D9CD0606DDFC 13010C7A1FBEBC6645E861BD28C495A94B4B82F936F51A902DD26750757340B2 354EC7E5E5F7740985345841815AF99B29B5BCE48FB9F3B54F7C095FC618943A 2CC5287E22F2E83D349B8CD3AB11EB89E6086C04FD0D2F4455158C1A9C32932B F6D897E1027DE99763F2EB37009E9B0E1D4FB2804B55D4CF9BC025E978F3B9E4 404693D943787920C2B0BA6F71B98CED4FCD9BCC76EEA7A0AE40FE0662328A85 3F8171A53ED8982658D597912251A492785C80EF95CEAD9E79DE701589CD8FD5 A2CCE367FDFA2AC6EAF9C71C76022785DD2BF37484163ED18140AB390F6CB1FA 5DFED7BF4B5848717E29C87754289B4DBB2C4C3E386D08E97F55B3588A865428 F3D63675906C9AF9AE9A0648ECBBCBD3CD7F65883D08A0DA1E9957E037004D21 FF7D688EDF33EAADE0F634C6E28AE693F33B1D41E16549B8370F13B1F4ED14CC 59A9682D23F3F9861B500FA4CA5B5DFB2302882C8F4099AD7E2695E73EF6DABF 06CFBB55E60398AC8E16FD04F89D8EC77820BD77A7C79DDABE4CE9B530D52961 796F6A276B3112A29B3C4D8B275740514F999F67464E16CBC69EF57317632B25 A2C6A4314D98EBAEB117FA38D541F79ECE931D116C06E1D1C6C3740D4D52FEF1 8B1C570A2331ADE9A539D89344F30254CA52ED21CF18ADD03BDBADE1A6339BD6 48503445E21554DAED6E3262DF5CE8435E5B3CBC83D234E1EDF89FAB9541D9CD 147C2A54274F0A94F5B2570BF7AB7DF5314A3EF78B02A82256208A360419449F BE25225B24A7032A6B8161A79F6D8BA83576DE0AE6554A8DA74433597BAB8459 E4D6AA23C6B96E0324352E075240180BC5214BBCCD7931FC4E4D09B3C7707A13 9BA6D15F0F8699950676738B6EFE98CB3186613C27C97E13756505AFDE06CB58 7A8D33E66EEEEA8619D2324B7E4171DA3015A31D2F3999BC2437F9B31A4CA190 33B35E8EF65DE297BDC3B7DC6FC6C5DCC3074DE0517933355965241D381B84F0 17BC30DAFFF1AB92A7F79B07BCAD4CE2FF5E3FEF424D21B8D9E708DDCF5F1829 3B42F3A62D93DE6938F3FD9C5F20B274F1B996CD915F513CFF4110F236E930C6 1047C632E713BF8F966E2427B41E5C69CE81860FA25B904785833D2D648A2116 06791617044403182C83BB4EA61D4A619C87F4F8E988E70A6DC1329F892424B0 F14256CBE394EC3E092A7BE42A31B19370C1AA6B07E032D3C684780103939879 C1BD449BD9DF2C13F10ED09CEEC6D563504D6BE4F4D643E75F69C30221318B28 175A8DFBFF1BEE2C730A7843EF59BBB84C55D6AC6A359C135D812C96A41B28AF D5A105C5D1F66E607E7B3B82848A91DC60E340C953F03FD83DED8625577E351A F42C26590CDF29FF5E8977EEB1B5CEF8A8A59117389712281666F384A133D2E4 2144A5CCE106192E56841378D6A4D2395A609AF42BAA0139DFAF27C8425AAD2C 72A5EC63D8625C905143805ED74D97F7C969B5F6AB757D6E06F54D5E08799F79 5B47B19C19AD326F584FF1BF8E9E93D3CD438FFDC6AA6B181543B8E5EBECA46F 64B4CF1EE7EA8EE3C685272352946AC63546110E82C7C2B7D0DDFF9FA0A792AE 5E734D8683911E15C141CACBCFD37688AE3356414EBD0F9A16F821CEE05F4459 0DC4EDF4C820DDC31E91FCDA26F4108D2E7025C512B254222D8EF0F2209070DB D70492B623C14B9885CE4F9852A98BC1DC22921E76FA35B4243FAA72E8383CE8 52A88D06AE7E7001FD7296587BBE85A8E5F3EFD43CEEA5FDFDB0EA96BCF5CC8B C64E02B4242D62F00B5A4E2327F5792411DB4E1581315AEFF13FD9B2ADC3D5A4 EEA3CE93B8C96A7E3B4EBD71E0025F3AABAE38DE77F0A2CD794C95B04801C7D5 1D26337D8D0AEFE939DACF12F604647F86EBB014C36662363DE562410728CC1F 4229D842651B79B5E7AEA73DA13DCFFE6133589ECBE40E03FA2B323B6A6C05A6 170C9E2A5C240E7F17424C3231B75AEA3B81FEE710F0626B7BBFAC989CED20F0 25B5488990794E9B06CD5BD86705795E76E475A995B9EB57876014BF96301070 0160696A120E51FD9A54DBF552CAD2A281CC396AF50E1DDB577619A6812419EC 0C0F60CE11DAE7C4A96CB557554FDD3781BF08A94228819A3358863C230D9BDD 50AF9C6E58CC47AAE22480FEE3DD11959149BE62DA274827FFC8CB4209FC4FCE C131637304FEDFD50DBEC3CCAA6A8E21268B0EFF7431408684D2F8A0B7826827 02FA5D2C15B26B496B33CC569BD66AE45F594D2CACF73B097F19B47236F3384B CD43466AAE493526DB6E7105D9A4F8E437F4AB101F267B83968E0649FE676CE2 A0084B374D68033929A8BB174747890A2E92227E6A86FA22BAD51A868BDF454B E5BE1D985EABAF07144A2CB58FF89BBBC77A6DA325BEF3D17F724927E5A8638B A5A945BCA8D080AF06FDD0B20E2356B0E03CB7A13AC4485E4582D0867252E690 02AC8C5952769E2511787BC35807D403C83749C46202DED17C5CF411D209B295 AC58B504D2DB1656E75D10C893D93B6CCDAA058C4CAF2F5C71EDF0F1B46A1962 E36A7083FE5F95D5792C7F22F234C4D1C1232C4A593510EFD274C71A1B7B3ACA 53B61FC0940A3D2AE96ECEF52B7FDB225AFE15B0118360B90D178844B77A6329 058B6A1F98C2209A0EE2343AD051C87FE2F819CDEA493D05CE21B37AA6186C27 A87C84A7E3041F1B96E35F34E696E8E53ABB74EAD63C8F62F500E396952A590A F34BE88B272AA003324C94415F97198FE08A9389BEE1C0684FFE2DD78361CB1E D23DFB1C249405BB0EA452146736BD66151B4F4CD2FC2FE7C85F79A8DCEB07BD B3969F1C940A862F697C604FC4E2F8572224652B486CEC51C0CD1851E9F9C306 CFA9BDCEE65F474EF78698809458597874754903597855709D9BA55FEDC33FF2 DD6D4E700032A64FC72F4EBD472D2860AA86E9282831A9DE50246ACDC0335150 41F30A4FF4BA2EED047689E917EBD63ABB0DD745EEAE0B591FC35779547DEC10 7A2A604F779F4C1846BCE5AB47C9FDB651C6A7A90B5E20F599B64CB7A6A3B678 C12BE84D2265BD2580B9EDAB9769AFB805AACE7852DBBF10509DB3199FF3A48D 87EFEA8741222126B2B469FA4CA769F55E980D00F0CD19550A409EA413950274 7F0253E171CC1A0CAC6972726D59DDB94F96C93AF78C9777595825838DA55E88 B9ADF3C9CC8023B19E163678BB2FC62C61D9557624BB0A302B64530166ED11D6 F21FEDDFFBE35E86A7DF9E3B8647F87539A76D21E2B094F0AA7FDFC5688554B4 FEF89C0DFAE10A55CDBF6D0CF483DE5732C7F939305DCD6B782D03F119CB64B8 E53C80E1AE5516B588AFFA4035B7194FD9D35121152DE664E67C2479FF6DA71E 771A263005F22B7EE045EBDA2D6AF2905EBA40667D7F8AE635189B9C1EF2B8EB 6B8072CAE291B6ACFB66F67D165A921F37FA80352C0986532EA7E89540EBFBE2 A6697FA7C40F12EBA58AD432FCF3E83BB781D038E7A734A7A8CD6D9DD1A594BD ACBDE07054E62875BE2B1BE2321E4894587B0A5A8B7C5C0C82A228C7D604F40D 0E2E7C33713EEBD366B96AF21A2E35A74946FEAAED1EBDD2423E70FFBBB3EAEF 54380CD7722E1FA0C5E22DBA443F9DB2F6D415700C1C41E6F7F5B95FCDCB4B11 2974685E19A564A00E44B243C023ED0D0F9BD88B122D4BD2DB19D09B1A57B7F7 86024E4F34B740B12C29AD07BB2C7DB84F26A91A6A892B9994142E5DDD8FDFE8 20858D2A574E0283A77BDCE7D24F919D7118E4C194FEA4A0BC8957701C7CEF8C 57B0E9D09E2E65D8E1FAE4F1CE3EBB4AC3A05B1ADD78267001A75127078B330F 4CAD02041B88A78C0DE5DA3164E88F7D7DF28AFBEE370DD860C4683CAD9EAC38 AB601F6BF61C87A8D401317892B2BE91B4E74CB9C46E91C6748766024CFDCA58 8E3AB74ECAA78EFCC716FA58A289ED16EC5E51138EC69FAF616E60502F0B015B 60BDDFFDFD6795CDCCF0A5403771984D239F93917D980CFE9663BAE68AF1D0B4 6A591EC7FE562B62D56A757BB2B82775DDBECD131FF58B7FF02D0F42FEC4C560 928736C6DB915169DA0DEF3ABED59761332EF2FC0B63A313A5EBC45548BF14B5 EAABCEDAD713FEF34D65775AF811080B9EAD0CDB1098B97EC4EAD2B3486ED34C B58B5E82605ACBC7A69105E2778627A590396EC2947CCD5752D07F77C1AC7AD2 B683107C901D76F7ABA12A91D3CA8944C6170015438FB837059FD179DC0E9447 BDE307293B7811F3C988E7919BAA9A588A8C3B87FD1CD58FC257A207452EDCC0 05EDB2C0A631785BAB2324CD7BE4154287AC9D2F786C9EB67B8AE3088A3F7CFF 840106A3E9470E76EEBFB5B1CE70745C319048497D1E9088B62651E5AE196F12 C101A44C717DB33434F5CF66ECA974CFB8128C5FC3F083CA323A046E55F39ECA 6555B2D7984FF1532C848B44DF3556D690FC7CE33E88693E651BBAA00D458A87 64D84358C40F5346A5EE62F36698D40865B363ED256890D6ED56931A94788D0B EBB99DA5F1887F0DF2107138975EF053468BE5E53FA5BDB70373BEDED86F9C45 C56C3ECB72E85D4F479B39C031564B8D25A496C817E7709FF1337079D2ED7152 EC496CD46C8FD231BB96F7BAAB54A26841403F2B0E8A76465428B1C48C16B593 C40BC388E671EAD7D4FE64C5F1B674F4394F97AC6564FC6E1CE25174E112F17D F0DC0F9D8CC50CCCF8EB389C3E6D7B091FE4A8B0ECACCB8ECF0439C1490E4197 EB0E60FE7083CA1B1A9EB31CD0F1787E546C956E0766878A1E91379158CD1513 85B29563411A0BF7631223B76667AEBF92B92E2156B55044761F2648EB89759C 785271463DA735D02E77166CA7EC0CF244C31C2035ED0898FAB03B7AC1AA7AC8 3D6F494E4767354AEE1D528E6F3E7D2207B60FCA468B96C3D367121068878078 CD309907E4E5168F58C633D9670FEC8F9E70AD9156E9439F9BC7F5C421595DB4 61042E6EADDBB773C7EA7EB7199A23CD04C0B510A95A21D27A0BB3C21F306D5E 31DC3E5E9845DC0750DCA50A5465B20EC66B08D45D5C8EBE88E05F3A9EE78E6D DBBA7A617B94384A841F30A2031CD64F5C10176862A43CE4794EB5FE998054E8 D690C33BA4B60D7FE547F437E4D867FE15C749DFAF9AC533960A1C0B2D0A5BAA 4D0FDA3629B565CCC419952FBAB0EF76AA42F02A8ACE114E904D7F6B1D0C7D5B FD6EDF4F6D050E4FB622C1EBE0F6C7526368F664E0C80637E92D15C8175FA682 506E892BF853FEB424704049A490CFADA989AB1A4428D1BB9334A461124C1BD2 B845625CA9EFCDDDF92CA67E348B397A86CD694F04767EE57FE7F6F2AF21AD03 7137EAE9B7D6EC896C00CDB9F5E842EA24D13F49A8063349851E8EE00329048D B588CFAEDE0CB9EBFAB6C63DAB81D152C7331389ED338C00D12A5511FD8D611D 3B6F6190DB6427A11CAD22291DBC3FFF8DBD873856FCF6A5239EB13BA61F7B62 72D7D69E4980672A3AD836A31BD5468B9AC25C99893EA90044783D0099DA92AF B5359932B469310128D4534DDCAD4E6AD7CB46EA96B02EA1BD17ABDBE5673DA8 041E470E5D63D313FECB911AED44C3FD397D6E978AC45ABF1C79FB36C7DBC8DC B51F383CF004BF362A86D021BDD68261069C555B11A0154A2AFDD3AD200719A7 4AFC5B7A198DCBCAB643472A588B05FDD990B534B4C5BC6CA31753962B114003 799DEBA92C5545A60505B264B03714111B86930E41ED179B785B9B9E1138536B 5F6000B21DEFE699DA533062FF10ACE2916EC0E9041DAF01D636BF010878E01A F60E205EDD627AA8B1C8A4451B26197EDE66B2883365E5D24D47EC52DAA5AD87 60B051A8D43597E94D93AE5B96C0B1D478B941D93A1D41994809F7C77F7CF837 58DEC5416CC9A7A859099AC92923A0CB92E162ADDE6FBF177E9F3C466768116A 7364C595022B0D1B676CAE416052F57D971CFB9909E699B8092C3B73E79D976E C8F785E3831D203CBA255548EA33FCDD8806DDA64A106CF78525E2975D6E1785 0CB295BA086E61E1E5208232D315E3A49314F9FC4BF48137576D3E91062DCF5E F3079570EA2925B46B0948A84598386666D183FFFDA51D2A07D39B389F4420C3 15966987B001000C5BF916FB8F1095DA35574F1C69926F75D5B5AA849D87012E EFBEA815F6DF80E303F7FD86F3211A292C3AA3C540B82EA05D2D7D18F91794F1 41D86F383BE75DD04C3B15B421FF4EA53461E67956B43B08E28F286346889690 EB5B49D565C561E53D28B0129EA4E2173EFCDC85203A33D3AED7F5BF05F82D30 CB5042390C1C442D2CC57892830AC5EA247B8F29E16339D3EC0F7BA12F16ACDB BCFB24B3B1C418C77F884D632F4EFD9CB8E87B9720FD98CEEF01DBDB976565FF E6787B741FEA531892F7511DA1955FFFBDA94F8CF44733DA002A405C2C647297 945404DB8C5D20E7DA588F6517FC00378A18CC7443542D4028BE48B910ED3089 9DED6E29234114422109093F1AAFA21DAC1FB99F86919E7DCB0DBB1FBF43B22A 8934E0A18F7B30E08CB0E81FA4FF1B01633363090031361C94A118FFF09F5C3F 508ABA993033CD37992C319D148797908BD24C37FFDBFA59F0A0ABA54DCC9A74 4E6E869202F4F0A7DB5F6DE7EEE196C9A11719736F1AA3C9686247D31381D88A FB6A714ED800B7016686E167C57E1490A47C9912CE81B4433AE8E05685773424 7D0717D5EBB46BCAF3A62B438AEDF092F6DAED237D179D9901294E7B5E9E58FE 91D068FA68EC53F93A191068A0D1C95176B5DABACA26BD64E20DF8092FACFE8C 5008CEECAD5FA89ECDFC8B2644083234D4494D511DC096DA2D1715A3797D4E38 27C02435849BE5B9018BC71A29D9C824C85B7F360940D9085245EE76E73D12A6 F640D735AB813376847802A9E9ADC1BA559DB8FDC7EC2F97018629CDAAEB6B9B 5688560220FB24A20CB799A785CEC705EFB49111D6255ED35EF36CD261B595BC C82A523AE52F6E711746582E61FEABC9A5FCD094FE4E0368208812A8E42273BD A4202CA8D8F39D22978E9813EE6AF774E47B4ACC5590EE15E5D123D349F65F75 D69F4CBE60EEA6E7B6FEBC6CDCDED467FDAB989E4CEAA555D4E3224F840C12F4 CDFFCD949C10AD5E3B866648B76EC5D450FA15EF100AEC9011C921554BA02652 EF2BF1AC50D827DA541418CBAF62E754B2E7E2B757414581E565E822D75F62C7 C43471C3504C977CC72AB9BB5F8EDBB4BD150FB0352467A271D3F8C7A5CDDC63 05FC7D9EA74AE79BCBFEF7DFB81EB8AD490BE6782E24E8EE6B611E25AFA462D8 00993AA11DC652BAB31A3C82ADF1DFDEEB3037DC3DFB6B47B5249564257FFA7F B32D6F80F56506D26D7005069767CCBF4D413AEC606B9DB37518DE5284C6EDE2 F11386550E4CEFC25872ABC3204B6EEA3D2AAC228E89E005AFE41858FA688CD6 1A912205FFC67ABD045C6CFF3E0394CE50402C1EEFA4E370BE315BBF3BFD5ED6 48FA2563081C5B33AB12903644F6A3151973256B67C85FDD1B08B5BFA9C816E8 65AFEF517B2B0ABAC69301C75980E6C5254751C3F7DFD98247152AE2BB5B7791 1C7951BB3BBE6409A9EC18818757526BB68651F5520AC58799DE35E0B448AE48 EA69FF7706704D54B394F1F3E8F02BE4940F0216D27A619A4822659A6721A29D 970D6A97FEC37321FD37245E194D8EE3A235A816A70663B6EC392B27DF147715 5F9638B77825C6F682E03ED7D03CF4F277A278AFD6C7E370F3691E1C1253370F 914BF3C934565EF64A1D9914F6CF33E524B33CBD0B04022E3EE9A2127DC9EC2A A1740AA86EEDEBABD4F72D84F546F3A257CBEBBB4A6FC89ED7574E65E31DBE8B 0B90B7653AF0D532C8F9C327E5114DDD879453D90525A157C401FE1EDEE81B1F 7ED4C5BA009C176274D83224E21C152D96BEECFE17245B58F5692B8B04A60DD6 EDDA032DFF686C0E090F1412AFF11A28EA566ED0716284E41E9209C37F0A23E4 EA4A95B26A95B902B81F6508C42E6D430243D630E34E8CB6EB4A5075E3B2A482 CE147A6309EBD349908C388E36958909E47D7BE8DB5CA68F7A1EA5FA668F3DA8 53317489429EC6647ED774E806DD2F6AB5B733B311D8B6B8B1B49E196F4F2558 E636FC224956D50B61617B54C667F5BFDCA82976A8CA3C10207966D652858407 0284C849C97F0B057DF7D2A3FB7D4E9764BC2898F207A5C8FCB975DEC0D70BC6 8DCA1CF954FBA736A737F7466D1B8A8FACE70534BD1EEDC7826B21694D884579 78BF96816D4833511E4DF7422B1E40C91D00B049795C40C4CC8EA9D0F9E2DE6E 0D0D0EE28D1EAAC25E980490877935ED2DD8574074576A3AF21F84D12B851963 F52BDE72643D6846D9C656B256FCBAB9153407FA3637D49534468F6793B0DBEF B898E3E407091ACB17CD3785BA06D0C4A7C8342852E20B67423231D8086BCA6F 495EAA78E72A0FFCC1B555C13CBEEBF78A80CA369AF8B11C9892A2E3C7AF6D47 194E907739D65D3EF7543EEB739473FE3E496D7A20580BADDCB5BD28F70E45D1 B772A69A70DD58B8D0D51616D556E9BA0659A21289C1A33C441C57DB52AE3509 AFBCE1308AABA0B2CD1770F6E23A24A562A182B957D560A846A1F22D182E6D9E FB9D99BB7ED07036D2A495818CFDCA5060D9E1E8C0CBAD84AD7BD6A9F971AD92 E84CBAF3671472FBCC6598DA5BCCF44D7E304C5614BD5501F89FFE34C3124FC2 8BF035F5AFBEFE5833862A64C19FA81929CC0515241BEA83AC5A1E5444D2AF97 56867C8D5500DC36E49F43255D899BD247AAA5777B770233ADCE3E7B1E5535EF 34B9C8708222432EF40D051E92603184C5DD2FFBE332CAB427771D3FA95ECAAC CA1F7806959A594B22871357F012960FD7B5C158C982D4BA48BC4956D10CB57D 1FEBC38D26B301085C3DC09A40A57A016A4211949B62E4F4CA440C2A22786A40 19A3AF4385467421AFB2663370455B5D8A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5 D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D 23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8 D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B 93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711 6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4 EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953 CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE 00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5 B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA 99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904 A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB 11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5 50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB62FBEFBEFA AD08ADD6648E354B05E584C970AACB6E015F56F3482678504279F10E01CDA446 6F6E039511BE0576EC00ACDBBDE8DAD593121F1D855D175D616711DB93645AB6 03227673BAF4CCF593EB7EF23AFEB7B2CB7AB053C26530E564BC01C2F74A3D1A 4C1279D91F1EF1383E34E8218B3A9918341FE9E346EB3EBFE627E7518D6AB787 8DC227C39FAF27D969769756B98A0A078058A6D04DBC5A18344ED6EC71C98E00 7996DD675B953CBDA5AAECA2AB8819E1FFFE61F2A2C48F13B70F8334E9A2CDAB 4603C68292AD8A93E29A04D262AFE205293FC10AD70F360DC07DC03E00CD12A1 5213BFEA869BE17CB485E81907A09B54E11FDBD10D0F96A93331A1C67F567735 D8103CDD80521A3C99A41D027814CF6D405E1ECCE56AD06878ED9DD601EC3D5F 77DFB141832D6A1205CD020AE2DC7F1184765AB81CB90EFD36FAAB3EBD0DD796 C157BF3E867C5BF7500CA0265053574EC2B493943E894ECBDD4FEECDCA195DEE 68A3F72351CE5732F1E466EF31F1454572113E8098A3433CB162DF809F6DFEFD 69F5D0C8050740755A41B1AFBAC031CB876EC4D1C8EEF3E35D9566BDA93F2AC3 55EB2BF661A9111BAE2534E4A8DFC1A37148F928D7F6D8DE1F4B4C5A32752F24 F22035330C53BF5999089DCEA2578E92512D265EAEB3A6E150EF343E22033DB8 A6B7CCBABA52215BF69218756FE289F3825F4650796FE1E23C575132F99FE2E9 E7919B06E71FBC1ED75F74DA20E4A0720D0023DDA270A6F104B03BE9775AB5C7 716C017D25245F778FBD409BD200B45217D2BE5573D15CECF99A6C94DF4717E0 1AE54B7651AC2E8D9C75FBD8D4C52671DA743A4A2C2FC7BCDAA07D1324FD54F4 02802A68267D6A35E576E2D2651A345DA8EC2119DDBEAE046781FF6A677251CB A68285646F9B064773A9A4D66A58FABFF0E128B6BBF24312763CAA7F37EE1EA8 CDC1E739E8E7A419818C8D193E1EFB1A872C0FDDB5130D0B988F019D86A3C6CA FC8A5EE6FC2B9063BE35DF5A72122D0315754F63894B5538827551930BA6A898 89294381A1DD355A55C3949FF9A4145A9160A095575E41396C102944C2985A46 12F92AFF15BBE9E6C21E87C40E90F5FA66378763D70DE9D8DBFBC61ADE23EB7F 530DEF99EB9C03851688DB6ABA5CFCC708D9D8C77599FB6006D06928DF952EE8 101AE91D90E154B2F18697F692A8651DD59CA10B4E4CD47B431283F2D4ADAB46 3D6C 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F D1F017CE45884D76EF2CB9BC5821FD25365DDEA6E45F332B5F68A44AD8A530F0 92A36FAC8D27F9087AFEEA2096F839A2BC4B937F24E080EF7C0F9374A18D565C 295A05210DB96A23175AC59A9BD0147A310EF49C551A417E0A22703F94FF7B75 409A5D417DA6730A69E310FA6A4229FC7E4F620B0FC4C63C50E99E179EB51E4C 4BC45217722F1E8E40F1E1428E792EAFE05C5A50D38C52114DFCD24D54027CBF 2512DD116F0463DE4052A7AD53B641A27E81E481947884CE35661B49153FA19E 0A2A860C7B61558671303DE6AE06A80E4E450E17067676E6BBB42A9A24ACBC3E B0CA7B7A3BFEA84FED39CCFB6D545BB2BCC49E5E16976407AB9D94556CD4F008 24EF579B6800B6DC3AAF840B3FC6822872368E3B4274DD06CA36AF8F6346C11B 43C772CC242F3B212C4BD7018D71A1A74C9A94ED0093A5FB6557F4E0751047AF D72098ECA301B8AE68110F983796E581F106144951DF5B750432A230FDA3B575 5A38B5E7972AABC12306A01A99FCF8189D71B8DBF49550BAEA9CF1B97CBFC7CC 96498ECC938B1A1710B670657DE923A659DB8757147B140A48067328E7E3F9C3 7D1888B284904301450CE0BC15EEEA00E48CCD6388F3FC3BEFD8D9C400015B65 0F2F536D035626B1FF0A69D732C7A1836D635C30C06BED4327737029E5BA5830 B9E88A4024C3326AD2F34F47B54739B48825AD6699F7D117EA4C4AEC4440BF6D AA0099DEFD326235965C63647921828BF269ECC87A2B1C8CAD6C78B6E561B007 97BE2BC7CA32B4534075F6491BE959D1F635463E71679E527F4F456F774B2AF8 FEF3D8C63B2F8B99FE0F73BA44B3CF15A613471EA3C7A1CD783D3EB41F4ACEE5 20759B6A4C4466E2D80EF7C7866BAD06E5DF0434D2C607FC82C9EBD4D8902EE4 0A7617C3AEACCB7CCE00319D0677AA6DB7E0250B51908F966977BD8C8D07FDBD F4D058444E7D7D91788DEA997CBE0545902E67194B7BA3CD0BF454FCA60B9A20 3E6BB526D2D5B5321EE18DD2A0B15E53BCB8E3E01067B30ED2DD2CB9B06D3122 A737435305D42DE9C6B614926BFD44DF10D14402EBEDFF0B144B1C9BD22D7379 5262FEEAFE31C8A721C2D46AA00C10681BA9970D09F1EA4FA1566B96E221864A 45A24ADAEC63F61C9FD18376D39E0FDDE3FB4FBCDD6A7B66068A99D31CF54CD7 DF2262DA91CCC72889CAA62B1D6F2155CC8E940A2C35D8CD3EC75326188E2D30 1090F31AB50F30AC77D2C445BAF7323389406C44641B3A72C26BCDA442504D03 6C22A3BA1A69E5F87EA400501A3B3231E46F96AC3A6C0E4A4F6F21E0B2BEEF53 E016F34D7003351FD12436520926C632218410359AF9FF167750D3CE0DAC3B91 B310C457402E05C316F400246C8C38B98CC8030F71104BC4FA0505B5EFA4F5C5 9E4FA27C3E790D698690336254D7E34451E692AE23BF5FFBACBDF33E25359BD2 B0E7A0686602568BC87422F32486CB50776C7EAAE7F1BF78B228CA3254510653 3D6368A4985C5FF5A48AEF16E1AB71D7CE2C6649F2CF4B2879D4FA042239B504 F988D2FBE87C3BC784E55B8EE36F1BB5EF14FD5836CA448E139EF8FE221E827D 0608A6B90E08CBF44A30669AF4E20CD5C0C80518B7AF4FC2F56904C2849F7F05 BD9E5029B6C79D25E34E18176A2755CA288597D1CC18D81511E93FE88B94DACB 67F312A4986FDFD913164AD228F5201FE02EA6C5FF3F6B1BD792FB99819E2589 7BFC7A527E99FD1C1163D10B83BD61D7CB962C4EA67E887FBA85DEA3B2A1698C 6A896388E3CBA13AEB278D02354D5D40ED45A86BAE6F213806E9A598FB92FF2E 8F498BA926D0DC8E167B32DDB47D5A71212CC63EE2BA1332B23C48433BF78C22 E5A050397513C7B9A954B20801ADE837DC725EE53845DAA89D59C4CC24F9C849 0A7DDD7808E5E31755CE6F8957C95FB68823B9F944BACC8E18307C10E9D566D1 D6A4BEA8A230E5C3ED80B9BD0F2A30F39C905F11843A9C3B873F2050025DD297 F61A7D44A58B63C18C16C4BDDEDBA73979AD1CC2C211E15E42F6AF3AFE4B686C 9EA058B6A330AF99BB0673333FC04ED65CF45BAFE78F1899DF782FC2E0C10A45 622720545FE9E04DC3703FF862999D20CD6BBC8944F7EF1EA84EE89A863FEFD2 9C2E61C7A244AA254CB70319C57F7BC4E7EC1B7ED0E2E0BEFB7BABA64360690B 32DE9FD9158DAE19BC5605AE0006A614D4E3D70321708BA09AF5774D4EF62EBF 6CDFD17652326A6BFDEDC298BCAAB0B20209AFB82CD9E4AA63BE5CAD1455AA9D C5D6170F697E088ACB6FAAE3427B3A26E0D8D0E14968C973CA0D8BC90F4278B1 BDB067AB3428719BEA95A88E93D13409A2A02A7EC0773CD94FD43625A90B2141 2B341C59871983359614089B5292C2BB9C184A5F3F9187988A4F6627C63FE9BF 1212A94D185FE803E6B9654524E569ADB223E8DE809E44DB791D1C46AFE2BD85 2E5382B3968CB9762BF37A38626A385D5F03D69C90B1989EB0996CEE0E1C7AF3 DD198CF50AC697B3489FBF119FC29242EA5A6F02B7041833027D327EB8A9AEE9 28681EF627A2AAD81E6881C369D9C09FAFCFDF22C504167CD5C4869C1B13A1C0 5114C83FF30BB4BF72E1D6B8495CC1460BA66BBD6E8DE75815F8D410B5D77A22 74828FF73C7EC70F5370B1BB98EBDDAC4E2E63DF156E8BAB1F5AE6C39F621B0C 720F21A356B8F2190C6691CEE300C7941CDB6860D4BC46F54F493FD96B2CA6B4 65E98B601C0170C8D54F157F074ECE9ED65ADC9205781E924A4063E4E25DD925 FA66D46F726A8CE7B67046E78A3CAC9E2D8216C16D99ACD2116419FDA1BE17C5 968423F46CB762901F9C54163B07EFFCCA2B2E311AF46EB51543FDD65CB9EF2B EE28228975ACCE6F5364B58D1EE0A8A6629E6562DDBDDEE40A44E222B51BA222 4C1D3202BB8229DD11B6E316115C211D52DA9591E1DDEE8EB40EFD6F0B464651 828ED6DBBAA8984E2166F32FB0D4B38BCA768373DC89035FBC6E7E1FF3F63E39 6D51E6B8B11F3191FA53D74D106E1DE90817504A18660FF263367F5FAE94B3A2 4AAA4FAA05ABA076BE36E37B8D5304C0280C1C7DE12628666C34F6E51C9CAC0D E750B0BAFBCEC91252E0A722B3C8D19DB8EF7901C243E4DFA737E11FEDCE2DEB C20F1A10823A5512CAF05F20718782E556BFE97989817C9C0F2A2FA009DC881B C881C281B856F1E102B8F4D7DCD6E466D2BB19DF4B0D42A7232374ED41146F2D B613F494F1089E787061776409BA492A259718E1CF97A6EB3C42F753D5F171E8 2F400F38B36039CBBC0FA17895FD1CEFB38CB30F1B65F54740AD7E6648229104 65103F8BBDC14C7AA2DF4886854C748951EEBE952753017C64C3077964235BD7 573513C778B4529C477BCDF1B09568F3D23EC51F960BB32511648D3AD9844870 BECBCB530AFFD0E5E6613464BFA058062D70522221D71D327D459AD9B41FAED4 D67085D9A176E4D92168A71C2D5F8F94E14770F844EBA8FB0917ABC66DA014EF 6EE31A3352B2AC8B21BE65D20B4C7C4479BF9941E5588DEB8DD37DA2C50D6392 EEA82D6FE12A004FF040B577EB875439C57FBF1E2ACE27002E63F1799D1E688D BA82980EDF1954DFE447441A58E8DDE89E7DE3DC812640002E8907F4CCB5DCD4 51092A6D6376A248225C22A99D6EC6F64DF1A6B60AFA5AF7F26AD47E3B2B8A8F 182C2A2116BFBE3A9EA503B4DC25987A7181FCBA4E32C342656CD03CBFF9B116 D909FF4BCCB999D9E08A79F45C88AB2F0A01EB5F91A6607E4B6D3F0C032789A0 95537F90D6A336796DBB847EFAC761FBED49A0A04BBAEB54800BDFFA2E259DBB 6E139B56B300E445160065762195021CD1FF876E7FE47DFE7EBF6A296EB8ACE3 0B166BE3A0980B5CA1A7E55B3CA7F3454D500252F9A15643ED3627B06F71C6CC 6E87CC01247AD3A8A8AC4519D89D4A48BF844B682B3EF0881E4522F3179806F1 F447529EDBDEFBBFA888DC0BF1E6FFB716CAAB5C7F70F7ED8BE9949C3BA42026 77B332DD2E8A533F44BCEE6C4D672D1363EC46A3D64DF8C3AB81E6D125E0CA4D 1A2836A003813FC14C685C9C88FCB992D87E233C01F83AAC905A7C778251011F 00DE68062C428E38D9BECCA0AC7CA141A7DFEDC3ABAADC08F1CBD0C03CDF5AC4 5812FCD7AA6452295C84E02DBCFE29B177A98363BE5E54078EF73FFEB4EDB620 005892E4B9731F5F95C36DC6DB6ACFE4B244C175A217B829AA9362F935EE56D6 58CD94ADAA7B8C69D1853F7618089C6C70B63795FE0E1B031D6B7F78A5C3C9F9 BC77DFFF6B91743123C2B90AEBCDFAADCEFD2E7A48A05DE546B7C17A329E109B 9B1E277CC84489F23F23BA0A4C02477C654F19F45FAC32CD483F465E34766C7B 951622E625C603C84ED130EAB92A23B41E8857F722268F6D6D8D0CD16EDFB382 ACDDFF54CED3DAF6B8D45AB2A95B3DE047B8968B1F32823337D55265D6E46AC0 1F3752D94DBF5E3FCA857EE335ED5B378A21852A2B0A7967BBE6AC7172787E20 F79225D99F4DAE9413B0FD1E2CFC2A0A2C5E2FB45748FCACD558B35C16AAC0B9 436636A129DA3A0C9845ACD65EA56C3C3C0176895F44E115576E650C23053A2C BA488682B264D6950BFFC6309C9D9C44F190EB0A2D25550734C429F281B104E7 E98C86AC0A633922A4F7BB311299F814FF6FDBD9933BC0B0C25DC18C823AA3F3 B479B83E55C39D8C28FC399D3B0F83F78D0357184CBF17468B9A54C90D0BB693 2B5AC1F0E0BD85C1749DA8EE648F345E47922AE9CEE797D015404DC709E9FC3B EB1D1CEA79B66A1B2A761E68FCDA7DED68138905A9ED07DE4658A1FCA7A2A62B BFCCDF04E6EC0FD5328E158A5C8A74E269D816ACD39FF273EFC3E999FD83B34B 7E7BAB221B7CD9628F602FC0745240F9380666A540AB1AEC1482B039015CD172 B1D39BA59057A2CD1171B77C2C8FB6A75D9EC2B5C5E050032F5C295FB3F9FCB5 73E70D7D31DC51B7CB5000F2A038E9BEDA048AB0385BBA86CFE17C5C10908967 D7FDD0D7D84AF6FB87708283492BA5F8F2586253D04BA161ED7CBABDE497A339 699ADFDC7F179B2B34949FEC0A0B4B3AEE3CB16A29A702F90D654E1EA3DB4B5C FBCBEB54126EEB0E3AAA5825818BE9A3F730313E1E429FF2EA52982C8849135C 71493B77D6C1C1A62A026786A4DDDA0FCC1B3D125B2D28A1A0CCFB95645CED53 141FC2B4CB52B4CDDB80CF58B8A03CA8D03F16C48510152A82ECBE91E43E9B81 A7C7D9B12A695A4A5C58153A6B04BC5F504EFED15B829063A3FAA7C939E0DB23 E25BD10A5096C1B6A60C21715335B00F83B0F12A75E0623D755099478E59F424 4C178C74E841330A1FDBFB80B27386129299833075A949761B25C3C494BC628B 3ED75388BF1259E659246C7C0B5FFD4D4150E039344F4A4B1F4EC21C2FC4ED2D 7A30FE72A65D1A1EC819A04B8541FA750844BEC9D043A8DB50690B7A3B5B449A 56ECC8321D15E059852957D01D55D97DD21570CEB7FBFA347ADB532EDCBD9FC3 2C98AB34B5A953E3DFFB80D24826F1419BDDD79D4451F9985A38B4EED072F2AE F6339D6C2EEE0F38B01F42D29505CDF134FCBE1EA09D456441A8BFDD50A25399 D6FC55707B67138142927FE4D7CCE226EA0588C43B0523A53039B07641BB8DE3 FBE6AE40DC35619B00BE47BC8A5502705BABBCE377EE38620A4BC9E633B4F989 4185DF26706CD1DFB9D971D6D0DB42E2DB0881E5BD29FDC24C36EF7038D7D0BE 6E20B58D8C0C4148A7C2B0BB2BB76227283CBE65C02C4EA6611BBFAE9AA51EB7 C003FEEFD342EE6C67E6070A59CEE17DC8A159A8EBCDDD1D8380F4191E365367 070E7EBDDB18B604AC43F349CC3717D31E3B2AE792878D733A0C1B810C622CA9 8BC98A1DD1F485A9B20DD230A0FEACD449478216EB64805D1D428F9D44944D6B 0BA3AA1C346FECD081489B738A11DBE93A6F6C68370ED490E6E1F768E5DFF2A7 4191E46EFA423D7A02520802C34D769F74816195BC6079A025F361F86B2DD27D B910C06F01E61562D0C57341C2484D39E0546131FB0CB698E5699C59473A4F6E 401F8EDA3B15F1BB712D6BD1F6CF3CF057945CA401B4A697C5F7AD2592316FB2 58B0E9470FFDC947DE1E9842A98DF67E30E5C803CBDE735E7F151F0F04EF2ECD BF5987A4CFBA716BB60508CFC476CFD1DB11F1291C10A6AA0BC69AD71A9DC086 BC4F9201358E46EF444400E27E02FF9A0B852D0E36E03A5A17AE070B92A40F19 D62D38D32790572A2A8944E033A17574DE2831AA4BCFA6CB187343ABE4958B96 9DCCDBD12A56F31D8221F5D6808EC126E715954F019A7017C26307B9A77B4A25 E43B72E3499693336F0720A6F7ACD3E99A48CA5E6C1EFF23E622656958B5F1DE 3B5BFEA5698B391BBF67D4897A2C5835EBF0A62E9692633E2EA9AB9A0A31A5C0 E499CECD1D908FC1F5D002FE93E74904C46AD7AD21F931DCB6C716167A697EBF 1E3C207FC8AA28670658B157921490732C72B9CC3BA5774E1FF1AF5D8DA4F869 3BA4CC8520D39B2DA0124F4126F19060AE2398DA2F6E1087C08188FB632C2162 D2DDF4582C3AB46870DE6AB0116EB41C8FC586B70C5F22A3D5A059C2C19D920A 853828F2B284107D4AE62CBF080847BA72327F9A5C7EBF7D6F519F500DC1B5F4 24223C860DD8A7469B59A46BADA307D0A44627F6480F7DA02A6C7B08108CEC83 6C0EB2340590B8F7751080D0CF1B420A4750291648FDD05B2955700CBC80CC73 DAF9917F8135552D101F63E00A189E80E63D3C94EEA469F191DAE45CFDA7AD86 F4FD3593CD1C5078F591F15F00E48A4B28FE5291E7316F74E62E192BD1960AC4 21E495FF8DAEE0F269C9E4D3E0DB9E5A991E9A6E139A39296E628FDBFCC1A127 9CC9E96077FBFC3381AE5EFDD9E8FC5F2E158167C69ACBB921E872CD4CA0C4C8 1667DAB7FE9D92E9989C9A5DEEAEA53B9CCE82845E899EFEB045403CB0026DEB C1585D95209B3863EAA52AB376097C95D11B413C3EBDFC55940C068B239935EB D3AAE912E814950D3574379DBDFB6D4DE25838E700C2D44151DC3E07B7D36FAD AC5ED727CB0DEBF9A66379B4AD7EED421D3CF82D4F1BC98BD3C405A9E4B46352 7E9CA36F17116211BC306BEE755B9BCDE6912F6FD765CCA22E818D9B5F8F5796 8BD84E1600344584D84C778576CE07BD3B6138C2D5487DB4D45C66668864E879 915800770CCB59FF7A45AC2A9B84DCD55852F74AC3CB4519E133CD0045474E8F 0F61911FCED4234177B9FDCD3F97C6B6BD4FACD1798A425EFD89EE4095BA73D6 233BB171022A4D01DB831553092469CEE1F437C237AAF00B02C388558B6C5CFF 7D59361BAF1C69F0ED8202C3A0EE8F5E2B0B1A7C008248808B11483EA50A013C 6E7F9333F4A1781D3C89DED2F2A41BD133DFD0F9F828057A991C3E7CCD2E4819 0CA78B2ABA6E6010DD9A4A43E1470ADA1690EF92239FA8FC1FCA4269E8A4D6B7 09AC7B9BFCB2FD39D1002716A2083A1F7838294FA6DBDED98BB9D8144187DE36 DCD1831CE6E6C29613EB03336B8A06EC13B730AC1B4AB27BD07D0983363BE046 20C0DDDEB3BA82F70C5FEE7A1C52BF5FB5ED184C3071FB772A946E564E75350A C772127E2B4DDC722F8BC226E7FD6D024F3F0802BFB2460E7E234F00D292FABC 811A30DDF5514EAA70AE9037C9A3E04DA578F1D9A49DC43886D0E3690F9D3462 BD940AF226808EAE7C63B47BC86F0FA3034E54066249C5EB4B1291BA6D48439E 8DCA8575F4E88F76BDC0DBE201C51F827DB0BC4378F274C3269D68F3FA0C87A0 A753033349B252EAC637E7A7EDEBD9762AD06770FA534DE8AA7963E29B3577A3 94CFF12D1F5203C062571BD8BA7BB6099F1DA5ADEE1872A029FF075A218A36D9 45AE4648797EC5C0D3CAC65F08F0725F6281724A76B4AFCE885BE0353B4C6C8C 69993806F29380BABD22B30DE6D26EC5176F7BE3098668AE9643383D4D44AC88 702C34B5FADB04C1DB69BCFFEB0F7F8DC048583A0E9700F9806E1760459A5E14 34E5DA5BD3476116DC18793F721A7549255E8B7A398D26B36853901E08D28540 E66D1A36F79B00FD4C732A64420C5048105C61072063D69C3F0609F96E15D400 B08BDF9F1C75F8FE302E52CEEB1955687AEF059DE174BE69D8AFB56FFE9044DC D47FEE09589864627E623BC70272DAE56887887113F3F34B5E4DD872A1382DDD 42A528D62F45889A306B8CC32B6926EC24B7E2281B761E11767B70C6307DF2DC 2F51066097394C5C400F5F7AF18257A954A23EA91FBDEDAD4904F7BD6C7882F9 AD374DA46D18D9623D46AE7743E5238B9456DE0BF31756D074304275937A8CB2 8F7D2BF3FE6DE124AE388399DAFEAA835FD1A6249973B50E70EC5AE493D89768 19FC9E30744DF2EA7643B3517687CD7AE28873E24B35146110DD85135F060483 6F0D029876B0E84C2488A08F7B786F430F013179351C480F14F2F05794D5738C EF711D95B277A7662C2C6058DB1D2D22E456F99644035C0DFEE911A20C0A1D37 3364F9701D0B183BB892C8AEEAB79BA274451D104F649CC4CECED157D7C6004B A58CC2A22FCABB8B75924142ABD98C583C608CA6D2735E2CAFF5F130F94D82EA 695B89279CCDEF05E124674EB7653E84AE09FF30FA82B00366166BFBC4AEEC7B AE501890549A94DA17D80B82C436D51F4EA47C54C126D4A73E5665D0F52B2B55 99B1B4025D222FCEFF9CB3690B08779291418C10F8D4BF5F911478A3AA4B1939 15AE9E21E1C2EAB9292CFDD70354169064F1B7BD9EEAA38A0B0A19A9E40BCBD7 8F0ADC5729E6DECAA46CCE5EAEBB4860C297D5BB443030040DBB8B6E0A490804 CBBC55CAE1A8383C3E9AB8E91D102DF96C1377D88947400A9D6E5C95874947AD FD4185E5F99D9AF3AA0AD7DF728073837B11E40BA088D5BC454F73C9BDC3D022 F023550532C2AD8F80B2D1F564E7E7981A65340FCAFAA889437C68C109EF6C93 42D3BDAB3F011F6265F5A7A35EDFDC1F2B98F2D029CCC63D6DF0D4BBA30D42C5 2F4F7478016F2A626ECE6012E8D3DCA5FB9E75B04C8352C9CFC8B06BAFA4831A E6084B876465C40253614FF60140457311E046167A61DB9713FA995451297241 32851E3E865950F8F9458C834543927EAC2E6ADF51BADE81DF2F687EFCE24618 1EF52623D22E04920866E7720675CFD3F1E5EDB7704136E0CF0F949477965AF6 04CFF5FCDCC905AB16139804733053C093DFAFF62E5BB45265E8E0989462F1D1 A0465AC9B16E8A6D08140CB99AD5D53741BC7DFCC4165E0C262D2E5A7694B6B8 03460145420347CD7064943D59B3D21F35BBD5C0776334C433F6D1A59672FA48 8889CA204D77A1998CC4A88CE3F79868C949828BE20C05132B9EE0C12B8DCC6D 9B69D516161178C75AB5C5609168DC568E0AD356E02CF7FC49E4EBA0FED16192 1A8531701486B592CB2418616E23BFE624AE8973292F81E77FEDC139D22846E1 8423FD1388746E003A4CCC230B2912467545D828C9BE85EB6C5B77E90A02E85C 5F3A05D0FBB921485FA0C88E72DE27F970780A0B56FFF2D9E2A7B8E2BCCF0C06 8AFCA13AA05FC0D73BA96BABABB562090C5129BAC581A430A032093AE771D093 2F4F48F443C4ABE86071F05D7DA515E8EACB70205761C94E17D2311B6562BCDC 8DF336B73722A03BE40DAB4CE1127D15B01CED889B837E590C8E69FAFA27B477 02DC7129B488F3843F2886DFEF539FF81CB625183257BE233BF4D5D27BCA480F E8F8FFAF01632778A5EE7FB70BC61F84B1BB6EAA5E891292AFECD88EB3CE7E71 B2B23DFA1E4176A7A46EF095E8A1E79B61353F93B7E002C7EE19C1786303C4FF 879EB4B0D28F59BCAEFFD22481CE9DC5C56AD56961002D7BAF6D780967CB2E9E 363FBC064D101D4DB316941EA262D7D7FEB17E341C6AEAEAACEE9EABFCB4323D 8CDE9A87A57D9F6D5E09C3A214B8A4BBAC2F5F1C89E7FE967E7BB073E2E3DBC4 96F99D4B3758533795642C5A1FEA669E6F11E84ECEDC31AC5DB1FD136EEF69AE 26C10E0865146BBFB64A1290CF52D0F72551BC31CE498D52C66DA182C16AB4DD 7461F21A71CBF3206124843FBB6878D31DEA3941CE97195C0CC5F21688FD3D77 DB52ADFFCF9BCD73426CE424CE8E2EBDC6A915377A1652A551049294C639936B D958224F783DD41F092155EC5F63C1609BF4D580B9AAE271DF3345EA47E15BD8 76C649EFC4643176938D7CC36FA5DA5E75AE174DE82819C9FAB79541E4E67D51 ADA8420AEA4137FD60EA6BB269BA25E1B1B9A1D095E873AE0E5312605C24DE99 D651D6F9ED5AB6ECCC2A53D48333534582A4305589F8FF4998D12A87400BB39D E32F9481D91F094EC587591F4CDD0CB1AEAD2DE4E510DC9519F66F2FC1EFAF3E 0A263523AA39BF2FD684CF372D3EFDA60E75C254B732E209B6E1B90C185FC3BD 5E646F9A1AE72C80B64FC47377EC42EC20638ADA4C7481660387C2D283327D94 0902B64EC5CD45648A3D728FBEFD2EB5FFDD771CE615121F9F9809A0E53423CA 7F874752F149F6E67E7DB8CB6A682A5462ABC2C25143437FCD3622373FFE3B9C FC328CA63F8F31B2BD3C43FF0E9B7BA93386DDF960BBEF5FDBFB2BE7EEE12061 2DC7C21410CF0A43BD0ABE86BBF3E45AE23C3F2509B41BF45DD4A3E479C63FE2 120EB569EAED5C8BF05C1D2D47D9AD33494DBF96890ED616377A613DEBC61A63 4DA8F435CD6706CE7DDFEC231819EC2A88AECB08B1B8F1F7F11181D2666F345C F1A2D68C5C0D6A2F8DA4A35EBC42131EAEF9F6E4FE6FDF9292869FDBB107CA8E D0979BEB65430D25DD4F30A5B3CE6A4E766E06982380BA973DA949ACB37DB54D 955FA01AF16776D3FE1F2DD6A8B66F2E7D16FA751E2B14E69EEA121F8DC09753 CA60F5D991E7B681E33435450FE94C36D746421DA004E6FCB36D410AB2798D3E 0DC832EC283661998DA878CBA9506745C07E649B7A7FDBB529EEFAA339EBE7F7 4B51D961BAFA5DF0B28171AA22273C7B0456728BFC684D0B5304274116428ABE 7D5487E9C3A74F859AE70E121BDC6AC006B7C2AE8BC2EF94ED19861E3D1A267F EFF2424573A1730A3A1BBA18A19877187F8634B7EAE086FD76C69688D4D313A2 D97DE5ACEC9E663EA03D72BE71BDDF5AFE73EAB60DF26F903EFBF5F190A09797 12D14C99F1D62153D54637D70287625EF2ED35BB248D4E2117B555F8B0128833 0DA225EFADAC98778B2E31D4114B9DB2F9F56A6E26B8574DACFE715117351B54 340B0BF4D766DE5AC7A15E4619B0754A12B03D9D9496EAD6BEEACCB35CFF3E6C 1B6EB5F8073CC9A1AD84338090F854C64DDEB7C64F8B9FB5F0166E25EA4B7280 A255D8A558708D6B4CF92DA7E695554E7C03A0655806E9F529225E7A13B9D2B7 23B4E6074C6F2E3100EEA6E67DB8C5EEA65C00402EA5322B6D5C5E65E6003D4B 67E26F6F4C637CBE7529370A179CA5CBB629AA74C19D81E48363F159EE9C3ADE 5818875F0B1A1F7F77E0AAC323A5D75850D354FD8735724A4221D264A594B36D 88C4D4B0E341BC861BBA8C657BD6EA9F4E7255D39538A2F97F08CBD956AFEA60 60C933969CC45EAF584318CF51779EC0FAECDE9428E18A24023D6F58613B9E6C C6B4FDE64D8CA40D7240C61BB7518A39DE992DA4C79BE5CF448EEBEB80170B1D EA774572B0FB87B9911F5F450D2972D34AFACD8F010E08FE6B06881776EC9FD1 23C38567AFD2748351F69A70D4136F07F4E6D27F63B000B40B510BEE538CB8F5 3B28DD19050B29F671FD712233CE9CDB1A567655CD7A2F58879B382A71F5ADF5 94486B52D46347F077E7D50ABFAFBB0051E3FDF892D9847FE057BB708797A952 09FF1ED28F16C8F8AE5F20C962A971B39015C6CB01650170643B3E041F83BF9C EDB8AAC1BC29409EBDD885C7E6CE956279CACE88EDFC72DE98E705E4D7CDEE46 F61E1AC759E03376DF16157B9C838E3D9A90EEAAA8386AD2A6F1B06679A1B8E0 B786F0D2C621FC9E84B32C8DF5B4E381A5587B413CE207C91FFDA9CCC5AE8085 C543AD8BFEFA813F338832D4E71FB50852326D873ADE0D42AF456BB469FC4743 A0F295A97BC16F2081ECBF961D79DFC3449AAC12448E130C992AB022E489940C B539690EF3C79425C98DE0D06530645CF2D94BCFCFF6635080167850BC6107F1 882D8967B5E68693AB054A18E1C0E3C0C3E0540AFE51C1450144BE4E38EF8467 49C79F4506C292433BB337779864DA5580033972A886D8AEB45310052ACE00BD 33806AEF5BE6F5A82565192740BB23324860A0315EF5F4D428B8F9DBAE6CBA10 F5ABEB2F324654AD766BCCB11CE14509C1AB10943227C0CAEC823E30FA35FE79 9A344B5B290BCAC24DC744DCCFA4188D82F62E5623FEF90FBDD886F0166E58DA 973632265AF5D76A80C500AD61DBFD53C591EC6047B8CAE04DB97002B5B08E80 94BEADB8A5640E1DC4F9B6862F9D744A9EFC2AB81C8A514E6DBB989A9335F090 18CDD359A5735A52A1240D01888588E680324AC29D3A8B5D2D4A650C392A4870 DD8473705E0484E4265A3B47917239B1858D079E7E2892B2B16D5D6EBB66F9A5 74FA714D29418F55F5677C14F2DDC23F7C74A28A6914D59A8B6B76CC2C85437E 09EF2D796D3EB2BFF069A26BDCC13DA0BC00E6B8435F70E94BD9FD2FC1B4C9A3 46556B26D19A55D402B3F8159D5FFE540E07BB2F6509061C5FBFAE7E7E2C70C7 685CD425B6911947714AD473126B84A38518C4092CF273743D8897498EE4D567 378F21A66BBCCEFC475D50EB9C74D7D8232F28A28FFF60C466991186C3FCA757 D1A0ABDABAC19E0379D5A02F027C576DA103DA9CAA0A666B5F9FF93960656094 83A02A23E0FAF96C2614A1513FD4EEB78E999F57436577D8A2D64CCF0F4E9265 081CFB9779C8DA1F82D871570C0338DB7BBB596B733400BA8F305F13F8927B21 5F14275CC45DD410E002B037A5C495E292E5A3F2417F1CFD212875DB8121C211 D9A46B72052755E24537EA9C0E10D3A189458A12EC40E5DEE6722D91DFBE267D 733918C43035E77DC5ADB4096B226E5E4C61F07A9117B04B1E2BA9EB028A2A32 39E9B7466B7F8F57438D3F43D46F7832A651DBD596FACF858C66793161FF6DF8 985CB1E9D0BE0C160B3E836A9017799A46FDC6ADF79A58FBDBEC197551A83173 015B90189D76C079537BA4D9DC7AFCCF3996C9504DEC889010CA507484EA4967 88A8B3CF784A42B2E08E21701E61F40F697E92BC0193C2153B3E96EA38AB022E 34EEE35CF50CAE1598F081FC3C46D14710E39B0634FC3479CC256916C49F67B5 7B082742B4BB2F9FF76A93EAE8F1C827D896F09CB0305F21ADBD53378F0B3D46 52DC956315B2EE15CB21FDA73F8526A0B94AAF97800C10A8061BF5E458BC454F E7620545B09B458AACCB25D7F21006ACE159010E126DFD4279A38F1E2CC47623 AFBF176FCD8435383133D12A2CD3153390D3DA45B3343D5C63D5A3C4DB0A051B 2EE8A67D7C145C40A914EDE5FE78E0E49013804D6952A958CBAB648CA9AFCE91 D3208B260E280642A819973C4E07E4D50B92CBFB44EABDA0FF0C909DFAD65436 DC1F43A0B3F741B503B13625F0FBFC581CDE3DD04B2C73CEB33DD19F8B1884E1 05C78B9BCD888E9ABC0D155CF2DF8A9F8D0AAD33DE97273D07BB4BAF594B4543 2AFBC6F575C58F0445E3366CF93638F1A349524CDD3C03E72473AC055F5AF94B CBE82A171A957E7AC47A9D43E0F6346C3A98E867099A9DCCE82FCD2AC4607A8E F0C627052FEF7CEA80AFD54258BB5C16A27E95D892B79873FA8DF6FB2BB84584 2ECB03E370CACBC1A23C742EA71AC3DF93DB897677D961A6275A3EF26D22FCDD A055921CC78AF8D9EDC1B2378E1036D65E6FE5306CCAAF7D7121866072FCFFF7 A0B5BF80058819216A9D5615AEF43E5E3B318D30A41E753345A9CE85C02A5A06 A91259AED8CE7ECF4B41D862BA7849566C0F7832BEDB592519B37910CA95C2C7 5096F516BC22B852AF04BCC2AF0BF6D4DB39219CEF5C1A381B048A50BFC4ED60 20FBCA4D077E083B902AC4CB9AC9E283CCC41203E880D864DDE39C27883172C2 E6F8721BA33BDC6185535AC1084A6960C391D0040F800478D3F87BAA0BBA4C2E DF8C0ACEBB1E4617240F1F553DFE57204B58EB9B1172B4EF99517759C4D3E066 A36B254B55A6B64996C2D4E6338DD7F296CB3CECE7664286CBC31F5C167C6211 88334E72CF337476C3D2F48BA77956CC99A281AC5C369166E6B9ED582BB61DB1 8F567AD1F5CA881CA121E4AEFB95DE9F0B0BDF4A7F2E74D1A7777982E04E57D8 C55EFA5E09CA61C78519C70CD0086D83F9B18639ECE7539063AC2336C054CDF9 FC057BDABC3BA09FE0262BBF3A1B456ECE879FFAF5CE9CEC278763BBA3BB29F8 A5BC4A34EC9A7D63D40B03DF7D8DFFBA413212A608DDE740DEEDC018EFB5075E 8276948C305E0B51FF81FDAE1D955CF591F3A2BE6BEBB79A61489CACE82C4AAD 1A4AD2063A1D2C3FF7E9846899C9EF5DDB8404290266E2551B3CFE93504048E0 FA426AB08DE05BA3DF68A6A15D51040D22D15BD447F7FC6889BAAE8B2DAED8E6 3CF6759C92F6206743FEC153E8E628E5EE6FB09D23020FEADBA32E772B19BFCC 11DE575738DFEA40EA9E04D5C91F349D8025583E685A242DA93030A3050A0499 3F929B055B345F879C5F84907C1BACC071CCD43AFCB7600486B367329F1A91F2 97AE550B1ADF37B04A0853E1BE982DD3D10CCBAAA9979CE79282207204788737 0159B7C2E39C0398162486BD24A6008AE624A5C01EE272E7FE8CA0BEECF277B7 A1F9F79A3CF20434C1C66B75E59E4D589725604327DD3C3372D5096CD0E12F0A A8F200105345295560311C13BCD1FE75AAF95D56E4FD3A9B2E427598FFE620CE D2C879224CA1D0627CE2102676E7194E1155D229D8948664A421F548E35B5BB2 2B6369C0E2251A98A814F180A739DEA849DE522C7A716016A44392A68099000B 98EC5BE5899E3285983FD643B076F350D00F68B04ADB31CD4A374E5532E79727 C3F32A16200451B2289897800995A50E995265D49F5C753EB5E59D04CADF7032 9E5DB5013C1879B91C408723F9E98BE92C773A0B8572A50152A35D9EEC232E7A 87D2FF896911335201E07CF32E943C3E6A4AF6FDBFAE1C7261DB86332498748B D2C615660231604AF4075322A31601F85451A3E5AD5A37BC19EA635689D01EE9 59AAB81B1DD881B3F7AA63C802914D2FF0ADAB190A798AB6A778AC4D6A8E17EC 7B67817C7AFF0CC610B8C86C9B1CE5E06E5B3956D575E127416E1E85F6366E59 13C07FC4D46619CFB7D6F4697CCCF26785468937FB23DFE3037D4D813703E0A7 0B3BFFE97CA2F8FC79D5CBAB6F5F0A8D2EDB052905C5CDF617113527E2771BBF C241DB4E16CA32690275F594939E925B6CAFE7F1B3436A8EE7BEF68ABDB21D97 D86BAAB335B431975F9FF098A2D6CCEB2945F14A2B97B5902FBEE3F76B15A0D6 FE0A40968C67C726C90C4955963A110B6BCFD3D2E7E340A8FA20F528E96A0062 0A60240BED5A8797BEA6451AFACC29AAB89078FD61CA8805B1C5D276523E77F8 3C10BA06D7EE566F6A43E1E4A5387FC5A834AD76AFC2D509518C0DF026576708 9983996EE6A0B2AAC06072F7223F2F3722A04E93392A1CB4D60A4648512D515F D8A10DD920F1E6C495F9406DDEFC43BDA2E69488017BD8C5111894DA0D4874B3 531AF401117413E10C26048305093E2D964265431CF37282D6BD35FE60107971 33221833C48440967C942BD714493B8A03C169366FEC53FEBB924D915EB562F1 E4D1BE7C0774684F3B60913546A484CF7B5DD45BB4CC0A3A990991189C92B760 0A44F2D2ABF210FC9EA204F92E64BD00E3D47E4DAA295BACBAE6A7E86C306CBA F398FE7F1C5BC9794E0ED04BB6AE14A8465F6A2961A0438587D3EBEB3B72807B 20E21ECDE975D3993A48182CD753B7EB029BCF92893DB6C7406176A75FF00C0B 8C3C8563C1E4B06967600ABCAAF67E2762DCB5D527D93392322B4BC5723DCFDC A286508FF9210F6B2CE7569554877F7130BE83BA9AFD5D34FCC1CE39116C4A31 1A6DBECAB588E4C57CA7CB0453FC2616C8E14A78167CB43C4FE25AA31F3B2219 C6E1F19F6C19212FD1F4B3BC2ABB5DE25764035A408418ABD71259D975210421 A1C2AB936A4946627D1CADFAA6E242848D3D14F8829D4436BF711ED69F5F74E1 B616FDA180F6423B4A8EF341283A0380B0B1D5DC56BE1619A8F2DB227740C59C 608F27F0062E6E10D5151B8D737F318A373B9740C50A71A18A686671181BA817 8CAEF593BF223D0C60822867E0770003F57403ED5FC4BE2F4268746598A00E41 EBE04B5084C8F59D38B5F3DD8692DBB165F566AE2CDCC53618B6AEC7CD839842 1AD23BAB54A481BC6DEA90F43FE0AC147D1B729827D775F566B65EDDCED53FE3 1B1371F9BA65303803F73F157C7285D3E67432B76CC1F243E5B02C9EFD8972A4 764D41416CE6C079508D69022466BC76DA207790790CCA03D29009D6C2B93B46 24B2C1E088CFC103DD51BDF5D5A5B21129ACEC0F9844A1AACA957FF9AC20F898 D7D4B6A99280018BB284FF6DE0A870BCCEC8748B1FF1ED782ACEBB768F8AA375 117796649BA884EBAC28933CE9007401442CF4A510F79975ACA25B3F13671DC3 2DD43AA33B9F16743B6605566DCC6223DA026FEF1F98C380A80737C87F762E8F 58A594CAE681560BF7F33971A7B67BAE6CA7CF4EBEC1C4022A8221003A4E416B 5984FBB8725F7031E135753EBA218DAB4A48CEEF50701456F60360F816F5290B 153397069311445DF085A4D09C98D1E2FB87BB4353BF38BCFF9EAEE00C3F391C BDACF8F3BCE0B92F94339E5189B5AD271CB5EA184DDBFE23E93E18E362DD6DF2 F3A0805D5176A1AFFE2EDB971C0553E0B8757736E6E770D08A94C8F7E434D417 C4C3AA353E4EA4A596E72845ACF82CFB49CA91DD1D5E9713ED048D4D6C0BE667 D591D8BBA0CF2B958AB969D51B106324B2482A800D9C38B2EC8738634417F331 E5DF897105F18D9BFD372712A90FD21C1247DBFF0263E90847730915B399DF4D 89BB1FE4547FC25E694990BE285723C8F934DCF2E4C0A29284AE7586B148832E 6D755710D2519B35EF0AB80AAEF88F92DA50E3BF75E830A33FB6F9C1FA032A20 C160D8CDB714CC46C74D901E275ED25915110FF23DB737B921975E433B591923 700CC5E4CBEB5CAF1856F650A9428CC9FF826F58A4520A88009D538799C10037 BD43BA2624A568F94D9765010097F2C7333C2E13A419D610626F3A2C2DA4DAD7 7C7E98A4DC6E565F03FB89F9E4068CB875DB5E0C70A3EFFF16C5134D456CC41F 48C26DFDBE8D98A6643844D2240A2C686202BFE418116041389D38B341557BAD E41B92187C1C9EFAF74C9223879E89525C26E0D7E638542108F47F6456D034FC A02EDDF1E5B0A891B378C0F2DCA0E14AD0A7702158EB23FCEBEFF740E9E60354 A7C150A3EA55DBE0618C1138DB92C99B2BE119F45E047176E033A9B71F149141 C02AA0BDD7511226C59EDD98B7614E9B7B6595F7E3D0BDA0F1B1079EB86912EA 23EF80FAFA064B07E3CB57A17568F2C8ABE255347F4DFAE1A3D3C16D87A808B3 370AB554BAFCC494EEE4B5EE4F40DB14202FA4C2217FE57BADD808BF9F2F03C6 4913DCB787755355D5E00ACB91BBA725F77398DFB570D78FD243CDD7A8DA09A8 1F89A81DB527CE3BF2536FBD95ED547A588C8FEDFF6DAF4C6A4EA4DA9F3087D4 01021DCB18B63B31CE4599BD9B5ECA0D1815B8A306CA56B9CDBA7D661F663F0D A69C1147E304EA18ED67182F5403304C7261D0CA6B3C62E866808979F8765EE4 75EE5691147204B71A0A7FF12BE5AEF79E27CEE1A9D23ABAF40C3F0C327C8987 2D47E53EBB608641CE82C9605BF17520C4EF6389428E9E4D86139FBF2D9C94BB 3765798CAE3FE74E140752A37D8146B49C4B77F24C9E1E3198F20D52CD06153F F9CCFC1528826F71A6CB50AD900C621A330D14210167A142A02E5711575F5103 55756696B19A3AA93E88FD7308444F418B8E37D690B4E07B850F8223013E926B 1A2EB2E24DE961AD5341EA50CFD2117827BBAE2E70C74B769171146751B6CE4D A63342C4AD94A9BEEFE12EC7E26C5A53EA5B03893295F9BDC230E50B64E78B0D 6889A2B4A763AE715E2AC68E87083B82EAF63F049842ECCB283469F0C90896E7 AD936410F2A5F9E5BA570B496614CCC69BCDED39A6AEC7C157CD5D7C733E3510 2A0218820DDEEDF43ED5439309F6CF2EB8B8FA697A90886A18D9256407B3DCB2 6BFF62B317114157ED0F4BA6C4D73DA730B3B22B56CFECC7C75B1187725EF506 EEB7585C2C157A5021D7A99088C8517560BDB7BB96533D3BD41C171B9FB3B71C CF0D1DEA76BB00C4EB5DFFF3D9B6CE4E22071BFFC5F2D5F535C150D089F3763A FC136B5DBC5182EF59923585F6A0754C5F737FF6CE4AA73290A0D8DF98949ACA 140A2641DFD174BBC2A955E6F69F547C12AEF25D6149CA05429AFDF736FCA3BB 8C0D56E1512057C1F7A867B817D074E90B0D76F676C51225C1D338E6BAF8E2A4 211B3AF81850FD797A1B8166C69E37A6D7848561F6AEF5F0B5C814FD30352B07 79F9224531FEB4BEA8B04007EE5A6A9CC03BDA014A23E648CD64AEA0DA8950EB 448DE37016ED99286A27212F3550AD70D9C3F801B3BF48B5AD3D3C13F6CF12F9 A6C1796D5DC75D0B7E540A2BA940E9CAF333CFC49FE742C86EF722C51D66D7DB A55ED3F050F6B53325801C3547CD47F297FE1B48D82C297ACF70C2E0D0678BFB 3AB266D578C4F5E3CAE9DF0642C172A03921C72EBCB0389079E7F1CF21318670 DBD84FCC849C82D1197B6BF89B2436370F8A345C506B6CD28CF78CFF1F5790B2 7E0206734FBE227441BFCE6C995D1E7E27A5E275D7097F958C50C88DB8012B9F 82927CE799C4253707236A1AF0A4F41ECE337850AC2B686DD6D8CF61E3B1BB03 DA471453F98EAE1C15E45079EF39401E836F39A959B7C5E68684D299AB16A141 78FE467D75860CCED51B1E97A5055160C5D61F2078D0A737CDDEE378480313AA 8C932DD0AE20098EEE5CDEC9BF3A075FEFC4879DABEB3A39723B5C0DF5466894 98CAAE910905DB540D8F7A8B6DF3A19B701836B16F6DB953A8DD8FC81365A7FB C526694A06BCE956CFEEC26219AA46BD3B06F0E9234E10CF32979E1A73D158C3 8A16CBA9CCBDD264437FAF502F9012B49EF89D9CEB45BC4E44A45929E19CDF5C B3AA750DF5C489C1863E7A32EC355454018CD4A01F0DADFC5D052EEE231CAEEF 9883DFEA40A4273C59FFEE5C46519198F45E65A73839FD56EC454553D843EF3B DD9556258961447EFD39FDB7066FEC55996843D7FE1B5D1B8EA3732BF810ADCD FFF113B77246956A9A389F083822982900E39026A52CA67C867C36709904F711 74C7C29B171F08E8C92DD5B7FC48A5D1CB6C91BA42AE315279888BC667FFF7F6 FC87B245FD0FD257144A17777C552AF6DBA15C279E194A3A9A1ACAFCAA868B5A 6BD5B3F1A196BDC55556D7607E43DAF4666842670A65214E8823E3D218AD7256 C12090FBB50730AD0984BDDD4358DAF1B0195F5F37769586EF1CAA3345A7D24A 976A96925843407E2CC38A82B7CF0F6C934D574B0648102082EAC5C56D09148A 88BC8EFC38E5A0644B08AD8A88FAB1DEABD2FC5BE8D5BE4EDD2849EED5DC60A3 BDEAC4E37D8952E0BF76152927389B77E26D12E9544817D274A49E252B87E308 68EE20B2D7A015A7A2B5B75A66A7981A30F706EAEC478B0D4C65FC823C42490B 69CFA194C7F888F2EA3036275CC37010D2F892F06519B0B81750BBE4AD026D4A 35B7AC5E824360F15637BE50FAAE48192B4482A0C3AC921DECDBF024A2A49CFD 81A2D70754DB9A397F8BB9CA0614F22E702F46F27652F3F31B4845BEE1CECA28 14261115E8A16D2FB2CA22CBDE27996A91750C54CAA3DE8B4CB4A357192925F4 608E25E4E12B68E2548F83599764ABFBC02F6523BD886B4412843EA658A11D2B 4870BCD1562629CE9FBA485E7390802F6DA44E505E91423B7555AB347BB77EE6 287D56D872F30DD23E46EC0D8934CE471C1119BC5E7AF6E31EAD17801A2F5AB4 36494C849518745B77A42C1D15D322C7331D16CF19BD10288D81F2F37211EF63 20842731D0F54EDC2402B9F6101685F9672B52EA006BF9291A704D30BDBB9BA2 256F8D67FBB67BE7485599CC319AD72426EF70D97DE86FD1F10CF35F7FEB4A3C 1B717D94E37D60323962A9465EE81F018B0208A93A4297A74D27CBB8355DF8C2 59083A453DD4E97AE9337FCDDDA6B852E6816F07F3E2C1E38CF457F9D6F2B0BA 723B6BAF87BE9A79B1D9665787AE2C9EAF8CE86267630149DAC314BD08EC1386 6ACE3CF273B19CBA7A04065BA225AF07E40DBDEE79D602FC5A18B15210BD9F74 60D3EBCE1974500E5FE577438BABB45C5A71D639D1E1508D781BB62C92B604E4 B46100330E95139FFF2C57D87488A6A9855CAC5279DC31BFE827AF872997C654 07D1834DA7FE0ECC244EA9EAD829D9470D429065C7558AAD1ED7DD60ACB10CDF 16D0D178AC5D7A5E587325D219CACD056C4149FFA792228D5D251BBA6F29DF48 852B747E4C51C67712DB9C9C5AEE906C688F8FB3513366156D2CAFBE59999FCA 055BBDBB270B1243334229D37EB369AC8F9723EA7EC65D9CDFB39A340AD4A879 67243143BD6BBB03A98B4D3062D3D185C5F7A905A453BB760C928AE36B35D76A 069171FCB8C45454A6ABACE2616264FA61822DC54AD4962ED5225420156B3A7D 6BCC9328E0D18E8B685CF60848A29738B29CE90B03AE8BAA58451D4E3BA68AD5 6B986F10F0374E48EAA7576FF48612C2E4F7233D7EC4A2AAB92E057313F76EDF E55993E18037F9FDFC5B3F752DFB615D160A86E708DDAC8970CA3E7D6BEC768F 5C71162E89FBA0B45E262D41F0BC2041550C83B8BFDB0AFDB38FB51B53BA9B00 5A316CCEF7B60AB6E8032FB3ED7A96D727B01DB184EC4B8FBD3718A3EA4FDF0E 55878C8399564E843A144F69504F1F3C4E9D247B61A9BA8B5E57473E78839EC4 834250ACCF0A53AE0C4AE83A12110BBF569252F26249377A8F146152606F6377 C2ABFA72EBA43113607B772B894C03EBC382CBD4A30017E6B3FC8F6033664258 A913E0CB71A35EE1C2A4CCEB073BCACDAB2AEB2DBD186DC5CD0BD044EA841458 15C8D09D7D8F957DAB2A96FB504082D1F649AC26B55B4C44182E997FE925055F 97B6162D5252D33D68069676E1283FC40446E70F728F9780998C28D78BD8FFD2 C2CE2E2A5EC559EC18C57709DFB3154B64F7DCE2661216A29B00D7A3C24BB5AA 828AE338462325A12190F2D53117232893E9F8E21E49CABA21EBF62C4E241DE6 C0CDA41B9BB25B7B0524D7B63FA82257C6B866895E2F9167D276AE8A40164EA7 4AC4F52C11F2721A12C07C7E6D7B69A9E78980452BD3B604FEFB899B9A80D531 853B0C68B6A588D9B1094AB1DD2849114C2644EDD08B9843442EF01D344D5B0B 8EA4FE351C818FBE98D1B4ADA3AD360C00810974370DF559F1B2902EA7A0A020 EA08855E0D61006B273A600360F682D1844071581A6CB1C1BC5C526B7BB7ECB3 D683ACE9DFDB1754EAE38CC8401284C6E0966BABDDD5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (eprint.dvi) @start /Fa 152[32 32 51[42 28[48 21[{ TeXbbad153fEncoding ReEncodeFont } 4 49.8132 /CMSY6 rf /Fb 129[39 3[39 39 39 39 39 39 39 39 39 1[39 39 39 39 39 39 1[39 39 39 39 39 39 39 39 39 38[39 2[39 4[39 39 1[39 39 39 45[{ TeX09fbbfacEncoding ReEncodeFont }32 74.7198 /CMTT9 rf /Fc 140[20 16[27 25 97[{ TeXf7b6d320Encoding ReEncodeFont }3 49.8132 /CMSS8 rf /Fd 184[52 41 44 69[{}3 66.4176 /MSBM7 rf /Fe 138[56 2[55 3[56 10[54 14[71 84[{ TeX0ef0afcaEncoding ReEncodeFont }5 90.9091 /CMCSC10 rf /Ff 170[69 67 11[72 6[67 65[{ TeXf7b6d320Encoding ReEncodeFont }4 90.9091 /CMSSBX10 rf /Fg 143[91 23[131 7[96 58[48 48 67 67 5[30 10[42 42{}10 90.9091 /CMEX10 rf /Fh 138[47 2[31 3[47 10[40 13[63 62 1[59 1[58 7[64 1[52 4[61 65[{ TeXf7b6d320Encoding ReEncodeFont }11 90.9091 /CMSSI10 rf /Fi 141[46 2[54 59 86 8[54 2[54 51[38 45[{ TeX74afc74cEncoding ReEncodeFont }7 90.9091 /CMBXTI10 rf /Fj 143[59 5[20 27 27 35 35 16[44 1[43 12[50 1[55 17[47 71 19 15[71 13[55 16[20 55{ TeXbbad153fEncoding ReEncodeFont }17 66.4176 /CMSY8 rf /Fk 134[33 2[33 36 1[27 24 1[36 1[36 56 1[34 1[17 36 35 22 31 36 31 36 34 10[47 48 48 39 10[50 6[47 65[{ TeXf7b6d320Encoding ReEncodeFont }24 66.4176 /CMSS8 rf /Fl 138[61 61 3[76 1[45 3[25 35 35 45 45 7[61 2[61 1[61 65 2[57 1[55 10[77 54 65 1[70 2[73 1[71 4[61 3[0 3[61 91 16[91 3[91 2[71 71 2[71 71 1[71 71 2[45 7[71 3[71 25 71{ TeXbbad153fEncoding ReEncodeFont }38 90.9091 /CMSY10 rf /Fm 249[80 6[{ TeXaae443f0Encoding ReEncodeFont }1 90.9091 /CMMIB10 rf /Fn 134[32 35 6[28 32 1[38 54 1[33 6[32 3[26 13[46 6[51 7[44 46 46 1[32 2[48 19 37[37 8[35 12[{ TeXaae443f0Encoding ReEncodeFont }19 49.8132 /CMMI6 rf /Fo 165[50 18[58 46 50 69[{}4 74.7198 /MSBM10 rf /Fp 144[38 2[21 2[21 3[34 1[34 43 31[54 58 65[{ TeXf7b6d320Encoding ReEncodeFont }8 74.7198 /CMSL9 rf /Fq 174[61 55 31[41 48[{ TeXf7b6d320Encoding ReEncodeFont }3 66.4176 /CMBX8 rf /Fr 249[88 6[{ TeXaae443f0Encoding ReEncodeFont }1 99.6264 /CMMIB10 rf /Fs 134[42 42 1[42 47 33 35 31 1[47 45 47 72 22 44 1[22 1[45 28 40 47 40 1[44 7[61 2[61 63 62 51 59 1[58 1[64 80 49 63 1[25 64 61 52 54 66 58 61 61 65[{ TeXf7b6d320Encoding ReEncodeFont }40 90.9091 /CMSS10 rf /Ft 133[33 35 40 1[34 2[33 1[32 36 1[43 62 1[37 29 24 1[34 34 33 36 1[30 37 29 7[58 4[43 53 1[45 4[60 5[52 2[53 53 1[35 1[35 1[20 20 30[40 5[41 9[45 11[{ TeXaae443f0Encoding ReEncodeFont }34 66.4176 /CMMI8 rf /Fu 165[61 18[71 56 61 69[{}4 90.9091 /MSBM10 rf /Fv 131[48 2[48 1[48 48 1[48 48 48 1[48 48 1[48 48 2[48 48 48 48 48 48 48 48 48 2[48 4[48 5[48 4[48 2[48 5[48 48 6[48 2[48 10[48 48 48 48 2[48 48 40[{ TeX09fbbfacEncoding ReEncodeFont } 35 90.9091 /CMTT10 rf /Fw 133[42 45 52 3[33 43 1[41 46 44 55 80 1[47 37 31 52 43 45 42 47 39 39 48 38 5[62 53 75 1[53 62 53 56 69 1[58 69 3[77 2[76 1[58 67 75 1[69 68 2[71 45 71 25 25 23[42 6[52 4[55 53 52 5[40 47 51 58 4[71 76 5[{ TeXaae443f0Encoding ReEncodeFont }55 90.9091 /CMMI10 rf /Fx 134[44 42 60 42 49 30 37 38 42 46 46 51 74 23 42 28 28 46 42 28 42 46 42 42 46 3[28 1[28 3[91 2[65 51 66 1[62 1[68 82 57 2[35 68 1[59 62 69 65 1[68 6[28 46 46 1[46 1[46 2[46 2[28 33 28 2[37 37 25[80 1[51 56 11[{ TeX74afc74cEncoding ReEncodeFont }56 90.9091 /CMTI10 rf /Fy 134[59 59 81 59 62 44 44 46 1[62 56 62 93 31 59 1[31 62 56 34 51 62 50 62 54 11[86 78 62 84 1[77 1[88 106 1[88 58 42 88 88 70 74 86 81 80 85 8[56 1[56 56 56 56 56 56 56 2[37 5[31 24[93 1[62 12[{ TeXf7b6d320Encoding ReEncodeFont }53 99.6264 /CMBX12 rf /Fz 132[52 46 55 55 76 55 58 41 41 43 55 58 52 58 87 29 55 32 29 58 52 32 48 58 46 58 51 3[29 1[29 3[108 1[80 73 58 78 79 71 79 82 99 63 82 1[40 82 82 66 69 80 76 74 79 6[29 52 52 52 52 52 52 52 52 52 52 1[29 35 29 2[41 41 29 24[87 1[58 12[{ TeXf7b6d320Encoding ReEncodeFont }69 90.9091 /CMBX10 rf /FA 132[39 1[37 35 51 35 41 25 31 32 1[39 39 43 63 20 2[24 39 35 24 35 39 35 35 39 11[57 55 43 56 1[52 59 57 69 2[40 30 57 59 50 52 58 55 54 57 7[39 39 39 39 1[39 39 39 39 39 1[24 27 5[24 19[39 19[{ TeX74afc74cEncoding ReEncodeFont }54 74.7198 /CMTI9 rf /FB 134[38 44 4[36 1[34 5[40 3[37 2[40 10[45 63 12[65 15[21 21 30[44 4[46 9[43 5[60 6[{ TeXaae443f0Encoding ReEncodeFont }16 74.7198 /CMMI9 rf /FC 139[34 35 36 8[25 1[44 3[39 49 43 14[66 66 60 9[56 4[67 14[44 44 2[25 46[{ TeXf7b6d320Encoding ReEncodeFont }16 74.7198 /CMBX9 rf /FD 150[30 30 38 38 68[77 77 30[21 60{ TeXbbad153fEncoding ReEncodeFont }8 74.7198 /CMSY9 rf /FE 134[35 35 1[35 40 28 29 26 40 40 38 40 61 18 38 1[18 40 38 23 34 40 34 40 37 4[38 6[53 52 43 50 1[49 57 1[67 1[53 1[21 54 51 44 1[56 49 1[51 51 14[38 38 1[21 26 21 9[38 34[{ TeXf7b6d320Encoding ReEncodeFont }46 74.7198 /CMSS9 rf /FF 128[38 38 2[38 34 41 41 55 41 43 30 30 30 41 43 38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 3[21 1[21 47 58 1[79 58 58 55 43 57 1[52 60 58 70 48 60 39 28 58 60 50 52 59 55 54 58 3[60 1[21 21 38 38 38 38 38 38 38 38 38 38 38 21 26 21 2[30 30 21 15[58 3[38 4[64 43 43 12[{ TeXf7b6d320Encoding ReEncodeFont }80 74.7198 /CMR9 rf /FG 129[30 74[30 30 30 30 48[{ TeXf7b6d320Encoding ReEncodeFont }5 49.8132 /CMR6 rf /FH 129[35 66[20 3[35 35 35 35 35 35 35 35 4[55 1[27 27 40[{ TeXf7b6d320Encoding ReEncodeFont }13 66.4176 /CMR8 rf /FI 129[45 1[91 45 40 48 48 66 48 51 35 36 36 48 51 45 51 76 25 48 28 25 51 45 28 40 51 40 51 45 3[25 45 25 56 68 1[93 68 68 66 51 67 1[62 71 68 83 57 71 47 33 68 71 59 62 69 66 64 68 3[71 1[25 25 45 45 45 45 45 45 45 45 45 45 45 25 30 25 71 1[35 35 25 1[76 1[76 45 25 18[76 51 51 53 11[{ TeXf7b6d320Encoding ReEncodeFont }85 90.9091 /CMR10 rf /FJ 134[71 71 1[71 1[52 53 55 2[67 75 112 3[37 3[61 75 60 1[65 14[100 6[105 5[88 103 68[{ TeXf7b6d320Encoding ReEncodeFont }18 119.552 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 645 -83 a FJ(Key)46 b(Deriv)-7 b(ation)46 b(and)f(Randomness)g(Extraction)265 220 y FI(Olivier)31 b(Chev)-5 b(assut)969 187 y FH(1)1008 220 y FI(,)31 b(Pierre-Alain)g(F)-8 b(ouque)1864 187 y FH(2)1904 220 y FI(,)31 b(Pierric)m(k)g(Gaudry)2602 187 y FH(3)2641 220 y FI(,)f(and)g(Da)m(vid)h(P)m(oin)m(tc)m(hev)-5 b(al)3592 187 y FH(2)622 363 y FG(1)695 394 y FF(La)n(wrence)27 b(Berk)n(eley)f(National)g(Lab.)g({)g(Berk)n(eley)-6 b(,)26 b(CA,)g(USA)e({)i FE(OChevassut@lbl.gov)296 454 y FG(2)369 486 y FF(CNRS-)615 467 y(\023)608 486 y(Ecole)g(normale)h (sup)n(\023)-36 b(erieure)25 b({)h(P)n(aris,)h(F)-6 b(rance)26 b({)g FD(f)p FE(Pierre-Alain.F)n(ouque,David.P)n(ointcheval)p FD(g)p FE(@ens.fr)640 545 y FG(3)713 577 y FF(CNRS-)959 558 y(\023)952 577 y(Ecole)g(p)r(olytec)n(hnique)e({)i(P)n(alaiseau,)i (F)-6 b(rance)26 b({)g FE(gaudry@lix.p)r(olytechnique.fr)178 863 y FC(Abstract.)47 b FF(Key)32 b(deriv)l(ation)h(refers)h(to)f(the)g (pro)r(cess)h(b)n(y)e(whic)n(h)h(an)g(agreed)h(up)r(on)e(large)j (random)e(n)n(um)n(b)r(er,)f(often)178 954 y(named)24 b(master)h(secret,)f(is)h(used)e(to)h(deriv)n(e)g(k)n(eys)f(to)h (encrypt)f(and)h(authen)n(ticate)g(data.)g(Practitioners)i(and)d (standard-)178 1045 y(ization)30 b(b)r(o)r(dies)f(ha)n(v)n(e)e(usually) i(used)f(the)g(random)g(oracle)i(mo)r(del)e(to)h(get)f(k)n(ey)g (material)h(from)h(a)e(Di\016e-Hellman)h(k)n(ey)178 1137 y(exc)n(hange.)i(Ho)n(w)n(ev)n(er,)f(pro)r(ofs)h(in)f(the)f(standard)h (mo)r(del)h(require)f(randomness)g(extractors)h(to)f(formally)h (extract)f(the)178 1228 y(en)n(trop)n(y)25 b(of)h(the)g(random)f (master)i(secret)f(in)n(to)g(a)g(seed)g(prior)g(to)g(deriv)n(e)f(other) h(k)n(eys.)178 1321 y(This)k(pap)r(er)g(\014rst)f(deals)h(with)g(the)f (proto)r(col)i FB(\006)1615 1329 y FG(0)1649 1321 y FF(,)f(in)f(whic)n (h)h(the)f(k)n(ey)f(deriv)l(ation)i(phase)f(is)h(\(delib)r(erately\))g (omitted,)178 1412 y(and)21 b(securit)n(y)f(inaccuracies)i(in)e(the)h (analysis)g(and)f(design)h(of)h(the)e(In)n(ternet)f(Key)h(Exc)n(hange)h (\(IKE)f(v)n(ersion)g(1\))h(proto)r(col,)178 1503 y(corrected)26 b(in)f(IKEv2.)g(They)f(do)h(not)g(endanger)g(the)g(practical)h(use)f (of)h(IKEv1,)f(since)h(the)e(securit)n(y)h(could)g(b)r(e)g(pro)n(v)n (ed,)178 1595 y(at)j(least,)g(in)f(the)g(random)g(oracle)h(mo)r(del.)g (Ho)n(w)n(ev)n(er,)g(in)f(the)f(standard)h(mo)r(del,)h(there)f(is)h (not)f(y)n(et)f(an)n(y)h(formal)h(global)178 1686 y(securit)n(y)20 b(pro)r(of,)h(but)e(just)g(separated)i(analyses)f(whic)n(h)g(do)g(not)f (\014t)g(together)h(w)n(ell.)i(The)d(\014rst)h(simpli\014cation)h(is)f (common)178 1777 y(in)33 b(the)f(theoretical)i(securit)n(y)e(analysis)i (of)f(sev)n(eral)g(k)n(ey)f(exc)n(hange)g(proto)r(cols,)j(whereas)e (the)f(k)n(ey)g(deriv)l(ation)g(phase)178 1869 y(is)37 b(a)f(crucial)h(step)e(for)i(theoretical)g(reasons,)g(but)e(also)j (practical)f(purp)r(ose,)f(and)f(requires)h(careful)h(analysis.)g(The) 178 1960 y(second)24 b(problem)f(is)h(a)g(gap)f(b)r(et)n(w)n(een)h(the) e(recen)n(t)i(theoretical)g(analysis)h(of)f(HMA)n(C)f(as)h(a)f(go)r(o)r (d)h(randomness)g(extractor)178 2051 y(\(functions)31 b(k)n(ey)n(ed)e(with)h(public)g(but)f(random)h(elemen)n(ts\))h(and)e (its)i(practical)g(use)f(in)g(IKEv1)g(\(the)g(k)n(ey)f(ma)n(y)h(not)g (b)r(e)178 2143 y(totally)c(random,)g(b)r(ecause)f(of)h(the)f(lac)n(k)g (of)h(clear)g(authen)n(tication)g(of)g(the)e(nonces\).)i(Since)f(the)g (latter)g(problem)h(comes)178 2234 y(from)37 b(the)f(probabilistic)i (prop)r(ert)n(y)e(of)h(this)f(extractor,)h(w)n(e)g(thereafter)g(review) g(some)g FA(deterministic)k FF(randomness)178 2325 y(extractors)31 b(and)e(suggest)i(the)e FA('Twist-A)n(Ugmente)l(d')40 b FF(tec)n(hnique,)29 b(a)i(new)e(extraction)i(metho)r(d)e(quite)g(w)n (ell-suited)i(for)178 2417 y(Di\016e-Hellman-lik)n(e)26 b(scenarios.)-58 2627 y Fz(Key)35 b(W)-9 b(ords:)31 b FI(Randomness)f(extractors,)i(Key)e(deriv)-5 b(ation,)32 b(Elliptic)f(curv)m(e)-58 2900 y Fy(1)112 b(In)m(tro)s(duction)-58 3119 y FI(Key)35 b(exc)m(hange)h(is)f(an)g(imp)s(ortan)m(t)g(problem)f (in)h(practice)h(and)e(sev)m(eral)j(sc)m(hemes)e(ha)m(v)m(e)h(b)s(een)e (designed)h(to)g(solv)m(e)-58 3232 y(it)c(since)f(the)g(seminal)h(w)m (ork)f(of)g(Di\016e)h(and)f(Hellman)h([20].)g(Recen)m(tly)-8 b(,)33 b(di\013eren)m(t)d(w)m(orks)g(ha)m(v)m(e)h(b)s(een)f(published)e (in)-58 3345 y(order)23 b(to)i(analyze)g(the)e(securit)m(y)i(of)f (those)g(sc)m(hemes)g(in)f(v)-5 b(arious)24 b(settings)h(\(passw)m (ord,)e(public-k)m(ey)-8 b(,)25 b(h)m(ybrid)d(setting\))-58 3458 y(and)k(securit)m(y)h(mo)s(dels)g(\(random)f(oracle,)i(common)f (reference)g(string,)g(standard)f(mo)s(del\).)h(But)g(for)f(sev)m(eral) i(y)m(ears,)-58 3571 y(e\016ciency)d(and)f(securit)m(y)h(in)f(the)h (standard)e(mo)s(del)h(are)h(one)g(of)f(the)h(main)f(goals)h(to)h(ac)m (hiev)m(e)g(in)e(cryptograph)m(y)-8 b(.)25 b(The)-58 3684 y(most)32 b(widely)g(used)f(net)m(w)m(ork)h(securit)m(y)h(proto)s (cols)f(no)m(w)m(ada)m(ys)h(are)f(the)g(TLS)f([47],)i(a.k.a)g(SSL,)e (and)g(the)g(In)m(ternet)-58 3797 y(Key)24 b(Exc)m(hange)g(\(IKE\))g (proto)s(cols)g([28,)16 b(35])25 b(from)e(the)h(IPSec)f(standard)g(of)g (the)h(IETF.)f(Sev)m(eral)i(pap)s(ers)d([18,)16 b(19,)h(37,)-58 3910 y(25,)f(22])31 b(ha)m(v)m(e)g(studied)e(the)h(securit)m(y)h(of)f (the)g(IKE)f(sc)m(hemes)h(and)f(prop)s(osed)g(a)h(securit)m(y)g (analysis)g(in)g(the)g Fx(standar)-5 b(d)-58 4023 y(mo)g(del)p FI(.)36 b(Ho)m(w)m(ev)m(er,)h(these)e(pap)s(ers)e(do)h(not)h(precisely) f(consider)h(the)f(proto)s(col)h(but)f(discuss)g(on)g(either)h (simpli\014ed)-58 4136 y(descriptions)25 b(of)h(some)f(parts,)g(or)h (isolated)g(primitiv)m(es,)h(whic)m(h)d(do)i(not)f Fx(rigor)-5 b(ously)35 b FI(matc)m(h)26 b(the)g(proto)s(col)g(designed)-58 4248 y(b)m(y)31 b(the)g(IETF.)g(Therefore,)h(there)f(can)g(b)s(e)g (some)g(gaps)h(b)s(et)m(w)m(een)f(the)h(formal)f(securit)m(y)h (analysis)g(and)e(the)h(actual)-58 4361 y(securit)m(y)g(of)g(the)f (proto)s(col.)-58 4631 y Fz(1.1)105 b(Motiv)-6 b(ation)-58 4818 y(The)35 b(Key)g(Deriv)-6 b(ation)36 b(Problem.)47 b FI(Di\016e-Hellman)33 b(\(DH\))f(based)e(k)m(ey)i(exc)m(hanges)g (establish)f(a)g(secure)g(com-)-58 4930 y(m)m(unication)38 b(c)m(hannel)f(b)s(et)m(w)m(een)g(t)m(w)m(o)h(parties)f(b)m(y)f (securely)h(negotiating)i(a)e(large)h(random)d(elemen)m(t)k(in)d(a)h (giv)m(en)-58 5043 y(cyclic)32 b(group,)e(called)h(master)f(secret.)i (Then,)d(this)h(secret)h(is)f(used)f(to)i(deriv)m(e)g(k)m(eys)g(for)e (encrypting)h(and)g(authen-)-58 5156 y(ticating)36 b(data.)e(These)f(k) m(eys)h(m)m(ust)g(b)s(e)e(bit-strings)i(of)g(some)g(sp)s(eci\014c)f (length)h(uniformly)e(distributed)h(and)g(used)-58 5269 y(as)39 b(input)f(parameters)h(to)g(symmetric)g(ciphers)f(\(for)h(priv) -5 b(acy\),)39 b(message)h(authen)m(tication)g(co)s(des)f(\(for)g (authen-)-58 5382 y(tication\),)h(and)c(pseudo-random)g(functions)h (\(for)g(expansion)g(of)g(a)h(seed)f(in)m(to)h(a)g(longer)f (bit-string\).)i(Ho)m(w)m(ev)m(er,)-58 5495 y(they)31 b(cannot)h(b)s(e)f(initialized)i(with)e(the)g Fx(simple)39 b FI(bit-string)31 b(enco)s(ding)g(of)h(the)f(master)g(secret.)i(Ev)m (en)e(though)g(this)p eop end %%Page: 2 2 TeXDict begin 2 1 bop -58 -83 a FI(secret)39 b(is)g(indistinguishable)e (from)h(a)h(random)e(elemen)m(t)j(in)e(the)g(cyclic)i(group)d(under)g (some)i(classical)h(compu-)-58 30 y(tational)f(assumptions,)e(suc)m(h)g (as)g(the)h(Decisional)h(Di\016e-Hellman)g(assumption)e(\(DDH\),)i(its) e(enco)s(ding)g(is)h(not)-58 143 y(indistinguishable)30 b(from)g(a)h(random)f(bit-string)h(with)f(a)h(uniform)e(distribution.)h (The)g(en)m(trop)m(y)h(of)g(the)f(bit-string)-58 256 y(enco)s(ded)37 b(secret)h(is)f(indeed)f(high)h(but)f(not)h(high)g (enough)g(to)h(immediately)g(obtain)f(an)g Fx(almost)i FI(uniformly)d(dis-)-58 369 y(tributed)c(random)g(bit-string:)h (pseudo-en)m(trop)m(y)g(generators)h(are)f(not)g(pseudo-random)f (generators)h(ev)m(en)h(when)-58 482 y(only)d(considering)f(the)h(prop) s(ert)m(y)e(of)i(computational)h(indistinguishabilit)m(y)f([29].)83 598 y(Most)i(of)f(the)g(cryptographic)g(proto)s(cols)g(do)g(not)g(tak)m (e)h(in)m(to)g(accoun)m(t)g(this)f(practical)h(problem)e(since)h(it)h (only)-58 710 y(app)s(ears)44 b(during)f(the)h(concrete)i(implemen)m (tation.)g(Cryptographers)d(indeed)h(use)g(\\elemen)m(ts)i(in)e(sets")h (when)-58 823 y(designing)21 b(their)g(algorithms)h(while)f (standardization)g(b)s(o)s(dies)f(represen)m(t)h(and)f(enco)s(de)h (these)h(elemen)m(ts.)g(Engineers)-58 936 y(are)g(left)g(clueless)g (when)f(elemen)m(ts)i(in)e(a)h(giv)m(en)g(set)g(do)f(not)h(necessarily) g(admit)g(a)g(compact)h(enco)s(ding)e(|in)g(bijection)-58 1049 y(with)j(a)g(set)h(of)f Fw(`)p FI(-bit)g(strings|)g(ev)m(en)g(for) g(a)g(w)m(ell-c)m(hosen)i Fw(`)p FI(.)e(Practitioners)i(ha)m(v)m(e)f (no)f(c)m(hoice)h(but)f(to)g(mak)m(e)h(educated)-58 1162 y(guesses)f(on)f(whic)m(h)f(enco)s(ding)i(to)f(use)g(and)g(so,)g(ma)m (y)h(in)m(tro)s(duce)f(securit)m(y)h(breac)m(hes.)g(This)e(is)i(the)f (case)h(of)f(the)h(Di\016e-)-58 1275 y(Hellman)37 b(v)m(ersion)f(of)g (the)f(SSL)g(proto)s(col)h([47])h(where)f(the)g(binary)e(enco)s(ding)i (of)g(the)g(random)f(elemen)m(t)i(is)f(used)-58 1388 y(as)g(it.)h(This)e(practice)j(can)e(not)g(b)s(e)g(pro)m(v)m(ed)g (secure)g(in)g(the)g(standard)f(mo)s(del,)h(although)h(the)f(proto)s (col)h(ma)m(y)f(b)s(e)-58 1501 y(secure)28 b(in)g(the)g(random)g (oracle)h(mo)s(del.)g(Ho)m(w)m(ev)m(er,)h(nob)s(o)s(dy)d(claims)i(an)m (y)f(securit)m(y)h(pro)s(of)e(despite)i(the)f(widely)g(use)-58 1614 y(of)j(SSL.)e(See)i(also)g([14])h(for)e(a)h(similar)f(remark)g(on) h(the)f(ElGamal)i(encryption)e(sc)m(heme.)-58 1891 y Fz(The)43 b(Case)h(of)f(IKE.)55 b FI(More)39 b(in)m(terestingly)-8 b(,)40 b(IKE)e(raises)g(this)g(problem)f(to)s(o.)i(It)f(can)h(b)s(e)e (emphasized)h(in)g(the)-58 2004 y(securit)m(y)44 b(analysis)f(of)f(the) h(basic)g(SIGMA)g(proto)s(col)h Fw(\006)1961 2018 y FH(0)2043 2004 y FI(pro)m(vided)e(b)m(y)g(Canetti)i(and)e(Kra)m(w)m(czyk)i([36,) 16 b(19,)g(37].)-58 2117 y(SIGMA)31 b(and)f(IKE)h(are)g(w)m (ell-designed)h(proto)s(cols)g(with)e(man)m(y)h(nice)h(prop)s(erties)e (and)g(all)i(the)f(previous)f(analysis)-58 2230 y(justify)e(the)g (whole)g(design.)g(In)g(particular,)g(IKE)g(explicitly)h(deals)g(with)f (the)g(extraction)i(issue)d(via)i(a)g(mec)m(hanism)-58 2343 y(analyzed)37 b(in)f([22].)h(Ho)m(w)m(ev)m(er,)i(there)d(is)g (some)h(inaccuracies)g(when)e(w)m(e)i(w)m(an)m(t)g(to)f(go)h(through)f (the)g(details.)h(The)-58 2455 y(authors)31 b([19])i(w)m(ere)f (de\014nitely)f(a)m(w)m(are)i(of)f(the)g(k)m(ey)g(deriv)-5 b(ation)32 b(problem)f(at)h(the)g(writing)f(time)h(for)f(sev)m(eral)i (y)m(ears)-58 2568 y(ago)g(but)d(they)i(c)m(hose)g(to)g(eliminate)h (the)e Fx(mandatory)43 b FI(k)m(ey)32 b(deriv)-5 b(ation)32 b(phase)e(in)h(this)h(basic)f(v)m(ersion)h(of)f(SIGMA,)-58 2681 y(without)40 b(an)m(y)h(justi\014cation)g(\(ma)m(yb)s(e)f(a)h (simpler)f(securit)m(y)h(pro)s(of)7 b(\).)40 b(They)g(just)f(referred)h (to)h(it)g(in)f(some)g(notes)-58 2794 y(and)e(section)i(later)f(in)f ([19],)i(and)e(in)g(the)h(last)g(app)s(endix)e(of)h(the)h(full)f(v)m (ersion)h(of)g(the)f(companion)h(pap)s(er)e([37].)-58 2907 y(Nev)m(ertheless,)27 b(some)e(sen)m(tences)h(of)f([19])i(are,)e (to)h(sa)m(y)g(the)f(least,)h Fx(ambiguous)33 b FI(ab)s(out)25 b(the)g(k)m(ey)h(deriv)-5 b(ation)25 b(problem,)-58 3020 y(whic)m(h)35 b(also)h(arises)g(in)e(the)i(securit)m(y)g(analysis,)g (ev)m(en)f(at)h(a)g(theoretical)h(lev)m(el,)h(and)c(not)h(only)h(for)f (practitioners.)-58 3133 y(They)d(could)h(lead)g(to)g Fx(annoying)41 b FI(misin)m(terpretation.)35 b(F)-8 b(urthermore,)32 b(the)h(same)g(omission)g(app)s(eared)e(elsewhere)-58 3246 y(in)i(the)h(literature,)h(and)e(namely)h(in)f(the)h(JFK)f(proto)s (col)h([2,)16 b(3].)35 b(Both)f(of)g(these)g(proto)s(cols)g(are)g(the)g (basis)f(of)h(the)-58 3359 y(second)d(v)m(ersion)f(of)h(IKE)f([35],)i (ho)m(w)m(ev)m(er)f(the)g(latter)h(a)m(v)m(oids)f(all)h(the)e(problems) g(w)m(e)h(men)m(tion)g(here.)83 3475 y(Since)c(the)h(k)m(ey)g(deriv)-5 b(ation)28 b(problem)e(is)i(a)f(v)m(ery)h(imp)s(ortan)m(t)f(step,)h(w)m (e)f(c)m(ho)s(ose)i(to)f(dra)m(w)e(atten)m(tion)k(to)e(it.)g(Ev)m(en) -58 3587 y(if)33 b(kno)m(wn)f(solutions)h(exist,)h(it)f(is)g(still)h(p) s(ossible)e(to)i(in)m(tro)s(duce)e(securit)m(y)i(breac)m(hes,)f(as)g (it)h(is)f(the)g(case)g(in)g(IKEv1.)-58 3700 y(These)c(breac)m(hes)h (do)g(not)g(lead)g(to)g(practical)h(attac)m(ks)h(on)d(the)h(proto)s (col,)h(but)d(they)i(m)m(ust)f(b)s(e)g(tak)m(en)i(in)m(to)f(accoun)m(t) -58 3813 y(in)g(a)h(theoretical)i(viewp)s(oin)m(t.)-58 4091 y Fz(1.2)105 b(Randomness)36 b(Extraction)f(and)g(Key)g(Deriv)-6 b(ation)35 b(Phase)-58 4285 y FI(The)g(proto)s(col)h Fw(\006)566 4299 y FH(0)641 4285 y FI(in)f([19])i(pro)m(vides)e(the)h (t)m(w)m(o)h(en)m(tities)g(with)e(a)h(master)f(secret)i(\(a)f (Di\016e-Hellman)h(v)-5 b(alue\))36 b(and)-58 4398 y(uses)k(it)h(as)g (a)g(k)m(ey)g(to)h(a)e(pseudo-random)g(function)g(\(PRF\).)i(As)e(w)m (e)h(previously)f(said,)h(ev)m(en)g(if)g(this)f(secret)i(is)-58 4511 y(indistinguishable)d(from)g(a)h(truly)f(random)g(elemen)m(t)i(in) e(a)h(group)f(under)f(the)h(DDH)i(assumption,)e(it)h(is)g(not)f(a)-58 4623 y(random)32 b(bit-string)g(uniformly)g(distributed)f(in)h(the)g(k) m(ey)h(space)g(of)g(the)f(PRF.)h(Suc)m(h)e(a)i(description)f(of)h(IKE)e (is)h(a)-58 4736 y(simpli\014ed)26 b(one,)g(and)g(th)m(us)g(the)h (theoretical)h(pap)s(er)d([19])j(do)s(es)e(not)g(pro)m(vide)h Fx(by)i(itself)45 b FI(a)27 b(full)f(justi\014cation)h(of)f(IKE.)-58 4849 y(More)34 b(precisely)-8 b(,)33 b(the)g(actual)h(IKE)e(proto)s (col)i(do)s(es)e(not)h(directly)h(use)e(the)h(master)g(secret)h(as)f(a) g(k)m(ey)g(of)g(the)g(PRF)-58 4962 y(\(as)e(analyzed)g(in)f([19]\))i (and)e(it)h(is)g(rather)f(apparen)m(tly)h(w)m(ell)g(done:)-58 5153 y Fz(Randomness)36 b(Extraction)46 b FI(in)23 b(a)i(\014rst)e (stage,)j(the)f(IKE)e(standard)h(uses)f(a)i(PRF)f(k)m(ey)m(ed)i(b)m(y)e Fx(r)-5 b(andom)29 b(and)f(public)108 5266 y(nonc)-5 b(es)39 b FI(and)30 b(applies)g(it)h(to)g(the)g(master)f(secret;)-58 5382 y Fz(Key)35 b(Deriv)-6 b(ation)46 b FI(in)34 b(the)h(second)g (stage,)h(the)f(output)f(is)g(used)g(as)h(a)g(k)m(ey)g(to)g(a)g(PRF,)g (with)g(kno)m(wn)f(inputs)f(in)108 5495 y(order)d(to)h(deriv)m(e)g (further)e(k)m(ey)i(material)h(to)f(create)h(a)f(secure)f(c)m(hannel.) 1927 5744 y(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop -58 -83 a FI(This)31 b(t)m(w)m(o-phases)h(proto)s (col)h(also)f(app)s(ears)f(in)g(the)h(random)e(generator)j(arc)m (hitecture)g(of)f(Barak)g(and)f(Halevi)i([4].)-58 30 y(The)g(aim)h(of)f(the)h(randomness)e(extractor)j(phase)e(is)h(to)g (generate)h(a)f(short)f(seed)g(concen)m(trating)j(the)e(en)m(trop)m(y)g (of)-58 143 y(the)f(source)f(and)g(then)g(in)h(the)f(k)m(ey)h(deriv)-5 b(ation,)34 b(this)e(seed)h(will)f(b)s(e)g(used)g(to)h(generate)h(k)m (eys.)f(It)g(is)f(imp)s(ortan)m(t)h(to)-58 256 y(separate)39 b(these)g(stages,)h(since)e(di\013eren)m(t)h(cryptographic)g(primitiv)m (es)f(are)h(needed:)f(the)h(PRF)f(is)g(used)f(for)h(t)m(w)m(o)-58 369 y(di\013eren)m(t)31 b(tasks!)83 500 y(Before)k(going)g(in)m(to)g (more)f(details,)h(let)g(us)f(review)g(informally)g(the)g(main)g (di\013erence)g(b)s(et)m(w)m(een)h(randomness)-58 613 y(extractors)i(and)e(PRF.)g(A)h(PRF)f(is)h(a)f(family)h(of)g (functions,)f(from)g(a)h(set)f(D)h(on)f(a)h(set)g(R,)g(suc)m(h)f(that)h (it)g(is)f(com-)-58 726 y(putationally)c(hard)e(to)i(distinguish)f(the) g(inputs/outputs)f(of)h(a)g(function)g(tak)m(en)h(at)g(random)e(from)h (the)g(set)h(of)f(all)-58 839 y(functions)g(from)h Fw(D)i FI(to)e Fw(R)h FI(and)e(of)h(a)g(function)f(tak)m(en)i(at)g(random)d (in)i(the)g(PRF)f(family)-8 b(.)32 b(It)f(is)g(imp)s(ortan)m(t)g(to)g (note)-58 952 y(that)38 b(the)f(k)m(ey)-8 b(,)38 b(or)f(the)g(index)g (of)g(the)g(function)g(tak)m(en)h(in)e(the)h(PRF)g(family)-8 b(,)38 b(m)m(ust)f(b)s(e)g(k)m(ept)g(secret,)h(otherwise)-58 1065 y(the)33 b(distinction)h(b)s(ecomes)g(easy)-8 b(.)34 b(A)f(randomness)f(extractor)j(has)e(the)g(prop)s(ert)m(y)g(that)g(the) h(output)e(distribution)-58 1178 y(is)j(close)h(to)g(the)f(uniform)e (one,)j(if)f(the)g(input)f(distribution)g(has)g(enough)h(en)m(trop)m(y) -8 b(.)36 b(If)f(the)g(index)f(is)h(kno)m(wn,)g(the)-58 1291 y(randomness)29 b(extractor)j(is)f(called)g(a)g Fx(str)-5 b(ong)40 b FI(randomness)29 b(extractor)2390 1258 y FH(1)2431 1291 y FI(.)83 1422 y(As)38 b(a)f(consequence,)i(one)e (can)h(easily)h(note)f(that)f(in)h(the)f(description)g(of)h(IKE)f(the)g (notation)i Fv(prf)d FI(has)h(t)m(w)m(o)-58 1535 y(purp)s(oses:)h (\(1\))j(\014rst)e(stage,)i Fv(prf)d FI(is)i(used)f(as)h(a)g (randomness)e(extractor,)j(with)e(public)g(and)g(random)g(k)m(ey)h(and) -58 1648 y(high-en)m(trop)m(y)30 b(input)f(\(but)g(not)g(as)h(a)g (PRF\);)g(\(2\))g(second)f(stage,)j Fv(prf)c FI(is)h(used)g(as)h(a)f (PRF,)h(to)g(build)e(a)i(PR)m(G.)g(The)-58 1761 y(HMA)m(C)h(function)f ([7],)i(designed)e(and)g(analyzed)h(as)g(a)f(secure)h(MA)m(C,)g(is)g (furthermore)e(the)h(default)h Fv(prf)e FI(in)h(IKE.)-58 2117 y Fz(1.3)105 b(HMA)m(C)35 b(as)g(a)f(Randomness)i(Extractor)-58 2390 y FI(HMA)m(C,)c(as)f(w)m(ell)g(as)g(some)g(other)g(constructions,) h(ha)m(v)m(e)g(b)s(een)d(recen)m(tly)j(studied)e(as)h(randomness)f (extractors)i(b)m(y)-58 2503 y(Do)s(dis)f Fx(et)h(al.)f FI(in)g([22].)h(This)e(is)g(the)h(\014rst)f(formal)h(analysis)g(of)g (practical)h(randomness)d(extractors.)j(They)f(namely)-58 2616 y(pro)m(v)m(e)j(that)g(these)g(constructions)f(are)h(almost)g (univ)m(ersal)g(hash)e(functions)h(under)e(v)-5 b(arious)34 b(assumptions.)e(They)-58 2729 y(basically)37 b(sho)m(w)f(ho)m(w)g(to)h (construct)f(a)g(v)-5 b(ariable-input)37 b(length)f(almost)h(univ)m (ersal)f(hash)f(function)h(family)g(from)-58 2842 y(a)30 b(\014xed-input)f(length)h(almost)h(univ)m(ersal)f(hash)f(function)h (family)g(\(or)h(ev)m(en)f(random)f(functions/p)s(erm)m(utations\).)-58 2955 y(Thereafter,)42 b(a)g(little)i(mo)s(di\014cation)e(of)f(the)h (Lefto)m(v)m(er)h(Hash)f(Lemma)g(\(LHL\))g([31])h(with)e(a)h Fx(r)-5 b(andomly)46 b(chosen)-58 3068 y(function)h FI(from)39 b(a)h(family)g(of)g(\(almost\))h(univ)m(ersal)f(hash)f(functions)g(can) h(b)s(e)e(used)h(to)i(extract)g(the)e(en)m(trop)m(y)i(of)-58 3181 y(a)j(random)f(source.)h(Suc)m(h)f(a)h(theoretical)i(result)d (seems)h(to)g(matc)m(h)h(with)e(the)h(use)f(of)h(HMA)m(C)g(in)f(IKE,)h (as)f(a)-58 3293 y(randomness)29 b(extractor.)k(A)m(t)e(least,)h(the)e (authors)g([22])i(claim)f(to)h(justify)d(the)i(design)f(of)h(IKE.)83 3425 y(Ho)m(w)m(ev)m(er,)37 b(if)e(one)g(carefully)h(lo)s(oks)f(at)h (the)f(description)g(of)g(IKEv1)g(\(in)g(the)g(signature)g(mo)s(de\))g (in)f(the)h(stan-)-58 3538 y(dard)22 b([28],)j(one)e(can)h(note)f(that) h(the)f(LHL)g(is)g(not)h(applied)e(in)h(an)g(appropriate)g(w)m(a)m(y:)i (the)e(k)m(ey)h(of)f(the)g(univ)m(ersal)h(hash)-58 3651 y(function)j(ma)m(y)h(b)s(e)e(c)m(hosen)i(b)m(y)f(the)g(adv)m(ersary)-8 b(.)28 b(There)f(is)g(th)m(us)g(no)g(guaran)m(tee)h(of)g(true)e (randomness,)h(while)g(this)g(is)-58 3764 y(the)i(basic)g(assumption.)g (More)h(precisely)-8 b(,)30 b(the)f(random)f(k)m(ey)h(is)g(join)m(tly)h (c)m(hosen)f(b)m(y)g(the)g(pla)m(y)m(ers,)h(but)e(not)i(clearly)-58 3877 y(authen)m(ticated.)j(An)d(adv)m(ersary)h(could)g(tak)m(e)i(adv)-5 b(an)m(tage)32 b(of)f(that)h(\(with)e(some)i(stupid)d(but)h (theoretically)k(secure)-58 3990 y(extractors\))h(to)e(con)m(trol)h (half)f(of)g(the)g(bits.)g(One)f(could)h(sa)m(y)g(that)g(one)g(honest)g (pla)m(y)m(er)h(is)f(enough)f(to)i(inject)f(high)-58 4103 y(en)m(trop)m(y)f(in)g(this)f(k)m(ey)-8 b(.)33 b(But)f(a)g (high-en)m(trop)m(y)g(bit-string)g Fx(is)i(not)41 b FI(a)32 b(random)f(bit-string.)h(F)-8 b(or)32 b(extracting)h(en)m(trop)m(y)-8 b(,)-58 4215 y(w)m(e)31 b(are)g(bac)m(k)h(to)f(our)f(initial)i (problem.)15 b(.)g(.)h(This)29 b(securit)m(y)j(problem)e(do)s(es)g(not) h(endanger)f(the)h(IKEv1)g(proto)s(col)g(in)-58 4328 y(practice,)36 b(due)e(to)h(the)f(use)g(of)g(a)h(sp)s(eci\014c)f (extractor)i(\(HMA)m(C\),)g(but)d(it)i(mak)m(es)g(imp)s(ossible)f(an)m (y)h(securit)m(y)g(pro)s(of)-58 4441 y(under)j(the)h(sole)h(assumption) f(of)h(\\almost)g(univ)m(ersal)g(hash)e(function".)i(Note)h(that)f(the) f(nonces)g(are)h(prop)s(erly)-58 4554 y(signed)30 b(in)g(IKEv2.)83 4686 y(F)-8 b(urthermore,)30 b(the)f(univ)m(ersal-hashing)h(prop)s(ert) m(y)e(of)i(HMA)m(C)g(is)f(pro)m(vided)g(in)g(three)h(analyses)g([22]:)h (the)f(\014rst)-58 4799 y(one)25 b(unfortunately)e(considers)h(a)h Fx(variant)34 b FI(of)24 b(HMA)m(C,)i(where)d(large)j(hash)d(functions) h(are)h(used,)e(with)h(a)h(truncated)-58 4912 y(output.)31 b(The)f(theoretical)j(analysis)e(is)g(indeed)f(delicate)i(since)f (compression)g(functions)f(are)h(families)g(where)g(the)-58 5025 y(size)h(of)f(the)f(k)m(ey)i(is)f(the)g(same)g(as)g(the)f(size)i (of)f(the)g(output.)f(Hence,)i(the)f(second)g(analysis,)g(whic)m(h)g (is)f(announced,)-58 5137 y(but)36 b(not)h(y)m(et)h(a)m(v)-5 b(ailable)39 b(ma)m(y)e(b)s(e)f(quite)h(in)m(tricate.)i(An)m(yw)m(a)m (y)-8 b(,)38 b(the)f(third)f(one)g(v)-5 b(alidates,)39 b(at)e(least)h(for)e(practical)-58 5250 y(purp)s(ose,)23 b(the)i(use)f(of)h(HMA)m(C,)g(since)g(this)f(is)h(an)f(analysis)h(of)g (the)f(real)h(HMA)m(C)h(in)e(the)g(random)g(oracle)i(mo)s(del)e([10].)p -58 5410 473 4 v -41 5463 a FG(1)19 5495 y FF(Hereafter,)j(w)n(e)f (only)f(lo)r(ok)i(at)f(strong)g(randomness)g(extractors)g(and)g(w)n(e)g (th)n(us)f(simply)g(call)i(them)e(randomness)i(extractors.)1927 5744 y FI(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop -58 -83 a Fz(1.4)105 b(Randomness)36 b(Extractors)-58 92 y FI(The)27 b(notion)h(of)g(randomness)e(extractor) j(is)f(th)m(us)f(v)m(ery)h(imp)s(ortan)m(t)f(from)g(a)h(practical)h(p)s (oin)m(t)f(of)f(view)h(and)f(is)g(often)-58 205 y(ignored)33 b(or)f(misused)g(b)m(y)g(cryptographers,)g(since)h(solutions)g(are)f (quite)h(theoretical.)i(Let)e(us)f(call)i(the)e(ratio)i Fw(k)s(=n)-58 318 y FI(of)d(a)g(random)f(source)h(of)f(blo)s(c)m (klength)i Fw(n)e FI(and)g(of)h(min-en)m(trop)m(y)g Fw(k)j FI(\(basically)e(the)f(n)m(um)m(b)s(er)e(of)i(random)f(bits\))h(the)-58 431 y Fx(entr)-5 b(opy)35 b(r)-5 b(ate)p FI(.)83 544 y(In)44 b(complexit)m(y)h(theory)-8 b(,)45 b(randomness)e(extraction)j (from)e(a)g(distribution)f(has)h(b)s(een)g(extensiv)m(ely)h(studied)-58 656 y(\(see)32 b([41])g(for)e(a)h(surv)m(ey\).)g(F)-8 b(or)31 b(certain)g(random)f(sources,)h(it)g(has)f(b)s(een)g(sho)m(wn)g (that)h(it)g(is)g(imp)s(ossible)f(to)h(extract)-58 769 y(ev)m(en)21 b(one)g(bit)f(of)h(randomness)e([39].)j(One)d(w)m(a)m(y)j (to)f(solv)m(e)g(this)g(last)g(problem)e(is)i(to)g(use)f(a)h(small)f(n) m(um)m(b)s(er)f(of)i(uniformly)-58 882 y(random)30 b(bits)h(as)g(a)g Fx(c)-5 b(atalyst)41 b FI(in)31 b(addition)g(to)g(the)g(bits)g(from)f (the)h(w)m(eak)h(random)e(source)h(as)g(in)f(the)h(LHL)g(as)g(said)-58 995 y(in)g([34].)i(Ho)m(w)m(ev)m(er,)g(in)e(some)g(cases,)h(w)m(e)g (can)f(eliminate)i(the)e(need)g(for)g(the)g(random)f(catalyst)k(b)m(y)d (restricting)h(the)-58 1108 y(class)27 b(of)f(w)m(eak)h(random)e (sources.)h(T)-8 b(revisan)26 b(and)g(V)-8 b(adhan)25 b(and)h(later)h(Do)s(dis)f([48,)16 b(21])27 b(ha)m(v)m(e)g(called)h (suc)m(h)d(functions)-58 1221 y Fx(deterministic)41 b(extr)-5 b(actors)p FI(.)41 b(In)c(cryptograph)m(y)-8 b(,)40 b(randomness)d (extractors)j(ha)m(v)m(e)f(b)s(een)f(studied)g(under)e(di\013eren)m(t) -58 1334 y(adv)m(ersaries)d(to)g(construct)g(truly)f(random)f (generators)j([5],)f(and)f(deterministic)h(extractors)h(ha)m(v)m(e)f(b) s(een)f(used)f(to)-58 1447 y(built)f(All-Or-Nothing-T)-8 b(ransform)31 b(\(A)m(ONTs\))g(sc)m(hemes)g(and)f(Exp)s(osure-Resilien) m(t)h(F)-8 b(unction)31 b(\(ERF\))g([17,)17 b(23].)83 1560 y(In)34 b(the)h(k)m(ey)h(exc)m(hange)g(setting,)g(the)f(problem)f (is)h(to)g(transform)f(the)h(randomness)f(in)g(a)h(uniform)f(source)h (of)-58 1673 y(small)23 b(en)m(trop)m(y)h(rate)f(in)m(to)h(a)f(source)g (of)g(en)m(trop)m(y)g(rate)g(1.)h(F)-8 b(or)23 b(example,)h(under)d (the)i(DDH)h(assumption)e(in)g(a)h(160-bit)-58 1786 y(prime)33 b(order)g Fw(q)j FI(subgroup)31 b(in)i Fu(Z)1088 1753 y Ft(?)1088 1808 y(p)1127 1786 y FI(,)h(w)m(e)g(kno)m(w)f(that)h(the)f (input)g(random)f(source)h(\(in)h(a)f(DH-based)h(k)m(ey)g(exc)m(hange) -58 1898 y(proto)s(col\))29 b(has)e(160)h(bits)f(of)h(min-en)m(trop)m (y)-8 b(.)28 b(So,)f(for)g(1024-bit)j(prime)d Fw(p)p FI(,)g(the)g(en)m(trop)m(y)h(rate)g(of)f(the)h(initial)g(source)g(is) -58 2011 y(160)p Fw(=)p FI(1024.)36 b(Because)e(of)e(the)g(sp)s (eci\014c)g(structure)g(of)g(the)g(source,)h(deterministic)g (extractors)g(\(whic)m(h)f(exploit)i(the)-58 2124 y(algebraic)f (structure\))e(ma)m(y)g(b)s(e)g(used)f(to)i(deriv)m(e)f(cryptographic)h (k)m(eys,)f(they)h(w)m(ould)e(a)m(v)m(oid)j(all)f(the)f(problems)f(w)m (e)-58 2237 y(presen)m(ted)g(b)s(efore.)h(W)-8 b(e)31 b(will)g(th)m(us)f(in)m(tro)s(duce)g(a)h(new)f(deterministic)h (extractor,)h(whic)m(h)e(tak)m(es)i(adv)-5 b(an)m(tage)32 b(of)f(the)-58 2350 y(sp)s(eci\014c)f(structure)g(of)h(elliptic)h(curv) m(es.)-58 2608 y Fz(1.5)105 b(Con)m(tribution)35 b(and)g(Organization) -58 2783 y FI(In)30 b(this)g(pap)s(er,)g(w)m(e)h(\014rst)e(fo)s(cus)h (on)g(inaccuracies)i(in)e(the)h(securit)m(y)g(analysis)g(of)f Fw(\006)2818 2797 y FH(0)2858 2783 y FI(,)g(and)g(in)g(the)h (analysis/design)-58 2896 y(of)f(IKE,)f(on)g(the)h(basis)g(of)f(the)h (original)h(do)s(cumen)m(ts)e([36,)17 b(28,)f(37].)31 b(W)-8 b(e)30 b(stress)g(one)g(more)f(time)i(that)f(ev)m(en)g(if)g (there)-58 3009 y(is)h(not)g(y)m(et)g(an)m(y)g(complete)h(pro)s(of)e (in)h(the)f(standard)g(mo)s(del,)h(the)g(IKE)f(proto)s(cols)h(ha)m(v)m (e)h(b)s(een)e(carefully)h(designed)-58 3122 y(and)h(there)g(is)g(no)g (attac)m(k)i(against)g(them,)e(just)f(theoretical)k(problems.)c(The)h (\014rst)f(one)h(is)g(ab)s(out)g(the)g(theoretical)-58 3234 y(analysis)f(of)g Fw(\006)459 3248 y FH(0)498 3234 y FI(.)g(The)f(second)g(one)h(is)g(ab)s(out)f(the)h(actual)h(use)e(of)g (HMA)m(C)i(in)e(IKEv1,)g(but)g(at)h(a)g(theoretical)i(lev)m(el)-58 3347 y(only)-8 b(.)25 b(It)f(has)f(b)s(een)h(in)m(tro)s(duced)f(in)g (the)h(signature)h(mo)s(de,)e(for)h(compatibilit)m(y)i(reasons)e(with)g (other)g(authen)m(tication)-58 3460 y(mo)s(des,)i(in)f(the)h(IKE)g (standard.)f(F)-8 b(ortunately)g(,)28 b(it)f(has)e(b)s(een)h(corrected) h(in)e(IKEv2)h([35,)17 b(30])27 b(mainly)f(b)m(y)f(Kra)m(w)m(czyk.)83 3573 y(Then,)44 b(w)m(e)g(discuss)g(in)f(more)i(details)g(on)f(v)-5 b(arious)44 b(tec)m(hniques)h(to)g(deriv)m(e)g(a)f(uniformly)f (distributed)g(bit-)-58 3686 y(string)33 b(from)g(a)g(high-en)m(trop)m (y)h(bit-string)f(source.)g(More)h(sp)s(eci\014cally)-8 b(,)34 b(w)m(e)g(apply)f(the)g(Kaliski's)h(tec)m(hnique)f([33],)-58 3799 y(with)c(quadratic)h(t)m(wists)g(of)f(elliptic)i(curv)m(es,)f(to)g (this)f(framew)m(ork.)h(It)f(is)h(quite)f(w)m(ell-suited)i(to)f(authen) m(ticated)h(k)m(ey)-58 3912 y(exc)m(hange,)26 b(since)f(it)g(already)h (w)m(orks)e(on)g(cyclic)j(groups.)d(Therefore,)g(it)h(is)g(more)g (e\016cien)m(t)h(than)e(the)h(Lefto)m(v)m(er)h(Hash)-58 4025 y(Lemma)e(while)g(retaining)g(the)g(same)h(securit)m(y)f (attributes,)h(and)e(b)s(eing)g Fx(deterministic)p FI(.)i(This)e ('Twist)h(A)m(Ugmen)m(ted')-58 4138 y(\()p Fs(T)-8 b(A)m(U)p FI(\))35 b(tec)m(hnique)g(is)g(pro)m(v)-5 b(ably)34 b(secure)h (assuming)f(only)g(the)h(in)m(tractabilit)m(y)i(of)e(the)f(decisional)i (Di\016e-Hellman)-58 4251 y(problem)30 b(on)g(elliptic)i(curv)m(es.)83 4364 y(Ev)m(en)c(though)m(t)h(quadratic)g(t)m(wists)f(w)m(ere)h (previously)f(in)m(tro)s(duced)f(in)h(the)g(literature,)i(their)e (practical)i(asp)s(ects)-58 4477 y(w)m(ere)h(not)g(fully)f(studied)f ([15,)17 b(16].)32 b(W)-8 b(e)31 b(th)m(us)f(also)i(sho)m(w)e(that)h (appropriate)f(curv)m(es)h(can)f(b)s(e)g(easily)i(generated.)-58 4738 y Fy(2)112 b(Securit)m(y)38 b(Problem)f(in)h(Securit)m(y)f(Pro)s (of)h(of)f Fr(\006)2098 4753 y Fq(0)-58 4946 y FI(In)23 b(this)h(section,)i(w)m(e)e(precisely)h(fo)s(cus)e(on)h(the)g(securit)m (y)h(pro)s(of)e(of)i(the)f(basic)g(SIGMA)g(proto)s(col,)i(named)d Fw(\006)3628 4960 y FH(0)3692 4946 y FI(in)g([19].)-58 5059 y(The)30 b(description)g(of)h(this)f(proto)s(col)1200 5026 y FH(2)1271 5059 y FI(is)g(giv)m(en)i(in)e(\014gure)g(1.)p -58 5136 473 4 v -41 5189 a FG(2)19 5221 y FF(As)d(suggested)i(in)f ([19],)h(w)n(e)f(enhanced)f(it)h(with)g(a)g(fourth)g(\015o)n(w,)g(whic) n(h)g(is)g(an)g(ac)n(kno)n(wledgmen)n(t)g(from)g(the)g(receiv)n(er)g (whic)n(h)f(means)19 5312 y(that)f(ev)n(erything)f(is)h(consisten)n(t)g (to)g(him.)h(Without)e(suc)n(h)h(a)g(\015o)n(w,)g(it)g(w)n(ould)h(b)r (e)e(easy)i(to)f(break)f(the)h(usual)g(m)n(utual)g(authen)n(tication)19 5404 y(notion,)f(b)n(y)f(simply)h(not)g(rela)n(ying)h(the)e(third)h (\015o)n(w.)g(F)-6 b(or)25 b(the)g(seman)n(tic)g(securit)n(y)-6 b(,)25 b(it)g(just)g(helps)g(in)g(the)g(pro)r(of,)h(since)f(activ)n(e)h (attac)n(ks)19 5495 y(can)g(then)f(b)r(e)g(easily)i(detected.)1927 5744 y FI(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop -11 -171 3923 4 v -11 2470 4 2642 v 1336 -3 a Fp(Alice)p 1336 10 169 4 v 922 w(Bob)p 2426 10 136 4 v 1244 179 a FF(Common)26 b(group)c(:)f Fo(G)h FF(=)f FD(h)p FB(g)s FD(i)j FF(of)j(prime)f(order)f FB(q)916 362 y FF(Signing)h(Key)21 b(:)g FE(sk)1454 370 y Fn(A)2426 362 y FF(Signing)26 b(Key)21 b(:)h FE(sk)2964 370 y Fn(B)769 453 y FF(V)-6 b(eri\014cation)26 b(Key)20 b(:)i FE(pk)1454 472 y Fn(A)2426 453 y FF(V)-6 b(eri\014cation)26 b(Key)21 b(:)g FE(pk)3111 472 y Fn(B)434 545 y FE(accept)g FD( )h FE(false)q FF(;)13 b FE(terminate)21 b FD( )g FE(false)923 b(accept)21 b FD( )g FE(false)q FF(;)14 b FE(terminate)21 b FD( )g FE(false)560 773 y FB(s)633 731 y Fn(R)617 773 y FD( )h(f)p FF(0)p FB(;)13 b FF(1)p FD(g)902 742 y Fn(?)939 773 y FB(;)g(x)1054 731 y Fn(R)1038 773 y FD( )21 b Fo(Z)1186 781 y Fn(q)1220 773 y FB(;)14 b(X)27 b FF(=)21 b FB(g)1466 742 y Fn(x)1896 723 y FB(s;)13 b(X)1581 773 y FD(\000)-35 b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f (\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)-34 b(!)77 b FB(y)2503 731 y Fn(R)2488 773 y FD( )21 b Fo(Z)2636 781 y Fn(q)2670 773 y FB(;)13 b(Y)38 b FF(=)21 b FB(g)2908 742 y Fn(y)2426 865 y FB(\033)2470 873 y Fn(B)2544 865 y FF(=)g FE(SIG)p FB(:)p FE(Sign)q FF(\()p FE(sk)2998 873 y Fn(B)3050 865 y FF(;)13 b(\()p FE(\\1")q FB(;)h(s;)f(X)r(;)g(Y)j FF(\)\))2426 956 y FB(K)27 b FF(=)21 b FB(X)2668 924 y Fn(y)2706 956 y FB(;)13 b(k)2780 964 y Fn(m)2860 956 y FF(=)21 b FE(MacKey)q FF(\()p FB(K)5 b FF(\))605 1094 y FB(K)27 b FF(=)21 b FB(Y)839 1063 y Fn(x)878 1094 y FB(;)13 b(k)952 1102 y Fn(m)1032 1094 y FF(=)21 b FE(MacKey)q FF(\()p FB(K)5 b FF(\))1689 1044 y FB(s;)13 b(Y)t(;)g Fp(Bob)q FB(;)g(\033)2056 1052 y Fn(B)2108 1044 y FB(;)g(\026)2188 1052 y Fn(B)1581 1094 y FD( )-35 b(\000)-17 b(\000)g(\000)g(\000)f (\000)h(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g (\000)f(\000)-33 b(\000)76 b FB(\026)2472 1102 y Fn(B)2546 1094 y FF(=)21 b FE(MA)n(C)p FB(:)p FE(Sign)q FF(\()p FB(k)3023 1102 y Fn(m)3082 1094 y FF(;)13 b(\()p FE(\\1")q FB(;)g(s;)g Fp(Bob)p FF(\)\))1044 1186 y(Chec)n(k)26 b FB(\026)1321 1194 y Fn(B)1374 1186 y FB(;)13 b(\033)1452 1194 y Fn(B)390 1277 y FB(\033)434 1285 y Fn(A)506 1277 y FF(=)21 b FE(SIG)p FB(:)p FE(Sign)p FF(\()p FE(sk)959 1285 y Fn(A)1009 1277 y FF(;)13 b(\()p FE(\\0")r FB(;)g(s;)g(Y)t(;)g(X) 6 b FF(\)\))340 1368 y FB(\026)386 1376 y Fn(A)458 1368 y FF(=)21 b FE(MA)n(C)p FB(:)p FE(Sign)q FF(\()p FB(k)935 1376 y Fn(m)993 1368 y FF(;)13 b(\()p FE(\\0")q FB(;)g(s;)g Fp(Alice)q FF(\)\))1051 1507 y FE(accept)21 b FD( )g FE(true)1717 1456 y FB(s;)13 b Fp(Alice)p FB(;)g(\033)2033 1464 y Fn(A)2083 1456 y FB(;)g(\026)2163 1464 y Fn(A)1581 1507 y FD(\000)-35 b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)f (\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000) -34 b(!)77 b FF(Chec)n(k)25 b FB(\026)2702 1515 y Fn(A)2753 1507 y FB(;)13 b(\033)2831 1515 y Fn(A)2426 1598 y FE(accept)21 b FD( )g FE(true)871 1716 y FF(w)n(ait)27 b(for)f(a)g(v)l(alid)g FB(\026)1453 1724 y Fn(C)1916 1666 y FB(\026)1962 1674 y Fn(C)1581 1716 y FD( )-35 b(\000)-17 b(\000)g(\000)g(\000)f(\000)h (\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f (\000)-33 b(\000)76 b FB(\026)2472 1724 y Fn(C)2545 1716 y FF(=)21 b FE(MA)n(C)p FB(:)p FE(Sign)q FF(\()p FB(k)3022 1724 y Fn(m)3081 1716 y FF(;)13 b FE(Ack)p FF(\))951 1808 y FE(terminate)22 b FD( )f FE(true)921 b(terminate)21 b FD( )g FE(true)846 1990 y(sk)i FF(=)g FE(SessionKey)r FF(\()p FB(K)5 b FF(\))825 2082 y FE(sid)24 b FF(=)f FB(s;)13 b(X)r(;)g(Y)t(;)g Fp(Alice)p FB(;)h Fp(Bob)p FB(;)f(\033)1687 2090 y Fn(A)1737 2082 y FB(;)g(\033)1815 2090 y Fn(B)1868 2082 y FB(;)g(\026)1948 2090 y Fn(A)1998 2082 y FB(;)h(\026)2079 2090 y Fn(B)691 2327 y FF(where)132 b FE(SessionKey)r FF(\()p FB(K)5 b FF(\))21 b(=)g FE(PRF)1749 2335 y Fn(K)1808 2327 y FF(\(0\))p FB(;)13 b FE(MacKey)q FF(\()p FB(K)5 b FF(\))22 b(=)f FE(PRF)2577 2335 y Fn(K)2635 2327 y FF(\(1\))1019 2418 y(and)k(when)h(a)g(c)n(hec)n(k)f(fails,)i (one)f(stops)g(the)g(execution:)f FE(terminate)d FD( )f FE(true)p 3908 2470 4 2642 v -11 2473 3923 4 v 1134 2617 a FC(Fig.)13 b(1.)26 b FF(An)e(honest)i(execution)g(of)g(the)f(proto)r (col)i FB(\006)2685 2625 y FG(0)2720 2617 y FF(.)-58 3018 y Fz(2.1)105 b(Securit)m(y)36 b(Pro)s(of)f(of)g Fm(\006)1078 3032 y Fq(0)1159 3018 y Fz([19])-58 3237 y FI(W)-8 b(e)29 b(only)e(fo)s(cus)g(on)g(the)h(seman)m(tic)h(securit)m (y)f(\(priv)-5 b(acy)28 b(of)f(the)h(session)f(k)m(ey\))i(of)e(a)h(k)m (ey)g(exc)m(hange)h(proto)s(col)g(and)d(w)m(e)-58 3349 y(quic)m(kly)h(explain)g(the)f(adv)m(ersarial)i(game.)f(A)f(passiv)m(e) h(adv)m(ersary)g(is)f(allo)m(w)m(ed)i(to)f(see)g(passiv)m(e)g (executions)g(b)s(et)m(w)m(een)-58 3462 y(t)m(w)m(o)34 b(honest)e(participan)m(ts)h(of)f(his)g(c)m(hoice)i(and)d(to)i(see)g (old)f(session)h(k)m(eys.)g(His)f(goal)i(is)e(to)h(distinguish)e(a)i (random)-58 3575 y(k)m(ey)h(from)e(the)g(real)i(session)e(k)m(ey)i(in)e (an)h(execution)g(of)g(the)g(proto)s(col)h(for)e(whic)m(h)g(he)h (cannot)g(ask)g(to)g(see)g(the)g(real)-58 3688 y(session)23 b(k)m(eys)g(to)g(an)m(y)f(partner.)g(Moreo)m(v)m(er,)j(if)d(activ)m(e)j (adv)m(ersaries)e(ha)m(v)m(e)g(to)h(b)s(e)d(tak)m(en)j(in)m(to)f (accoun)m(t,)h(the)f(adv)m(ersary)-58 3801 y(can)33 b(inject)h(in)f (the)g(proto)s(col)h(his)e(o)m(wn)h(messages,)h(and)f(receiv)m(es)h (the)f(corresp)s(onding)f(answ)m(er)h(according)h(to)g(the)-58 3914 y(proto)s(col.)e(The)e(securit)m(y)h(goal)h(is)e(the)h(same.)g (More)g(details)g(are)g(giv)m(en)g(in)f(the)h(app)s(endix)e(A.)83 4035 y(A)g(securit)m(y)g(pro)s(of)f(consists)h(in)f(sho)m(wing)h(that)g (the)g(adv)m(ersary)g(adv)-5 b(an)m(tage)30 b(in)e(winning)g(the)h (securit)m(y)g(game)h(is)-58 4148 y(negligible.)c(T)-8 b(o)24 b(this)f(end,)g(the)h(general)h(tec)m(hnique)f(is)g(to)g (describ)s(e)f(a)h(p)s(olynomial)g(sequence)g(of)f(h)m(ybrid)g(games)h ([45].)-58 4261 y(The)f(\014rst)g(one)g(is)h(usually)f(the)g(real)h (securit)m(y)h(game)f(while)f(the)h(last)g(one)g(is)f(a)h(securit)m(y)g (game)g(where)f(the)h(adv)-5 b(an)m(tage)-58 4373 y(of)32 b(the)f(adv)m(ersary)h(can)g(\\easily")i(b)s(e)c(pro)m(v)m(ed)i(to)g(b) s(e)f(zero.)i(Finally)-8 b(,)33 b(it)f(remains)f(to)h(sho)m(w)g(that)g (the)g(statistical)i(or)-58 4486 y(computational)e(distance)f(b)s(et)m (w)m(een)g(eac)m(h)h(pair)e(of)g(sequen)m(tial)i(games)f(is)g (negligible.)83 4607 y(Let)h(us)f(recall)h(the)g(de\014nition)f(of)g (pseudo-random)f(functions)h(according)h(to)g(Goldreic)m(h)h([26])g (since)e(this)g(will)-58 4720 y(b)s(e)f(a)h(crucial)g(to)s(ol)g (\(other)g(more)g(classical)h(primitiv)m(es)f(and)f(assumptions)g(are)g (review)m(ed)h(in)f(app)s(endix)f(B.\))-58 4922 y Fz(De\014nition)35 b(1)46 b(\(Pseudo-Random)37 b(F)-9 b(unctions\).)36 b FI(A)c(pseudo-random)d(function)i(family)h(\()p Fs(PRF)p FI(\))f(is)g(a)g(family)-58 5035 y(of)j(functions)g Fl(F)40 b FI(=)31 b(\()p Fw(f)732 5050 y Ft(k)775 5035 y FI(\))810 5050 y Ft(k)887 5035 y FI(in)i Fl(F)1061 5049 y Ft(n;m)1191 5035 y FI(,)h(the)g(set)g(of)g(the)h(functions)e(from)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2657 5002 y Ft(n)2740 5035 y FI(in)m(to)35 b Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3148 5002 y Ft(m)3216 5035 y FI(,)34 b(indexed)g(b)m(y)g(a)g(k)m (ey)-58 5148 y Fw(k)29 b Fl(2)24 b(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)323 5115 y Ft(`)359 5148 y FI(,)26 b(so)h(that)g(for)f(a) h(randomly)f(c)m(hosen)g Fw(`)p FI(-bit)h(string)f(k)m(ey)i Fw(k)s FI(,)e(no)h(adv)m(ersary)f(can)h(distinguish)f(the)g(function) -58 5269 y Fw(f)-13 5284 y Ft(k)55 5269 y FI(from)g(a)g(truly)g(random) f(function)h(in)g Fl(F)1406 5283 y Ft(n;m)1535 5269 y FI(:)g Fs(Adv)1737 5225 y Fk(p)n(rf)1737 5298 y Fj(F)1826 5269 y FI(\()p Fl(D)s Fw(;)15 b(q)s FI(\))26 b(=)f Fl(j)15 b FI(Pr)2313 5284 y Ft(k)2355 5269 y FI([1)26 b Fl( )g(D)2641 5236 y Ft(f)2675 5248 y Fn(k)2716 5269 y FI(])12 b Fl(\000)g FI(Pr)2933 5284 y Ft(f)2978 5269 y FI([1)26 b Fl( )f(D)3263 5236 y Ft(f)3308 5269 y FI(])p Fl(j)i FI(m)m(ust)f(b)s(e)f(small,)-58 5382 y(where)j Fl(D)i FI(is)e(a)g(distinguisher,)g(with)g(an)f(oracle)j (access)f(to)g(either)f(a)h(random)e(instance)h Fw(f)3045 5397 y Ft(k)3115 5382 y FI(in)g(the)g(giv)m(en)h(family)g Fl(F)-58 5495 y FI(or)k(a)h(truly)e(random)h(function)g Fw(f)42 b FI(in)33 b Fl(F)1319 5509 y Ft(n;m)1448 5495 y FI(,)g(and)g(m)m(ust)g(distinguish)f(the)i(t)m(w)m(o)g(cases)g(with)f (at)h(most)f Fw(q)j FI(queries)d(to)1927 5744 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop -58 -83 a FI(the)29 b(function)f(oracle.)i(W)-8 b(e)29 b(sa)m(y)g(that)g(suc)m(h)f(a)h(family)g(is)f(a)h(\()p Fw(q)s(;)15 b(";)g(t)p FI(\)-)p Fs(PRF)30 b FI(if)e(for)g(an)m(y)h (distinguisher)f(asking)g(at)h(most)-58 30 y Fw(q)k FI(queries)e(to)g (the)f(oracle,)i(its)f(adv)-5 b(an)m(tage)32 b(is)f(less)g(than)f Fw(")p FI(,)h(after)g(a)f(running)f(time)i(b)s(ounded)d(b)m(y)i Fw(t)p FI(.)83 201 y(Let)22 b(us)f(no)m(w)g(review)h(the)g(pro)s(of)e (of)i(seman)m(tic)h(securit)m(y)f Fw(\006)2042 215 y FH(0)2081 201 y FI(,)g(depicted)g(on)f(Figure)h(1.)g(While)g([19])h(is) f(a)f(theoretical)-58 314 y(pap)s(er,)32 b(assumptions)g(in)h(the)g (securit)m(y)h(claim)g(and)e(the)h(securit)m(y)h(pro)s(of)e(remain)h (quite)h(informal)e(since)i(at)f(some)-58 427 y(place)28 b(one)g(can)f(\014nd)f(\\)p Fx(we)k(wil)5 b(l)30 b(assume)g(the)g(se)-5 b(curity)30 b(of)g(the)g(other)h(underlying)g(crypto)-5 b(gr)g(aphic)32 b(primitives)f(in)e(the)-58 540 y(pr)-5 b(oto)g(c)g(ol)40 b(\(.)14 b(.)g(.)g(\))35 b(under)i(the)g(standar)-5 b(d)39 b(se)-5 b(curity)36 b(notions)i(in)e(the)g(crypto)-5 b(gr)g(aphic)39 b(liter)-5 b(atur)g(e)7 b FI(",)37 b(and)c(\\)p Fx(We)k(use)e(the)-58 652 y(notation)40 b(r)-5 b(andom)s FI(\(\))38 b Fx(to)h(r)-5 b(epr)g(esent)40 b(a)f(r)-5 b(andom)40 b(\(and)g(indep)-5 b(endent\))39 b(choic)-5 b(e)39 b(of)g(a)f(string)h(of)f(some)h(appr)-5 b(opriate)-58 765 y(length)7 b FI(".)27 b(The)f(latter)h(statemen)m(t)h(allo)m(ws)f (pro)s(ofs)e(in)h(the)g(standard)f(mo)s(del,)h Fx(i.e.)f FI(without)h(making)h(an)m(y)f(unrealistic)-58 878 y(assumption,)d(suc) m(h)g(as)g(in)g(the)g(random)g(oracle)h(mo)s(del)f([10].)i(Ho)m(w)m(ev) m(er,)h(the)d(actual)h(securit)m(y)g(result)f(relies)h(on)f Fi(non-)-58 991 y Fx(standar)-5 b(d)37 b(se)-5 b(curity)34 b(notions)g(in)g(the)g(crypto)-5 b(gr)g(aphic)37 b(liter)-5 b(atur)g(e)40 b FI(con)m(trary)32 b(to)g(the)g(former)f(statemen)m(t.)i (The)e(main)-58 1104 y(problem)h(comes)h(from)f(the)h(PRF)f(whic)m(h)g (is)h(usually)f(assumed)f(to)i(b)s(e)f(indexed)g(b)m(y)g(k)m(eys)h (uniformly)f(distributed)-58 1217 y(in)e Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)268 1184 y Ft(`)303 1217 y FI(,)31 b(for)f(some)h(length)g Fw(`)f FI(\(as)h(review)m(ed)g(ab)s(o)m(v)m (e\).)83 1330 y(The)42 b(securit)m(y)h(pro)s(of)f([19])h(uses)f(the)h (follo)m(wing)h(h)m(ybrid)d(sequence)h(of)h(games)g(where)f(w)m(e)h (only)f(de\014ne)g(the)-58 1443 y(di\013erence)32 b(with)g(the)g (original)g(securit)m(y)h(game)g Fs(REAL)p FI(.)e(In)g(fact,)i(the)f (securit)m(y)h(games)f(are)g(iden)m(tical,)i(except)f(the)-58 1556 y(generation)f(of)e(some)h(k)m(eys)g(whic)m(h)f(v)-5 b(aries)31 b(b)s(et)m(w)m(een)g(the)g(games.)-8 1735 y(1.)46 b Fs(REAL)p FI(:)31 b Fw(k)434 1749 y Ft(m)526 1735 y FI(=)25 b Fs(MacKey)p FI(\()p Fw(K)7 b FI(\))25 b(=)g Fs(PRF)1375 1749 y Ft(g)1411 1730 y Fn(xy)1487 1735 y FI(\(1\))32 b(and)e Fs(sk)25 b FI(=)g Fs(SessionKey)p FI(\()p Fw(K)7 b FI(\))26 b(=)f Fs(PRF)2875 1749 y Ft(g)2911 1730 y Fn(xy)2988 1735 y FI(\(0\))-8 1848 y(2.)46 b Fs(RPRF)p FI(:)30 b Fw(k)438 1862 y Ft(m)530 1848 y FI(=)25 b Fs(PRF)795 1862 y Ft(K)863 1848 y FI(\(1\))31 b(and)f Fs(sk)c FI(=)f Fs(PRF)1555 1862 y Ft(K)1624 1848 y FI(\(0\),)31 b(for)g Fw(K)h Fl( )25 b Fx(r)-5 b(andom)2458 1862 y FH(1)2498 1848 y FI(\(\))-8 1961 y(3.)46 b Fs(ALLR)p FI(:)31 b Fw(k)429 1975 y Ft(m)521 1961 y Fl( )25 b Fx(r)-5 b(andom)935 1975 y FH(2)975 1961 y FI(\(\))31 b(and)f Fs(sk)25 b Fl( )g Fx(r)-5 b(andom)1772 1975 y FH(2)1811 1961 y FI(\(\))-8 2073 y(4.)46 b Fs(HYBR)p FI(:)30 b Fw(k)455 2087 y Ft(m)547 2073 y FI(=)25 b Fs(PRF)812 2087 y Ft(K)880 2073 y FI(\(1\))32 b(for)e Fw(K)i Fl( )25 b Fx(r)-5 b(andom)1689 2087 y FH(1)1729 2073 y FI(\(\),)31 b(and)f Fs(sk)25 b Fl( )h Fx(r)-5 b(andom)2551 2087 y FH(2)2590 2073 y FI(\(\))-8 2186 y(5.)46 b Fs(RAND)p FI(:)30 b Fw(k)460 2200 y Ft(m)552 2186 y FI(=)25 b Fs(PRF)817 2200 y Ft(g)853 2181 y Fn(xy)929 2186 y FI(\(1\))32 b(and)d Fs(sk)d Fl( )f Fx(r)-5 b(andom)1772 2200 y FH(2)1811 2186 y FI(\(\))83 2365 y(Ho)m(w)m(ev)m(er,)41 b(in)d(the)g(securit)m(y)h(pro)s(of)f(of)g(Canetti)i(and)d(Kra)m(w)m (czyk)j([19],)g(w)m(e)e(can)h(sho)m(w)f(that)h(under)e(classical)-58 2478 y(assumptions,)d(the)h(distance)g(b)s(et)m(w)m(een)g(some)g(games) h(cannot)f(b)s(e)f(negligible,)i(but)e(ev)m(en)h(close)h(to)f(1)g(and)f (conse-)-58 2591 y(quen)m(tly)h Fx(no)40 b FI(securit)m(y)35 b(can)f(hold)g(in)g(the)g(standard)g(mo)s(del.)g(More)h(precisely)-8 b(,)35 b(w)m(e)g(sho)m(w)f(that)g(w)m(e)h(can)f(construct)-58 2704 y(PRF)d(for)f(whic)m(h)g(the)g(sc)m(heme)h(b)s(ecomes)g(insecure)f (while)h(the)f(authors)g(of)h([19])h(claims)f(securit)m(y)g(for)f(an)m (y)h(PRF.)-58 2966 y Fz(2.2)105 b(Informal)35 b(Evidence)g(that)f Fm(\006)1358 2980 y Fq(0)1438 2966 y Fz(\(without)g(Randomness)i (Extraction\))f(is)g(Insecure)-58 3145 y FI(In)24 b(the)g(follo)m (wing,)i(w)m(e)f(presen)m(t)g(a)g(distance)g(b)s(et)m(w)m(een)g(game)g Fs(REAL)f FI(and)g(game)h Fs(ALLR)p FI(,)g(but)e(the)i(same)g(gap)g (app)s(ears)-58 3258 y(b)s(et)m(w)m(een)32 b(games)g Fs(ALLR)f FI(and)f Fs(RAND)p FI(.)h(The)g Fs(REAL)g FI(game)h(is)f(the) g(game)i(the)e(adv)m(ersary)g(actually)i(pla)m(ys,)f(while)f(in)-58 3371 y(the)39 b Fs(RAND)f FI(game,)i(it)g(is)f(clear)h(that)f(its)g (adv)-5 b(an)m(tage)41 b(is)e(exactly)i(zero)e(since)h(the)f(session)g (k)m(ey)g(is)g(random)f(and)-58 3484 y(indep)s(enden)m(t)g(of)h(the)g (c)m(hallenger)h(bit.)f(According)h(to)f(the)g(\\appropriate")h(range)f (of)g(the)g(random)f(generation)-58 3597 y Fx(r)-5 b(andom)241 3611 y FH(1)280 3597 y FI(\(\),)31 b(either)g(the)g(gap)f(from)g Fs(RPRF)g FI(to)h Fs(ALLR)f FI(or)h(from)e Fs(REAL)i FI(to)g Fs(RPRF)e FI(ma)m(y)i(not)g(b)s(e)f(indistinguishable.)-58 3801 y Fz(Case)k(1:)i Fi(r)-5 b(andom)655 3815 y FH(1)694 3801 y FI(\(\))36 b Fz(outputs)f(random)g(elemen)m(ts)g(in)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2342 3768 y Ft(`)2377 3801 y Fz(.)46 b FI(In)30 b(this)h(\014rst)g(case,)h Fs(RPRF)f FI(and)f Fs(ALLR)h FI(are)108 3938 y(computationally)f (indistinguishable)e(under)f(the)h(assumption)g(that)h Fl(F)38 b FI(is)28 b(a)h Fs(PRF)e FI(in)h Fl(F)3191 3952 y Ft(n;m)3349 3938 y FI(for)g Fw(k)3580 3886 y Ft(R)3561 3938 y Fl( )d(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3897 3905 y Ft(`)3933 3938 y FI(.)108 4051 y(Ho)m(w)m(ev)m(er,)25 b Fs(REAL)e FI(and)f Fs(RPRF)g FI(are)h(not)g(indistinguishable)g(with) f(the)h(ab)s(o)m(v)m(e)h(parameters:)g(in)e(the)h Fs(REAL)g FI(game,)108 4183 y Fw(k)29 b FI(=)c Fw(g)326 4150 y Ft(xy)433 4183 y Fl(2)f Fu(G)p FI(,)30 b(while)g(in)g(the)g Fs(RPRF)f FI(game,)i Fw(k)1757 4131 y Ft(R)1738 4183 y Fl( )25 b(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2074 4150 y Ft(`)2109 4183 y FI(.)30 b(The)g(latter)h(is)f(in)g Fu(G)f FI(with)h(negligible)i(probabilit)m(y)-8 b(,)108 4296 y(and)30 b(th)m(us)g(the)h(Decisional)h(Di\016e-Hellman)g (assumption)e(is)h(not)f(enough.)-58 4409 y Fz(Case)k(2:)i Fi(r)-5 b(andom)655 4423 y FH(1)694 4409 y FI(\(\))36 b Fz(outputs)f(random)g(elemen)m(ts)g(in)g Fu(G)p Fz(.)45 b FI(In)29 b(this)g(case,)i(the)f(t)m(w)m(o)h(\014rst)e(games)h Fs(REAL)f FI(and)108 4522 y Fs(RPRF)23 b FI(are)h(computationally)h (indistinguishable)e(under)f(the)i(assumption)f(of)h(the)f(in)m (tractabilit)m(y)k(of)c(the)h(deci-)108 4634 y(sional)k (Di\016e-Hellman)i(problem.)d(Ho)m(w)m(ev)m(er,)j Fs(RPRF)c FI(and)h Fs(ALLR)g FI(are)h(not)g(indistinguishable)f(using)g (classical)108 4747 y(pseudo-random)e(functions,)h(where)f(the)i(k)m (eys)f(\(the)h(indices\))f(m)m(ust)g(b)s(e)g(uniformly)f(distributed)g Fw(`)p FI(-bit)h(strings)108 4860 y(to)31 b(pro)m(vide)g (\\almost-random")h(functions)e(as)g(w)m(e)h(will)g(illustrate)g(in)f (the)h(follo)m(wing)h(subsection.)-58 5122 y Fz(2.3)105 b(F)-9 b(ormal)35 b(Evidence)h(that)e Fm(\006)1286 5136 y Fq(0)1366 5122 y Fz(\(without)g(Randomness)i(Extraction\))e(is)h (Insecure)-58 5301 y FI(The)30 b(follo)m(wing)i(theorem)f(con)m (tradicts)h(the)e(main)g(theorem)h(6)g(from)f([19]:)-58 5472 y Fz(Theorem)35 b(2.)46 b Fx(Ther)-5 b(e)33 b(exists)g Fh(PRF)f Fx(for)h(which)h Fw(\006)1696 5486 y FH(0)1768 5472 y Fx(\(without)g(any)f(r)-5 b(andomness)35 b(extr)-5 b(action\))35 b(c)-5 b(an)33 b(b)-5 b(e)33 b(br)-5 b(oken.)1927 5744 y FI(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop -58 -83 a Fx(Pr)-5 b(o)g(of.)47 b FI(Let)35 b(us)f(sho)m(w)h(with)f(the)h(follo)m(wing)h(easy)g Fz(coun)m(ter-example)g FI(that)f(the)g(ab)s(o)m(v)m(e)h(standard)d (assumption)-58 30 y(ab)s(out)41 b(pseudo-random)e(functions)i(is)f (not)h(enough)g(here:)g(let)h(us)e(assume,)h(as)g(suggested)g(in)g ([19],)h(that)f Fu(G)g FI(is)-58 143 y(the)f(subgroup)f(of)h(prime)g (order)g Fw(q)j FI(in)c Fu(Z)1402 110 y Ft(?)1402 165 y(p)1442 143 y FI(,)h(where)g Fw(q)s Fl(j)p Fw(p)26 b Fl(\000)h FI(1.)40 b(This)g(usually)g(means)g(that)h Fw(p)e FI(is)i(an)f Fw(`)p FI(-bit)g(prime,)-58 266 y(with)f Fw(`)g Fl(\025)g FI(1024,)i(while)e Fw(q)i FI(is)e(160-bit)i(long.)e(F) -8 b(or)40 b(clarit)m(y)-8 b(,)41 b(let)f(us)e(assume)h(that)g(2)2885 233 y Ft(`)p Fj(\000)p FH(1)3048 266 y Fw(<)g(p)g(<)g FI(2)3398 233 y Ft(`)3432 266 y FI(.)g(Let)g Fl(F)48 b FI(b)s(e)38 b(a)-58 379 y Fs(PRF)f FI(in)h Fl(F)327 393 y Ft(n;m)456 379 y FI(,)g(for)f Fw(k)k FI(randomly)c(dra)m(wn)g (from)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1892 346 y Ft(`)1927 379 y FI(.)38 b(Let)g(us)f(consider)h(the)f(follo)m(wing)i (family)f(of)g(functions)-58 492 y Fl(G)d FI(=)30 b(\()p Fw(g)210 507 y Ft(k)253 492 y FI(\))288 507 y Ft(k)331 492 y FI(:)j(if)g Fw(k)g Fl(2)d Fu(G)p FI(,)j(then)g Fw(g)1028 507 y Ft(k)1071 492 y FI(\()p Fw(x)p FI(\))d(=)f(0)1368 459 y Ft(m)1468 492 y FI(for)k(an)m(y)h Fw(x)29 b Fl(2)h(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2177 459 y Ft(n)2226 492 y FI(,)33 b(else)h Fw(g)2502 507 y Ft(k)2575 492 y FI(=)29 b Fw(f)2720 507 y Ft(k)2763 492 y FI(.)k(Since)g(w)m(e)g(mo)s(dify)g(a) g(negligible)-58 604 y(subfamily)44 b(of)g Fl(F)9 b FI(,)44 b(the)h(family)f Fl(G)50 b FI(is)44 b(also)h(a)f Fs(PRF)g FI(for)g Fw(k)j FI(in)d Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2387 571 y Ft(`)2466 604 y FI(or)44 b Fw(k)k FI(in)43 b Fu(Z)2866 571 y Ft(?)2866 627 y(p)2906 604 y FI(,)h(but)f(clearly)j (not)e(for)g Fw(k)j FI(in)-58 727 y Fu(G)25 b FI(=)g Fl(f)p Fw(k)k Fl(2)c(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)561 694 y Ft(`)611 727 y Fl(j)g Fw(k)701 694 y Ft(q)765 727 y FI(=)25 b(1)h(mo)s(d)e Fw(p)p Fl(g)p FI(.)83 840 y(Ev)m(en)37 b(a)g(passiv)m(e)g(adv)m(ersary)f(can)h(learn)g(the)f(session)h(k)m (eys,)g(since)g(they)f(are)h(all)g(equal)g(to)g(0)3376 807 y Ft(m)3443 840 y FI(.)g(Indeed,)f(the)-58 953 y(master)31 b(secret)g(is)g(alw)m(a)m(ys)h(a)e(Di\016e-Hellman)j(v)-5 b(alue,)31 b(and)e(th)m(us)h(in)g Fu(G)p FI(.)1499 b Fl(u)-61 b(t)-58 1147 y FI(The)28 b(same)g(argumen)m(t)h(prohibits)e (the)i(use)e(of)i(the)f(ElGamal)h(encryption)f([24])i(for)e(messages)h (whic)m(h)f(do)g(not)g(lie)h(in)-58 1260 y(the)i(group.)g(The)g (conclusion)g(of)h(this)f(section)h(is)f(that)h(new)e(to)s(ols)i(are)f (needed)g(to)h(\014ll)f(the)g(theoretical)j(gap.)d(The)-58 1373 y(designers)c(of)g(SIGMA/IKE)g(w)m(ere)g(a)m(w)m(are)h(of)f(that,) h(as)f(explained)g(in)f(the)h(app)s(endices)f(of)h(the)g(full)g(v)m (ersion)g(of)g([37].)-58 1486 y(It)34 b(has)f(also)h(b)s(een)e (discussed)h(in)g(the)g(IETF)g(mailing)h(list)g([30].)h(Ho)m(w)m(ev)m (er,)h(one)d(can)h(explicitly)h(read)e(in)g([19])i(the)-58 1599 y(t)m(w)m(o)d(follo)m(wing)g(statemen)m(ts.)g(First,)f(in)f(the)h (notes)f(righ)m(t)h(after)g(the)g(description)f(of)h(the)f(proto)s(col) i Fw(\006)3473 1613 y FH(0)3512 1599 y FI(,)f(one)f(reads)108 1776 y(In)37 b(practice,)i(it)f(is)g(recommended)f(not)g(to)i(use)e (the)h(plain)f(v)-5 b(alue)38 b Fw(g)2522 1743 y Ft(xy)2641 1776 y FI(of)g(the)g(DH)g(k)m(ey)g(but)f(a)h(hashed)108 1889 y(v)-5 b(alue)37 b Fw(H)7 b FI(\()p Fw(g)513 1856 y Ft(xy)596 1889 y FI(\))37 b(where)f Fw(H)44 b FI(is)36 b(a)i(hash)e(function)g(\(e.g.)j(a)e(cryptographic)g(hash)f(function)g (suc)m(h)h(as)g(SHA)108 2002 y(or)44 b(a)h(univ)m(ersal)f(hash)g (function,)g(etc.\).)i(This)d(has)h(the)g(e\013ect)i(of)e(pro)s(ducing) f(a)h(n)m(um)m(b)s(er)f(of)h(bits)h(as)108 2115 y(required)35 b(to)h(k)m(ey)h(the)f(PRF,)g(and)f(\(dep)s(ending)f(on)i(the)f(prop)s (erties)g(of)h(the)g(hash)f(function\))h(ma)m(y)g(also)108 2228 y(help)i(to)h(\\extracting)h(the)f(securit)m(y)g(en)m(trop)m(y")g (from)f(the)g Fw(g)2246 2195 y Ft(xy)2366 2228 y FI(output.)g Fz(If)43 b(the)h(plain)g Fw(g)3318 2195 y Ft(xy)3443 2228 y Fz(is)g(used,)108 2341 y(our)36 b(securit)m(y)g(results)g(hold)f (under)h(the)f(DDH)g(assumption.)d FI(Using)f(a)g(hashed)f(v)-5 b(alue)31 b(of)g Fw(g)3618 2308 y Ft(xy)3731 2341 y FI(is)108 2454 y(secure)g(under)d(the)j(\(p)s(ossibly)f(w)m(eak)m(er\))i(HDH)f (assumption.)-58 2632 y(It)g(then)f(refers)g(to)h(the)f(subsection)h (5.6,)g(where)f(w)m(e)h(can)g(\014nd)108 2809 y(W)-8 b(e)33 b(men)m(tioned)f(in)f(Section)i(3)f([the)g(ab)s(o)m(v)m(e)h (note])f(that)g(it)h(is)e Fz(advisable)h FI(in)f(practice)i(to)g(hash)d (the)i(DH)108 2922 y(v)-5 b(alue)21 b Fw(g)379 2889 y Ft(xy)482 2922 y FI(to)g(the)g(length)h(of)f(the)g(PRF's)g(k)m(ey)g (from)g(whic)m(h)f(further)g(k)m(eys)h(are)g(deriv)m(ed.)g(In)f (particular,)i Fz(this)108 3035 y(ma)m(y)28 b(result)g(in)g(b)s(etter)f (securit)m(y)f FI(of)e(the)g(resultan)m(t)h(hashed)f(bits)g(relativ)m (e)i(to)f(the)f(initial)i(plain)e(string)108 3148 y Fw(g)154 3115 y Ft(xy)236 3148 y FI(.)29 b Fz(The)k(use)g(of)g(all)g(of)g Fw(g)1104 3115 y Ft(xy)1219 3148 y Fz(as)g(if)g(they)f(w)m(ere)h(all)g (p)s(erfectly)g(random)g(is)h(generally)f(justi\014ed)108 3261 y(b)m(y)j(the)f(DDH)h(assumption.)c FI(Ho)m(w)m(ev)m(er,)h(while)e (this)g(assumption)f(is)h(considered)g(\\standard")g(these)108 3374 y(da)m(ys,)j(it)f(actually)i(constitutes)f(a)g(v)m(ery)f(strong)h (conjecture)g(ab)s(out)e(the)i(strength)f(of)g(the)g(DH)h(k)m(ey)g Fw(g)3685 3341 y Ft(xy)3767 3374 y FI(:)108 3487 y(namely)43 b(that)g Fx(al)5 b(l)53 b FI(bits)42 b(in)g(this)h(k)m(ey)g(are)g(sim)m (ultaneously)g(indistinguishable)g(from)f(random)g(for)g(an)108 3600 y(observ)m(er)31 b(of)f Fw(g)617 3567 y Ft(x)692 3600 y FI(and)g Fw(g)915 3567 y Ft(y)957 3600 y FI(.)-58 3778 y(Con)m(trary)k(to)h(these)g(claims,)g(the)f(DDH)h(assumption)f (do)s(es)g(not)g(sa)m(y)h(that)f Fz(all)39 b(bits)h(in)f(this)g(k)m(ey) g(are)g(sim)m(ul-)-58 3891 y(taneously)g(indistinguishable)h(from)g (random)p FI(,)34 b(but)g(just)f(that)i(the)f(min-en)m(trop)m(y)h(is)f (of)g(log)17 b Fw(q)s FI(,)34 b(where)g Fw(q)j FI(is)-58 4003 y(the)29 b(prime)g(order)g(of)g(the)g(group.)g(Our)f(\014rst)g (goal)j(in)e(this)g(pap)s(er)f(is)h(th)m(us)g(to)h(insist)f(on)g(this)g (usual)g(simpli\014cation.)-58 4116 y(The)i(practical)j(solution)e(is)g (th)m(us)f(the)h(use)f(of)h(a)g(randomness)f(extractor,)i(and)e(namely) h(the)g(use)f(of)h(the)g(Lefto)m(v)m(er)-58 4229 y(Hash)e(Lemma)h([32]) h(with)e(\(almost\))i(univ)m(ersal)e(hash)g(functions)g([32,)17 b(22].)-58 4494 y Fy(3)112 b(T)-9 b(o)m(w)m(ards)38 b(a)g (Justi\014cation)g(of)f(IKE)-58 4705 y FI(Con)m(trary)42 b(to)h(the)g(ab)s(o)m(v)m(e)g Fw(\006)975 4719 y FH(0)1057 4705 y FI(proto)s(col,)g(IKE)f(indeed)g(applies)g(a)h(preliminary)e (transformation)i(randomness)-58 4818 y(extraction\))d(to)f(the)g (master)f(secret,)h(also)g(denoted)g Fv(prf)p FI(.)e(It)h(furthermore)f (suggests)i(to)g(implemen)m(t)g Fv(prf)e FI(with)-58 4930 y(HMA)m(C.)42 b(Do)s(dis)f Fx(et)i(al.)f FI([22])g(analyzed)g (usual)f(MA)m(Cs,)h(namely)f(the)g(CBC-MA)m(C)h(and)f(HMA)m(C,)h(and)f (iterated)-58 5043 y(hash)34 b(functions)f(\(Cascade\))j(as)f (randomness)e(extractors)i(\(RE\).)g(In)f(fact,)h(they)g(pro)m(v)m(e)g (that)g(NMA)m(C)g(is)f(a)h(go)s(o)s(d)-58 5156 y(randomness)g (extractor.)j(But,)f(what)f(do)s(es)f(happ)s(en)g(if)h(a)h(PRF)f(is)g (used.)g(W)-8 b(e)37 b(sho)m(w)f(here)g(that)h(some)f(PRF)g(are)-58 5269 y(go)s(o)s(d)f(RE.)f(It)h(is)g(w)m(orth)m(while)g(to)g(sa)m(y)h (here)e(that)h(as)g(noted)g(with)f(an)h(example)g(in)g([22],)h(not)f (all)g(PRF)g(are)g(go)s(o)s(d)-58 5382 y(RE.)d(Moreo)m(v)m(er,)h(w)m(e) f(recall)h(some)f(results)f(in)g(order)g(to)h(b)s(etter)g(explain)g (the)f(gap)h(b)s(et)m(w)m(een)g(theory)g(and)e(practice)-58 5495 y(in)g(the)h(follo)m(wing)h(section.)1927 5744 y(7)p eop end %%Page: 8 8 TeXDict begin 8 7 bop -58 -83 a Fz(3.1)105 b(Almost)35 b(Univ)m(ersal)h(Hash)f(F)-9 b(unctions)36 b(and)f(the)f(Lefto)m(v)m (er)h(Hash)g(Lemma)-58 89 y FI(More)42 b(precisely)-8 b(,)42 b(in)e([22])i(the)f(authors)g(pro)m(v)m(ed)g(the)g(prop)s(ert)m (y)f(of)h(go)s(o)s(d)g(randomness)f(extractors)i(for)e(sev)m(eral)-58 202 y(constructions)34 b(under)d(v)-5 b(arious)33 b(kinds)f(of)i (assumptions,)e(and)h(namely)g(the)g(univ)m(ersal)g(hashing)g(prop)s (ert)m(y)f(of)i(the)-58 315 y(compression)28 b(functions.)g(Under)f (suc)m(h)g(an)h(assumption,)g(they)g(manage)h(to)g(pro)m(v)m(e)f(that)h (the)f(global)h(construction)-58 428 y(pro)m(vides)h(an)h(almost)g (univ)m(ersal)g(hash)e(function)h(family)h(\()p Fs(A)m(UH)p FI(\).)-58 615 y Fz(De\014nition)k(3)46 b(\(Statistical)26 b(Distance\).)h FI(If)d Fl(D)i FI(is)d(a)h(distribution)f(o)m(v)m(er)i (some)f(\014nite)g(set)g Fw(S)29 b FI(and)23 b Fw(s)h Fl(2)h Fw(S)5 b FI(,)24 b(then)f(w)m(e)-58 728 y(denote)29 b(b)m(y)f Fl(D)s FI(\()p Fw(s)p FI(\))g(the)g(probabilit)m(y)h(of)f Fw(s)f FI(according)i(to)g Fl(D)i FI(and)c(similarly)-8 b(,)30 b(if)e Fw(X)k Fl(\022)25 b Fw(S)5 b FI(,)29 b(then)e Fl(D)s FI(\()p Fw(X)7 b FI(\))27 b(=)3488 660 y Fg(P)3584 755 y Ft(s)p Fj(2)p Ft(X)3747 728 y Fl(D)s FI(\()p Fw(s)p FI(\).)83 841 y(Let)k Fl(D)316 855 y FH(1)356 841 y Fw(;)15 b Fl(D)466 855 y FH(2)536 841 y FI(b)s(e)29 b(t)m(w)m(o)j (distributions)d(o)m(v)m(er)j(some)f(\014nite)f(set)h Fw(S)5 b FI(.)30 b(The)g(statistical)j(distance)e(b)s(et)m(w)m(een)g Fl(D)3652 855 y FH(1)3691 841 y Fw(;)15 b Fl(D)3801 855 y FH(2)3841 841 y FI(,)31 b(is)-58 954 y(de\014ned)e(as)748 1082 y Fl(jD)843 1096 y FH(1)903 1082 y Fl(\000)20 b(D)1064 1096 y FH(2)1103 1082 y Fl(j)26 b FI(=)1260 1021 y(1)p 1260 1061 46 4 v 1260 1145 a(2)1335 1082 y Fl(\001)1381 996 y Fg(X)1383 1193 y Ft(s)p Fj(2)p Ft(S)1527 1082 y Fl(jD)1622 1096 y FH(1)1662 1082 y FI(\()p Fw(s)p FI(\))20 b Fl(\000)g(D)1956 1096 y FH(2)1996 1082 y FI(\()p Fw(s)p FI(\))p Fl(j)26 b FI(=)f(max)2258 1143 y Ft(X)5 b Fj(\022)p Ft(S)2440 1082 y Fl(jD)2535 1096 y FH(1)2575 1082 y FI(\()p Fw(X)i FI(\))21 b Fl(\000)f(D)2909 1096 y FH(2)2949 1082 y FI(\()p Fw(X)7 b FI(\))p Fl(j)p Fw(:)-58 1326 y FI(W)-8 b(e)37 b(sa)m(y)f(that)g(a)g(random)f(v)-5 b(ariable)36 b Fw(X)43 b FI(on)36 b Fw(S)k FI(is)c Fw(\016)s FI(-)p Fz(uniform)h FI(if)e(the)h(statistical)i(distance)f(b)s(et)m(w)m(een)f Fw(X)43 b FI(and)35 b(the)-58 1439 y(uniform)29 b(distribution)h(on)g Fw(S)36 b FI(is)30 b(equal)h(to)g Fw(\016)s FI(.)-58 1626 y Fz(De\014nition)k(4)46 b(\(Almost)c(Univ)m(ersal)i(Hash)e(F)-9 b(unctions\).)43 b FI(Let)37 b Fl(H)g FI(=)f(\()p Fw(h)2719 1641 y Ft(k)2762 1626 y FI(\))2797 1641 y Ft(k)2877 1626 y FI(b)s(e)g(a)h(family)h(of)f(functions)f(in)-58 1739 y Fl(F)7 1753 y Ft(n;m)136 1739 y FI(,)31 b(the)h(set)f(of)g(the)g (functions)f(from)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1581 1706 y Ft(n)1661 1739 y FI(in)m(to)31 b Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2065 1706 y Ft(m)2134 1739 y FI(,)31 b(indexed)g(b)m(y)f(a)i(k)m(ey)f Fw(k)e Fl(2)d(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3277 1706 y Ft(`)3312 1739 y FI(.)31 b(W)-8 b(e)32 b(sa)m(y)g(that)f Fl(H)-58 1852 y FI(is)g(a)f Fw(\016)s FI(-almost)j(univ)m(ersal)d(hash)g(\()p Fw(\016)s FI(-)p Fs(A)m(UH)p FI(\))i(function)e(family)h(if)941 2046 y(for)f(an)m(y)g Fw(x;)15 b(y)29 b Fl(2)c(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1723 2008 y Ft(n)1772 2046 y Fw(;)g(x)26 b Fl(6)p FI(=)e Fw(y)s(;)15 b FI(Pr)2103 2107 y Ft(k)2171 2046 y FI([)p Fw(h)2248 2061 y Ft(k)2291 2046 y FI(\()p Fw(x)p FI(\))26 b(=)f Fw(h)2587 2061 y Ft(k)2630 2046 y FI(\()p Fw(y)s FI(\)])h Fl(\024)f Fw(\016)n(:)-58 2273 y FI(Note)34 b(that)g(suc)m(h)f(a)g(family)h(is)f(called)h(a)f(univ)m (ersal)g(hash)g(function)f(family)i(if)f Fw(\016)g FI(=)d(1)p Fw(=)p FI(2)3000 2240 y Ft(m)3068 2273 y FI(.)j(Consequen)m(tly)-8 b(,)34 b(w)m(e)f(set)-58 2386 y Fw(\016)c FI(=)c(1)p Fw(=)p FI(2)242 2353 y Ft(m)330 2386 y FI(+)20 b Fw(")p FI(.)-58 2573 y Fz(De\014nition)35 b(5)46 b(\(Min)e(and)h(Ren)m(yi)g (En)m(trop)m(y)f([44]\).)h FI(Let)39 b Fw(X)46 b FI(b)s(e)38 b(a)g(random)g(v)-5 b(ariable)40 b(taking)f(v)-5 b(alues)39 b(on)f(a)-58 2686 y(\014nite)d(set)h Fl(S)7 b FI(.)36 b(W)-8 b(e)36 b(de\014ne)f(the)h Fz(guessing)41 b(probabilit)m(y)d Fw(\015)5 b FI(\()p Fw(X)i FI(\))36 b(of)g Fw(X)43 b FI(and)34 b(the)i Fz(collision)42 b(probabilit)m(y)37 b Fw(\024)p FI(\()p Fw(X)7 b FI(\))-58 2799 y(of)37 b Fw(X)44 b FI(as)37 b Fw(\015)5 b FI(\()p Fw(X)i FI(\))36 b(=)g(max)p Fl(f)p FI(Pr[)p Fw(X)43 b FI(=)35 b Fw(s)p FI(])h(:)g Fw(s)f Fl(2)g(S)7 b(g)37 b FI(and)f Fw(\024)p FI(\()p Fw(X)7 b FI(\))37 b(=)2210 2731 y Fg(P)2306 2826 y Ft(s)p Fj(2S)2453 2799 y FI(Pr)o([)p Fw(X)44 b FI(=)35 b Fw(s)p FI(])2868 2766 y FH(2)2907 2799 y FI(.)i(The)f Fz(min)42 b(en)m(trop)m(y)d FI(of)d Fw(X)-58 2912 y FI(is)e Fz(H)119 2926 y Fj(1)226 2912 y FI(=)d(log)446 2934 y FH(2)485 2912 y FI(\(1)p Fw(=\015)5 b FI(\()p Fw(X)i FI(\)\))37 b(while)d(the)h Fz(Ren)m(yi)40 b(en)m(trop)m(y)c FI(is)e Fz(H)2155 2926 y FH(2)2226 2912 y FI(=)e(log)2446 2934 y FH(2)2485 2912 y FI(\(1)p Fw(=\024)p FI(\()p Fw(X)7 b FI(\)\),)38 b(and)c(w)m(e)g(ha)m(v)m(e)i(the)e(follo)m(wing)-58 3025 y(inequalit)m(y)e Fw(\015)5 b FI(\()p Fw(X)i FI(\))568 2992 y FH(2)634 3025 y Fl(\024)25 b Fw(\024)p FI(\()p Fw(X)7 b FI(\))27 b Fl(\024)e Fw(\015)5 b FI(\()p Fw(X)i FI(\).)-58 3212 y(The)30 b(Lefto)m(v)m(er)i(Hash)e(Lemma)h([32,)16 b(31])32 b(pro)m(vides)e(the)h(most)g(w)m(ell-kno)m(wn)g Fx(pr)-5 b(ob)g(abilistic)34 b(r)-5 b(andomness)36 b(extr)-5 b(actor)10 b FI(:)-58 3376 y Fz(Lemma)35 b(6)46 b(\([32]\).)37 b Fx(L)-5 b(et)35 b Fl(D)j Fx(b)-5 b(e)34 b(a)h(pr)-5 b(ob)g(abilistic)37 b(distribution)f(over)f Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2597 3343 y Ft(n)2681 3376 y Fx(with)36 b(min-entr)-5 b(opy)36 b(at)g(le)-5 b(ast)36 b Fw(\033)s Fx(.)e(L)-5 b(et)-58 3489 y Fw(e)37 b Fx(b)-5 b(e)37 b(an)h(inte)-5 b(ger)37 b(and)h Fw(m)33 b FI(=)g Fw(\033)26 b Fl(\000)d FI(2)p Fw(e)p Fx(.)38 b(L)-5 b(et)37 b Fl(H)d FI(=)f Fl(f)p Fw(h)1773 3504 y Ft(k)1816 3489 y Fl(g)1861 3504 y Ft(k)1905 3489 y Fx(,)j(with)i Fw(h)2223 3504 y Ft(k)2299 3489 y Fl(2)33 b(F)2458 3503 y Ft(n;m)2624 3489 y Fx(for)38 b(any)g Fw(k)e Fl(2)d(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3350 3456 y Ft(`)3385 3489 y Fx(,)37 b(b)-5 b(e)37 b(an)g(almost)-58 3602 y(universal)i(hash)g(function)g(family.)g (L)-5 b(et)38 b Fw(H)45 b Fx(b)-5 b(e)38 b(a)h(r)-5 b(andom)40 b(variable)f(uniformly)h(distribute)-5 b(d)39 b(on)g Fl(H)q Fx(,)e Fw(X)46 b Fx(denotes)-58 3715 y(a)39 b(r)-5 b(andom)42 b(variable)d(taking)g(value)g(in)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1568 3682 y Ft(n)1617 3715 y Fx(,)38 b(and)i Fw(H)r(;)15 b(X)47 b Fx(ar)-5 b(e)39 b(indep)-5 b(endent.)40 b(Then,)f FI(\()p Fw(H)r(;)15 b(H)7 b FI(\()p Fw(X)g FI(\)\))41 b Fx(is)e FI(2)3688 3682 y Fj(\000)p FH(\()p Ft(e)p FH(+1\))3925 3715 y Fx(-)-58 3828 y(uniform)33 b(on)h Fl(H)20 b(\002)g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)828 3795 y Ft(m)897 3828 y Fx(.)-58 3992 y FI(Impagliazzo)35 b(and)e(Zuc)m(k)m(erman)g(in)g([32])h(pro)m(v) m(e)g(the)f(lemma)h(with)e(almost)i(univ)m(ersal)g(hash)e(function)h (where)f Fw(")e FI(=)-58 4105 y(1)p Fw(=)p FI(2)77 4072 y Ft(n)125 4105 y FI(.)i(In)e([22],)i(it)g(is)f(pro)m(v)m(ed)g(for)g (an)m(y)g Fw(\016)s FI(-almost)i(univ)m(ersal)f(hash)e(function)g (family)i(for)f Fw(")26 b Fl(\034)g FI(1)p Fw(=)p FI(2)3347 4072 y Ft(m)3415 4105 y FI(.)31 b(See)h(also)f([44])-58 4218 y(for)26 b(a)h(pro)s(of.)f(Therefore,)g(com)m(bined)h(with)f(the)h (analysis)g(of)f(NMA)m(C)h(as)g(a)g Fw(\016)s FI(-)p Fs(A)m(UH)g FI(function,)f(this)h(ma)m(y)g(justify)f(the)-58 4330 y(design)31 b(of)g(IKE)g(when)f(HMA)m(C)h(is)g(used)g(under)e(a)i (sp)s(eci\014c)g(assumption)g(on)g(the)g(indep)s(endence)e(of)j(the)f (t)m(w)m(o)h(k)m(eys)-58 4443 y(in)k(NMA)m(C.)g(W)-8 b(e)37 b(sho)m(w)f(in)g(the)g(follo)m(wing)h(that)f(the)g(same)g (result)g(holds)f(for)h(some)g(PRF)g(pro)m(vided)f Fw(")i FI(b)s(e)e(tak)m(en)-58 4556 y(in)m(to)d(accoun)m(t)g(to)f(estimate)i (the)e(size)g(of)g(the)g(output.)g(Ho)m(w)m(ev)m(er,)i(w)m(e)e(b)s (egin)f(to)i(pro)m(v)m(e)f(a)g(sligh)m(t)h(generalization)i(of)-58 4669 y(the)d(LHL,)f(similar)h(to)g([22].)-58 4856 y Fz(Lemma)k(7)46 b(\(LHL)28 b(with)h FI(\(1)p Fw(=)p FI(2)1091 4823 y Ft(m)1171 4856 y FI(+)11 b Fw(")p FI(\))p Fz(-)p Ff(A)m(UH)p Fz(\).)30 b Fx(L)-5 b(et)28 b Fl(D)j Fx(b)-5 b(e)29 b(a)g(pr)-5 b(ob)g(abilistic)30 b(distribution)f(over)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3501 4823 y Ft(n)3579 4856 y Fx(with)29 b(min-)-58 4969 y(entr)-5 b(opy)36 b(at)e(le)-5 b(ast)35 b Fw(\033)s Fx(.)f(L)-5 b(et)34 b Fw(e)g Fx(b)-5 b(e)34 b(an)h(inte)-5 b(ger)34 b(and)h Fw(m)27 b Fl(\024)g Fw(\013)22 b Fl(\000)f FI(2)p Fw(e)34 b Fx(wher)-5 b(e)35 b Fw(\013)28 b FI(=)f(min\()p Fw(\033)n(;)15 b FI(log)2999 4991 y FH(2)3039 4969 y FI(\(1)p Fw(=")p FI(\)\))p Fx(.)36 b(L)-5 b(et)34 b Fl(H)28 b FI(=)f Fl(f)p Fw(h)3798 4984 y Ft(k)3842 4969 y Fl(g)3887 4984 y Ft(k)3930 4969 y Fx(,)-58 5082 y(with)35 b Fw(h)193 5097 y Ft(k)264 5082 y Fl(2)28 b(F)418 5096 y Ft(n;m)582 5082 y Fx(for)34 b(any)h Fw(k)d Fl(2)27 b(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1291 5049 y Ft(`)1327 5082 y Fx(,)34 b(b)-5 b(e)34 b(a)g FI(\(1)p Fw(=)p FI(2)1752 5049 y Ft(m)1842 5082 y FI(+)21 b Fw(")p FI(\))p Fx(-almost)36 b(universal)f(hash)h(function)e(family.)h(L)-5 b(et)35 b Fw(H)41 b Fx(b)-5 b(e)-58 5195 y(a)35 b(r)-5 b(andom)37 b(variable)e(uniformly)h(distribute)-5 b(d)36 b(on)f Fl(H)q Fx(,)f Fw(X)42 b Fx(denotes)36 b(a)f(r)-5 b(andom)37 b(variable)e(taking)g(value)f(in)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3881 5162 y Ft(n)3930 5195 y Fx(,)-58 5308 y(and)34 b Fw(H)r(;)15 b(X)40 b Fx(ar)-5 b(e)33 b(indep)-5 b(endent.)34 b(Then,)f FI(\()p Fw(H)r(;)15 b(H)7 b FI(\()p Fw(X)g FI(\)\))35 b Fx(is)e FI(2)1904 5275 y Fj(\000)p Ft(e)1996 5308 y Fx(-uniform)g(on)g Fl(H)21 b(\002)e(f)p FI(0)p Fw(;)c FI(1)p Fl(g)2914 5275 y Ft(m)2983 5308 y Fx(.)-58 5495 y(Pr)-5 b(o)g(of.)47 b FI(The)30 b(pro)s(of)f(relies)j (on)e(t)m(w)m(o)i(claims.)1927 5744 y(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop -58 -83 a Fx(Claim)47 b(\([44]\).)38 b FI(Let)f Fw(X)43 b FI(b)s(e)35 b(a)i(random)e(v)-5 b(ariable)37 b(distributed)e(according)i(a)f(distribution)g Fl(D)s FI(,)g(taking)h(v)-5 b(alues)36 b(on)-58 30 y(the)30 b(\014nite)g(set)h Fw(S)k FI(and)29 b(of)h(collision)i(probabilit)m(y)f Fw(\024)25 b FI(=)g Fw(\024)p FI(\()p Fw(X)7 b FI(\).)32 b(If)d Fw(X)38 b FI(is)30 b Fw(\016)s FI(-uniform)g(on)g Fw(S)5 b FI(,)30 b(then)g Fw(\024)25 b Fl(\025)g FI(\(1)20 b(+)g(4)p Fw(\016)3700 -3 y FH(2)3740 30 y FI(\))p Fw(=)p Fl(j)p Fw(S)5 b Fl(j)p FI(.)-58 181 y(The)23 b(second)h(claim)h (studies)e(the)h(collision)h(probabilit)m(y)f Fw(\024)i FI(=)f Fw(\024)p FI(\()p Fw(H)r(;)15 b(H)7 b FI(\()p Fw(X)g FI(\)\))26 b(where)d Fw(H)30 b FI(denotes)24 b(a)g(random)f(v)-5 b(ariable)-58 294 y(with)36 b(uniform)f(probabilit)m(y)h(on)g Fl(H)q FI(,)g Fw(X)43 b FI(denotes)36 b(a)h(random)e(v)-5 b(ariable)37 b(on)f(the)g(set)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3124 261 y Ft(n)3173 294 y FI(,)37 b(and)e Fw(H)43 b FI(and)35 b Fw(X)43 b FI(are)-58 407 y(indep)s(enden)m(t.)31 b(W)-8 b(e)32 b(can)g(easily)h(adapt)f(the)f(pro)s(of)g(of)h([44])h(to) f(pro)m(v)m(e)g(that)g(the)g(statistical)i(distance)e(b)s(et)m(w)m(een) h(the)-58 520 y(distribution)e(of)i(\()p Fw(H)r(;)15 b(H)7 b FI(\()p Fw(X)g FI(\)\))34 b(and)d(the)h(uniform)f(distribution) h(on)f Fl(H)22 b(\002)f(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2717 487 y Ft(m)2818 520 y FI(is)32 b Fw(\016)s FI(,)h(whic)m(h)f(is)g(at)h (most)f(\(1)p Fw(=)p FI(2\))24 b Fl(\001)-58 555 y Fg(p)p 33 555 455 4 v 78 x FI(2)78 607 y Ft(m)165 633 y Fl(\001)d FI(\()p Fw(\024)g FI(+)f Fw(")p FI(\).)32 b(So)g(it)h(can)f(b)s(e)f (upp)s(er-b)s(ounded)d(b)m(y)k(\(1)p Fw(=)p FI(2\))23 b Fl(\001)2093 555 y Fg(p)p 2184 555 550 4 v 78 x FI(2)2229 607 y Ft(m)2317 633 y Fl(\001)d FI(\(2)2442 607 y Fj(\000)p Ft(\033)2565 633 y FI(+)g Fw(")p FI(\),)33 b(since)f(the)g(collision)h (probabilit)m(y)-58 746 y Fw(\024)e FI(is)f(less)h(than)f(the)h (guessing)f(probabilit)m(y)h Fw(\015)36 b FI(as)30 b(noted)h(in)f (de\014nition)g(5.)83 859 y(If)g(w)m(e)h(denote)g(b)m(y)f Fw(\013)25 b FI(=)g(min\()p Fw(\033)n(;)15 b FI(log)1301 881 y FH(2)1341 859 y FI(\(1)p Fw(=")p FI(\)\),)32 b(then)e(w)m(e)h (can)g(upp)s(er-b)s(ound)26 b Fw(\016)34 b FI(b)m(y)c(\(1)p Fw(=)p FI(2\))22 b Fl(\001)3155 780 y(p)p 3231 780 439 4 v 79 x FI(2)3276 833 y Ft(m)3363 859 y Fl(\001)f FI(2)f Fl(\001)h FI(2)3565 833 y Fj(\000)p Ft(\013)3700 859 y FI(and)30 b(so)-58 972 y(if)g(w)m(e)h(w)m(an)m(t)h(a)e(bias)h(of)f(2) 793 939 y Fj(\000)p Ft(e)916 972 y FI(w)m(e)h(need)f Fw(m)25 b Fl(\024)g Fw(\013)20 b Fl(\000)g FI(2)p Fw(e)p FI(.)2153 b Fl(u)-61 b(t)-58 1143 y Fx(R)-5 b(emark)34 b(8.)46 b FI(This)38 b(requires)h Fw(")h Fl(\034)f FI(1)p Fw(=)p FI(2)1313 1110 y Ft(m)1420 1143 y FI(as)g(it)h(is)f(observ)m(ed) g(in)f([22],)j(but)d Fw(")i Fl(\024)f FI(1)p Fw(=)p FI(2)2945 1110 y Ft(m)p FH(+2)p Ft(e)3175 1143 y FI(is)g(enough.)g(An)m(yw)m(a)m (y)-8 b(,)-58 1256 y(this)35 b(de\014nitely)f(excludes)h(functions)f (families)i(where)e(the)h(k)m(ey-length)h(is)f(the)g(same)g(as)f(the)h (output-length)g(\(as)-58 1369 y(compression)30 b(functions\).)-58 1612 y Fz(3.2)105 b(Pseudo-Random)39 b(F)-9 b(unctions,)39 b(Almost)f(Univ)m(ersal)g(Hash)f(F)-9 b(unctions)39 b(and)e(Randomness) 180 1725 y(Extractors)-58 1885 y FI(W)-8 b(e)37 b(ha)m(v)m(e)g(already) f(discussed)f(the)h(practical)h(meaning)f(of)g(the)f(univ)m(ersal)h (hashing)f(prop)s(ert)m(y)g(for)h(compression)-58 1998 y(functions.)25 b(Ho)m(w)m(ev)m(er,)i(the)e(design)f(of)h(IKE)f([28,)17 b(35])26 b(uses)e(the)h(acron)m(ym)g Fv(prf)f FI(at)h(sev)m(eral)h (places,)g(for)f(di\013eren)m(t)g(pur-)-58 2110 y(p)s(oses:)j (randomness)g(extractors)h(and)f(actual)i(PRF.)f(Ho)m(w)m(ev)m(er,)i(w) m(e)e(recall)g(here)g(the)f Fx(crucial)38 b FI(di\013erence)29 b(b)s(et)m(w)m(een)-58 2223 y(pseudo-random)35 b(function)h(and)f (randomness)g(extraction:)j(the)e(former)g(uses)g(random)f Fx(se)-5 b(cr)g(et)46 b FI(k)m(eys,)37 b(while)f(the)-58 2336 y(latter)d(uses)f(random)f Fx(but)i(known)40 b FI(k)m(eys.)32 b(W)-8 b(e)33 b(th)m(us)f(sho)m(w)f(b)s(elo)m(w)h(that)h(the)f Fx(str)-5 b(ong)41 b FI(assumption)31 b(of)h(PRF)g(implies)-58 2449 y(the)26 b(almost)h(univ)m(ersal)f(hashing)g(prop)s(ert)m(y)-8 b(.)26 b(Therefore,)f(the)i(Lefto)m(v)m(er)g(Hash)f(Lemma)g(7)g (applied)g(with)f(some)i(PRF)-58 2562 y(\(namely)e(k)m(ey)m(ed)h(with)f (uniform)e(random)h(bit-strings)h(and)f(with)h(adv)-5 b(an)m(tage)26 b(su\016cien)m(tly)g(small\))f(pro)m(vides)g(a)g(go)s(o) s(d)-58 2675 y(randomness)k(extractor.)-58 2826 y Fz(Theorem)35 b(9.)46 b Fx(If)26 b(a)h(family)h(of)e(functions)h Fl(F)36 b Fx(is)27 b(a)g FI(\(2)p Fw(;)15 b(";)g FI(2)p Fw(T)2001 2841 y Ft(f)2049 2826 y FI(\))p Fx(-)p Fh(PRF)26 b Fx(in)g Fl(F)2482 2840 y Ft(n;m)2611 2826 y Fx(,)h(then)g(it)f(is)h(a)g FI(\(1)p Fw(=)p FI(2)3281 2794 y Ft(m)3356 2826 y FI(+)7 b Fw(")p FI(\))p Fx(-)p Fh(A)m(UH)27 b Fx(func-)-58 2939 y(tion)33 b(family,)h(wher)-5 b(e)33 b Fw(T)744 2954 y Ft(f)822 2939 y Fx(denotes)h(the)f(maximal)h(time)f(to)g(evaluate)g (an)h(instanc)-5 b(e)33 b(of)g Fl(F)42 b Fx(on)33 b(any)g Fw(x)25 b Fl(2)g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3724 2906 y Ft(n)3773 2939 y Fx(.)-58 3111 y(Pr)-5 b(o)g(of.)47 b FI(W)-8 b(e)30 b(w)m(an)m(t)g(to)f(sho)m(w)g(that)g(if)g(an)g(univ)m (ersal)g(hash)f(function)g(family)i(is)f(not)g(\(1)p Fw(=)p FI(2)2983 3078 y Ft(m)3068 3111 y FI(+)17 b Fw(")p FI(\))p Fl(\000)p FI(secure,)29 b Fx(i.e.)g FI(there)-58 3224 y(exist)f Fw(x;)15 b(y)30 b FI(suc)m(h)d(that)g(Pr)814 3239 y Ft(k)856 3224 y FI([)p Fw(h)933 3239 y Ft(k)977 3224 y FI(\()p Fw(x)p FI(\))f(=)f Fw(h)1273 3239 y Ft(k)1316 3224 y FI(\()p Fw(y)s FI(\)])h Fw(>)f FI(1)p Fw(=)p FI(2)1716 3191 y Ft(m)1797 3224 y FI(+)13 b Fw(")p FI(,)28 b(then)e(w)m(e)i(can)f (\014nd)e(an)i(adv)m(ersary)g(against)i(a)e(PRF)g(with)-58 3337 y(adv)-5 b(an)m(tage)32 b(at)g(least)f Fw(")p FI(.)83 3450 y(Let)44 b(us)f(consider)h(the)f(follo)m(wing)i(family)f(of)g (distinguishers,)f Fl(D)2412 3464 y Ft(x;y)2556 3450 y FI(for)g(eac)m(h)i(pair)e(\()p Fw(x;)15 b(y)s FI(\))45 b(of)e(elemen)m(ts)i(in)-58 3563 y Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)162 3530 y Ft(n)211 3563 y FI(.)31 b(The)g(distinguisher) f Fl(D)1062 3577 y Ft(x;y)1193 3563 y FI(queries)h(the)g(oracle)i (\(either)e Fw(f)2259 3578 y Ft(k)2332 3563 y FI(for)g(a)g(random)f Fw(k)k FI(or)d(a)g(random)f(function\))h(to)-58 3675 y(get)h Fw(X)g FI(=)25 b Fw(f)10 b FI(\()p Fw(x)p FI(\))31 b(and)e Fw(Y)46 b FI(=)25 b Fw(f)10 b FI(\()p Fw(y)s FI(\),)30 b(and)g(simply)g(answ)m(ers)g(1)g(if)h Fw(X)i FI(=)24 b Fw(Y)51 b FI(and)30 b(0)g(otherwise.)83 3788 y(Supp)s(ose)k(that)i Fl(F)45 b FI(is)36 b(not)f(a)h(\(1)p Fw(=)p FI(2)1271 3755 y Ft(m)1363 3788 y FI(+)24 b Fw(")p FI(\)-)p Fs(A)m(UH)36 b FI(function)g(family)-8 b(.)36 b(It)g(means)f(there)h(exists)g(a)g(pair)g(\()p Fw(x;)15 b(y)s FI(\))36 b(for)-58 3901 y(whic)m(h)25 b(Pr)294 3916 y Ft(k)337 3901 y FI([)p Fw(f)407 3916 y Ft(k)449 3901 y FI(\()p Fw(x)p FI(\))h(=)f Fw(f)738 3916 y Ft(k)780 3901 y FI(\()p Fw(y)s FI(\)])h Fw(>)f FI(1)p Fw(=)p FI(2)1180 3868 y Ft(m)1258 3901 y FI(+)9 b Fw(")p FI(.)26 b(Let)f(us)f(consider)h (the)g(adv)-5 b(an)m(tage)27 b(of)e(the)h(corresp)s(onding)e (distinguisher)-58 4014 y Fl(D)12 4028 y Ft(x;y)113 4014 y FI(:)37 b(if)f Fw(f)46 b FI(is)36 b(a)h(truly)g(random)e(function)h (in)h Fl(F)1645 4028 y Ft(n;m)1774 4014 y FI(,)g(the)f(set)i(of)e(all)i (functions)e(from)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3228 3981 y Ft(n)3313 4014 y FI(to)38 b Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3651 3981 y Ft(m)3719 4014 y FI(,)37 b(then)-58 4127 y(Pr[)p Fl(D)135 4141 y Ft(x;y)283 4127 y FI(=)46 b(1])i(=)e(1)p Fw(=)p FI(2)770 4094 y Ft(m)838 4127 y FI(;)e(if)f Fw(f)53 b FI(is)43 b(a)h(randomly)e(c)m(hosen)i Fw(f)2062 4142 y Ft(k)2148 4127 y FI(in)f Fl(F)9 b FI(,)44 b(then)f(Pr)o([)p Fl(D)2822 4141 y Ft(x;y)2970 4127 y FI(=)k(1])g Fw(>)g FI(1)p Fw(=)p FI(2)3458 4094 y Ft(m)3555 4127 y FI(+)28 b Fw(")p FI(.)44 b(As)f(a)-58 4240 y(consequence,)34 b(the)e(adv)-5 b(an)m(tage)35 b(of)d Fl(D)1248 4254 y Ft(x;y)1382 4240 y FI(is)g(not)h(less)g(than)f Fw(")p FI(,)h(whic)m(h)f(is)h(in)f(con)m(tradiction)i(with)e(the)h(ab)s(o)m(v) m(e)h(PRF)-58 4353 y(prop)s(ert)m(y)-8 b(.)3596 b Fl(u)-61 b(t)83 4524 y FI(Therefore,)31 b(w)m(e)f(ha)m(v)m(e)i(the)f(follo)m (wing)g(corollary)h(b)m(y)f(com)m(bining)f(lemma)h(7)g(with)f(the)h (previous)f(theorem.)-58 4676 y Fz(Corollary)35 b(10.)46 b Fx(L)-5 b(et)34 b Fl(F)44 b Fx(b)-5 b(e)33 b(a)i(family)f(of)g (functions)h(in)e Fl(F)2005 4690 y Ft(n;m)2135 4676 y Fx(,)g(and)i Fw(T)2427 4691 y Ft(f)2506 4676 y Fx(denote)g(the)f (maximal)i(time)e(to)g(evaluate)-58 4789 y(an)e(instanc)-5 b(e)32 b(of)f Fl(F)41 b Fx(on)31 b(any)h Fw(x)25 b Fl(2)g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1320 4756 y Ft(n)1369 4789 y Fx(.)31 b(If)g Fl(F)41 b Fx(is)31 b(a)g FI(\(2)p Fw(;)15 b(";)g FI(2)p Fw(T)2101 4804 y Ft(f)2149 4789 y FI(\))p Fx(-)p Fh(PRF)p Fx(,)31 b(when)h(applie)-5 b(d)33 b(on)f(a)f(r)-5 b(andom)34 b(sour)-5 b(c)g(e)32 b(with)-58 4902 y(min-entr)-5 b(opy)34 b(at)g(le)-5 b(ast)33 b Fw(\033)s Fx(,)g(then)g(it)g(is)f(a)h (go)-5 b(o)g(d)35 b(r)-5 b(andomness)35 b(extr)-5 b(actor,)35 b(of)d(bias)h(b)-5 b(ounde)g(d)34 b(by)f FI(1)p Fw(=)p FI(2)3362 4869 y Ft(e)3400 4902 y Fx(,)g(as)g(so)-5 b(on)34 b(as)1401 5077 y Fw(m)25 b Fl(\024)g FI(min)o(\()p Fw(\033)n(;)15 b FI(log)1996 5098 y FH(2)2036 5077 y FI(\(1)p Fw(=")p FI(\)\))22 b Fl(\000)e FI(2)p Fw(e:)-58 5252 y Fx(R)-5 b(emark)34 b(11.)46 b FI(This)32 b(result)h(is)g(not)g(in)f(con)m (tradiction)j(with)d(the)h(example)h(describ)s(ed)e(in)g([22],)i(since) g(if)e Fw(")e FI(=)f(1)p Fw(=)p FI(2)3890 5219 y Ft(m)-58 5364 y FI(with)34 b Fw(m)g FI(bits)g(of)g(output,)g(then)g(clearly)h (min)o(\()p Fw(\033)n(;)15 b FI(log)1782 5386 y FH(2)1821 5364 y FI(\(1)p Fw(=")p FI(\)\))34 b Fl(\024)d Fw(m)p FI(.)j(The)g(ab)s(o)m(v)m(e)h(corollary)g(just)f(claims)h(that)g(the) -58 5477 y(bias)c(is)f(less)h(than)f(1.)h(As)f(a)h(consequence,)g(w)m (e)g(cannot)g(extract)h Fw(m)e FI(bits.)1927 5744 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop -58 -83 a Fy(4)112 b(Mismatc)m(hes)39 b(b)s(et)m(w)m(een)f(Theory)f(and)i(Practice)-58 162 y FI(The)k(ab)s(o)m(v)m(e)h(argumen)m(ts)f(all)i(together)f(seem)g(to)f (constitute)i(a)e(strong)h(justi\014cation)f(of)h(the)f(design)g(and)g (the)-58 274 y(securit)m(y)30 b(of)f(IKE)f(as)h(it)g(\014lls)g(the)g (gap)g(from)f(the)h(securit)m(y)h(pro)s(of)e(of)g Fw(\006)2380 288 y FH(0)2449 274 y FI(\(without)h(randomness)e(extraction\))k(with) -58 387 y(the)e(use)g(of)f(HMA)m(C,)i(as)f(a)g(randomness)f(extractor.) j(Ho)m(w)m(ev)m(er,)g(let)e(tak)m(e)i(a)e(closer)g(lo)s(ok)h(at)f(the)g (actual)h(use)f(of)g Fv(prf)-58 500 y FI(in)f(IKEv1)h([28].)h(W)-8 b(e)30 b(stress)e(again)i(that)f(these)g(mismatc)m(hes)h(do)e(not)h (endanger)f(the)h(use)f(of)h(IKE)f(and)g(are)h(only)g(of)-58 613 y(theoretical)k(in)m(terest.)-58 907 y Fz(4.1)105 b(Securit)m(y)36 b(Inaccuracy)g(in)f(the)f(Randomness)i(Extraction)f (Phase)g(of)g(IKE)-58 1119 y(Informal)44 b(Evidence)g(that)f(NO)g (Securit)m(y)h(Pro)s(of)g(of)g(IKE)f(can)h(b)s(e)g(Simply)g(Based)g(on) g(the)f(LHL.)-58 1232 y FI(In)32 b(IKE)g(\(in)h(the)f(signature)h(mo)s (de\),)g(the)g(master)g(k)m(ey)g Fv(SKEYSEED)e FI(\(whic)m(h)h(should)g (b)s(e)g(a)h(pseudo-uniformly)e(dis-)-58 1345 y(tributed)24 b(bit-string\))i(is)f(deriv)m(ed)g(with)g(the)g(ab)s(o)m(v)m(e)h Fw(\016)s FI(-)p Fs(A)m(UH)g FI(construction,)g Fv(SKEYSEED)45 b(=)j(prf\(Ni)e(|)h(Nr,)g(g^ir\))p FI(,)-58 1457 y(where)21 b Fv(Ni)f FI(and)h Fv(Nr)f FI(are)h(random)g(nonces)g Fx(chosen)29 b FI(b)m(y)21 b(the)g(participan)m(ts,)h(and)e Fv(g^ir)g FI(is)h(the)h(common)f(Di\016e-Hellman)-58 1570 y(secret.)83 1690 y(More)40 b(precisely)-8 b(,)41 b(the)e(random)f(nonces)i(sp)s(ecifying)f(the)g(c)m(hoice)i(of)e(the)h (function)f(in)g(the)g Fw(\016)s FI(-)p Fs(A)m(UH)h FI(function)-58 1803 y(family)31 b(are)g(c)m(hosen)g(b)m(y)f(the)h(pla)m(y)m(ers)g(and) f(nev)m(er)h(signed:)g(the)g(adv)m(ersary)f(could)h(edit)g(one)g(of)f (the)h(nonces|)p Fv(Ni)f FI(or)-58 1915 y Fv(Nr)p FI(|and)f(th)m(us)h (ha)m(v)m(e)i(some)f(con)m(trol)g(o)m(v)m(er)h(the)f(v)-5 b(alue)31 b Fv(SKEYSEED)p FI(.)83 2035 y(Indeed,)25 b(the)h(securit)m (y)h(results)e(pro)m(vided)h(in)f([22])i(guaran)m(tee)g(the)f(qualit)m (y)h(of)f Fv(SKEYSEED)d FI(if)j(one)g(uses)f Fz(random)-58 2148 y Fx(but)35 b(known)40 b FI(k)m(eys.)34 b(In)e(the)h(sp)s (eci\014cation)h(of)e(IKEv1,)h(the)g(adv)m(ersary)g(has)g(some)g(con)m (trol)h(o)m(v)m(er)g(this)f(random)f(k)m(ey)-58 2261 y(\(whic)m(h)f(is)f(no)g(longer)h(the)g(case)g(in)f(IKEv2.\))-58 2555 y Fz(F)-9 b(ormal)34 b(Evidence)f(of)g(the)g(Securit)m(y)h(Lev)m (el)f(of)g(the)g(LHL)f(with)h(P)m(artially)g(Random)h(Keys.)44 b FI(In)28 b(order)-58 2668 y(to)43 b(ha)m(v)m(e)g(a)f(go)s(o)s(d)f (picture)h(of)g(that,)h(let)f(us)f(\014rst)g(apply)h(the)g(LHL)f(with)h (a)g Fx(p)-5 b(erfe)g(ct)51 b FI(univ)m(ersal)42 b(hash)f(function)-58 2781 y(family)-8 b(.)37 b(The)e(linear)i(congruen)m(tial)g(hashing)e (is)h(a)g(w)m(ell-kno)m(wn)h(metho)s(d:)f(it)g(w)m(orks)g(in)f Fu(F)3101 2795 y FH(2)3136 2775 y Fn(n)3219 2781 y FI(in)g(order)h(to)g (output)-58 2894 y Fw(n)p FI(-bit)28 b(strings,)g(whic)m(h)g(are)h (thereafter)g(truncated)f(to)h(the)f Fw(m)p FI(-righ)m(tmost)h(bits.)g (More)g(precisely)-8 b(,)29 b(the)f(k)m(ey)h(is)g(a)f(pair)-58 3007 y(\()p Fw(a;)15 b(b)p FI(\))33 b Fl(2)e Fu(F)320 2974 y FH(2)320 3031 y(2)355 3012 y Fn(n)402 3007 y FI(,)j(and)g(on)g (the)h(input)e Fw(x)f Fl(2)f(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1575 2974 y Ft(n)1624 3007 y FI(,)35 b(the)f(function)g Fw(h)2256 3022 y Ft(a;b)2382 3007 y FI(outputs)g Fs(T)-8 b(runc)2939 3021 y Ft(m)3006 3007 y FI(\()p Fw(ax)23 b FI(+)g Fw(b)p FI(\).)35 b(This)e(family)i(of)-58 3119 y(2)-13 3086 y FH(2)p Ft(n)101 3119 y FI(functions)30 b(is)i(a)f(univ)m(ersal)g(hash)g(function)f(family)i(in)e Fl(F)2067 3133 y Ft(n;m)2197 3119 y FI(.)h(And)f(th)m(us,)h(the)g(ab)s (o)m(v)m(e)i(LHL)d(applies)i(p)s(erfectly)-58 3232 y(to)f(extract)h (random)e(bits.)-58 3460 y Fz(Theorem)35 b(12.)46 b Fx(Ther)-5 b(e)32 b(exist)f(universal)h(hash)g(functions)g(and)g(pseudo-r)-5 b(andom)34 b(functions)d(which)h(le)-5 b(ad)33 b(to)e(inse-)-58 3573 y(cur)-5 b(e)33 b(r)-5 b(andomness)35 b(extr)-5 b(actors,)35 b(when)e(the)g(key)f(is)h(only)h(p)-5 b(artial)5 b(ly)34 b(r)-5 b(andom.)-58 3795 y(Pr)g(o)g(of.)47 b FI(Let)31 b(us)f(consider)h(the)g(ab)s(o)m(v)m(e)g(linear)h(congruen)m (tial)g(hash.)e(By)h(making)g Fw(a)26 b FI(=)f(0,)32 b(the)e(\014nal)h(k)m(ey)g(is)g(equal)g(to)-58 3907 y Fw(b)p FI(.)g(Since)f(the)h(latter)g(is)g(public,)f(the)g(adv)m(ersary) h(kno)m(ws)f(the)h(\014nal)f(k)m(ey)-8 b(.)83 4027 y(Ma)m(yb)s(e,)27 b(a)f Fs(PRF)f FI(\(as)h(required)f(b)m(y)h(IKE\))f(w)m(ould)g(a)m(v)m (oid)j(this)d(w)m(eakness.)i(But)f(let)g(us)f(exhibit)h(another)g(coun) m(ter-)-58 4140 y(example,)h(starting)g(from)f(an)m(y)i Fs(PRF)e Fl(F)34 b FI(=)25 b(\()p Fw(f)1504 4155 y Ft(k)1547 4140 y FI(\))1582 4155 y Ft(k)1651 4140 y FI(\(p)s(ossibly)h(the)g(ab)s (o)m(v)m(e)h Fl(G)32 b FI(one,)27 b(de\014ned)e(in)h(the)g(previous)g (coun)m(ter-)-58 4253 y(example\),)38 b(with)d Fw(`)p FI(-bit)i(k)m(eys,)g(where)f Fw(`)e FI(=)h(2)p Fw(\025)p FI(.)i(Let)g(us)e(de\014ne)g(the)i(new)e(family)i Fl(H)f FI(=)e(\()p Fw(h)3134 4271 y Ft(a)p Fj(jj)p Ft(b)3246 4253 y FI(\))3281 4271 y Ft(a)p Fj(j)p Ft(b)3373 4253 y FI(,)i(b)m(y)g Fw(h)3618 4271 y Ft(a)p Fj(jj)p Ft(b)3730 4253 y FI(\()p Fw(x)p FI(\))f(=)-58 4375 y Fw(f)-13 4394 y Ft(a)p Fj(jj)p Ft(b)98 4375 y FI(\()p Fw(x)p FI(\))e(if)g Fw(a)d Fl(6)p FI(=)f(0)562 4342 y Ft(\025)608 4375 y FI(,)k(and)f Fw(h)897 4397 y FH(0)932 4378 y Fn(\025)974 4397 y Fj(jj)p Ft(b)1047 4375 y FI(\()p Fw(x)p FI(\))e(=)g(0)1345 4342 y Ft(n)1392 4375 y FI(.)j(W)-8 b(e)34 b(again)g(mo)s(dify)e(a)i (negligible)g(fraction)g(of)f Fl(F)9 b FI(,)34 b(and)e(th)m(us)g Fl(H)i FI(is)f(still)-58 4488 y(a)k Fs(PRF)p FI(.)f(Ho)m(w)m(ev)m(er,)i (with)e(the)h(con)m(trol)h(of)e(half)g(of)h(the)f(bits,)g(the)h(adv)m (ersary)f(can)h(mak)m(e)g(the)g(master)f(k)m(ey)h(to)g(b)s(e)-58 4601 y(alw)m(a)m(ys)32 b(0)278 4568 y Ft(n)325 4601 y FI(:)f(all)g(the)g(deriv)m(ed)f(k)m(eys)h(are)g(th)m(us)f(kno)m(wn)g (to)h(him.)1787 b Fl(u)-61 b(t)83 4822 y FI(In)39 b(IKEv1,)g(the)g (nonces)g(are)h(not)f(signed,)h(but)e(some)i(MA)m(C)g(are)f(applied)g (later)h(whic)m(h)f(mak)m(es)h(the)g(ab)s(o)m(v)m(e)-58 4935 y(coun)m(ter-example)32 b(irrelev)-5 b(an)m(t.)32 b(Ho)m(w)m(ev)m(er,)h(some)d(other)h(coun)m(ter-examples)h(exist:)270 5159 y Fw(h)322 5177 y FH(\()p Ft(a)386 5186 y FG(0)421 5177 y Ft(;a)478 5186 y FG(1)513 5177 y FH(\))p Ft(;)p FH(\()p Ft(b)617 5186 y FG(0)652 5177 y Ft(;b)702 5186 y FG(1)737 5177 y FH(\))768 5159 y FI(\()p Fw(x)p FI(\))26 b(=)f Fs(T)-8 b(runc)1232 5173 y Ft(m)1298 5159 y FI(\()p Fw(a)1381 5173 y FH(0)1421 5159 y Fw(b)1460 5173 y FH(0)1500 5159 y Fw(x)20 b FI(+)g Fw(a)1711 5173 y FH(1)1750 5159 y Fw(b)1789 5173 y FH(1)1829 5159 y FI(\))p Fw(;)15 b FI(with)31 b Fv(Ni)24 b FI(=)h(\()p Fw(a)2411 5173 y FH(0)2451 5159 y Fw(;)15 b(a)2539 5173 y FH(1)2579 5159 y FI(\))31 b(and)e Fv(Nr)c FI(=)g(\()p Fw(b)3112 5173 y FH(0)3152 5159 y Fw(;)15 b(b)3231 5173 y FH(1)3271 5159 y FI(\),)31 b(in)f Fu(F)3524 5173 y FH(2)3559 5153 y Fn(n)3605 5159 y Fw(:)-58 5382 y FI(This)40 b(result)h(clearly)h(sho) m(ws)f(that)g(the)g(securit)m(y)h(of)f(IKEv1)f(cannot)i(only)f(rely)g (on)f(the)h(general)h(de\014nition)f(of)-58 5495 y(univ)m(ersal)31 b(hash)e(functions)h(or)h(pseudo-random)e(functions.)1905 5744 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop -58 -83 a Fz(4.2)105 b(Coun)m(termeasure:)35 b(Certi\014ed)f(Keys)-58 86 y FI(F)-8 b(or)34 b(the)f(IKE)g (application,)h(a)g(m)m(uc)m(h)f(more)g(simple)g(alternativ)m(e)j (consists)e(in)e(signing)i(the)f(nonces.)g(It)h(is)f(almost)-58 199 y(at)28 b(no)e(cost)i(to)f(include)g(the)g(nonces)f(in)h(the)g(v)-5 b(alues)27 b(to)g(b)s(e)f(signed)h(b)m(y)g(the)f(users.)h(This)e(w)m (as)j(prop)s(osed)d(in)h(SIGMA,)-58 312 y(and)k(included)g(in)g(IKEv2.) 83 425 y(Another)37 b(solution)g(to)h(cop)s(e)f(with)f(the)h (randomness)f(extraction)i(error)e(is)h(as)g(noticed)h(b)m(y)e(Shoup)f ([44])j(and)-58 538 y(also)30 b(b)m(y)f(Barak)g Fx(et)j(al.)d FI(in)g([5])g(to)h(use)e(the)i(same)f(\\certi\014ed)h(k)m(ey")g(or)e (the)i(same)f(hard-co)s(ded)f(k)m(ey)h(in)g(the)g(soft)m(w)m(are.)-58 651 y(Indeed,)f(they)g(suggest)h(an)f(extension)h(of)f(the)g(LHL)g (whic)m(h)g(allo)m(ws)i(the)e(deriv)-5 b(ation)29 b(of)f(man)m(y)g (random)g(bit-strings)-58 764 y(with)38 b(a)h Fx(unique)h(r)-5 b(andom)47 b FI(k)m(ey)-8 b(,)40 b(and)e(th)m(us)h(a)f Fx(public)j(and)g(\014xe)-5 b(d)48 b FI(hash)38 b(function.)h(Ho)m(w)m (ev)m(er,)h(the)f(qualit)m(y)h(of)f(the)-58 877 y(extracted)26 b(randomness)e(decreases)i(linearly)f(with)g(the)g(n)m(um)m(b)s(er)f (of)h(extractions)h({)f(due)g(to)g(the)g(h)m(ybrid)f(tec)m(hnique.)-58 989 y(Nev)m(ertheless,)32 b(this)f(is)f(often)h(the)f(unique)g (solution.)-58 1245 y Fy(5)112 b(Deterministic)38 b(Randomness)h (Extractors)-58 1447 y FI(Other)32 b(alternativ)m(es)j(to)e(the)g(LHL)g (are)g(also)g(a)m(v)-5 b(ailable,)35 b(namely)e(when)f(no)g (certi\014cation)j(is)d(a)m(v)-5 b(ailable,)36 b(as)c(in)h(the)-58 1560 y(passw)m(ord-based)k(setting,)j(b)m(y)d(using)h(deterministic)g (randomness)f(extractors.)j(Sev)m(eral)f(of)f(them)f(exist)i(in)f(the) -58 1673 y(literature)31 b(and)d(ha)m(v)m(e)j(already)f(b)s(een)e (emplo)m(y)m(ed)j(b)m(y)e(standardization)h(b)s(o)s(dies)f(to)h(con)m (v)m(ert)h(a)e(random)g(elemen)m(t)i(of)-58 1786 y(a)g(group)f(in)m(to) h(a)g(random)e(bit-string)i(as)g(in)f([42].)-58 2038 y Fz(5.1)105 b(Hash-Di\016e-Hellman)-58 2207 y FI(The)40 b(\014rst)g(one,)h(from)f(a)h(practical)i(p)s(oin)m(t)d(of)h(view,)g (is)g(the)f(use)h(of)f(a)h(hash)f(function.)h(In)f(the)g(random)g (oracle)-58 2320 y(mo)s(del)35 b([10],)h(this)f(giv)m(es)h(a)g(p)s (erfect)f(random)f(bit-string,)h(under)f(the)h(so-called)h (computational)h(Di\016e-Hellman)-58 2433 y(assumption.)c(In)f(the)h (standard)f(mo)s(del,)h(a)g(w)m(eak)m(er)i(assumption)d(has)h(b)s(een)f (de\014ned,)g(the)h(Hash)g(Di\016e-Hellman)-58 2546 y(assumption)41 b([1,)16 b(25].)43 b(But)e(this)g(assumption)g(is,)h(in)f(some)h (sense,)f(the)h(assumption)e(that)i(a)g(hash)f(function)g(is)-58 2659 y(p)s(erfectly)28 b(suited)g(to)g(this)g(goal,)h(while)f(this)g (is)f(not)h(the)g(applications)h(that)f(designers)g(of)g(hash)f (functions)g(ha)m(v)m(e)i(in)-58 2772 y(mind.)g(Ev)m(eryb)s(o)s(dy)f (ma)m(y)i(agree)g(on)f(the)h(practical)h(v)-5 b(alidit)m(y)30 b(of)g(suc)m(h)f(a)g(construction,)h(but)f(it)h(de\014nitely)f (requires)-58 2885 y(non-standard)g(assumptions,)h(from)g(a)h (theoretical)i(p)s(oin)m(t)d(of)h(view.)-58 3137 y Fz(5.2)105 b(A)35 b(Simple)g(Deterministic)h(Extractor)-58 3306 y FI(Basically)-8 b(,)30 b(what)d(w)m(e)g(w)m(an)m(t)h(is)f(an)g (extractor)h(of)f(the)g(en)m(trop)m(y)h(from)e(a)i(random)e (\(uniformly)g(distributed\))g(elemen)m(t)-58 3419 y(in)k(a)g(cyclic)i (group)d Fu(G)g FI(of)h(order)g Fw(q)s FI(.)g(A)g(bijection)g(from)g Fu(G)f FI(to)i Fu(Z)2125 3433 y Ft(q)2193 3419 y FI(w)m(ould)e(do)h (the)g(job,)g(since)g(it)h(w)m(ould)e(transfer)h(the)-58 3532 y(uniform)c(distribution)h Fu(G)g FI(in)m(to)h(a)f(uniform)f (distribution)h(in)g Fu(Z)2119 3546 y Ft(q)2184 3532 y FI(\(an)g(appropriate)g(c)m(hoice)i(for)e Fw(q)j FI(thereafter)e (allo)m(ws)-58 3644 y(the)j(truncation)f(to)i(the)e(log)18 b Fw(q)s FI(-righ)m(tmost)31 b(bits)f(to)i(get)f(a)g(uniformly)e (distributed)h(bit-string\).)-58 3828 y Fz(Theorem)35 b(13.)46 b Fx(Ther)-5 b(e)35 b(is)f(an)h(e\016cient)e(bije)-5 b(ction)35 b(fr)-5 b(om)35 b(a)g(sub)-5 b(gr)g(oup)35 b Fu(G)f Fx(of)g(prime)h(or)-5 b(der)36 b Fw(q)h Fx(in)d Fu(Z)3414 3795 y Ft(?)3414 3850 y(p)3487 3828 y Fx(to)h Fu(Z)3659 3842 y Ft(q)3696 3828 y Fx(,)f(when)-58 3940 y Fw(p)25 b FI(=)g(2)p Fw(q)f FI(+)19 b(1)p Fx(.)-58 4124 y(Pr)-5 b(o)g(of.)47 b FI(Let)27 b(us)f(use)h(a)g(\014nite)g (\014eld)f Fu(Z)1208 4138 y Ft(p)1248 4124 y FI(,)h(with)f Fw(p)f FI(=)g(2)p Fw(q)16 b FI(+)d(1)27 b(\(a)h(safe)f(prime\))g(and)f (w)m(ork)h(in)g(the)g(cyclic)h(group)e(of)h(order)-58 4237 y Fw(q)s FI(:)i(the)f(group)g Fu(G)g FI(of)h(the)g(quadratic)g (residues)f(mo)s(dulo)g Fw(p)p FI(.)g(Since)h Fw(p)c FI(=)f(3)i(mo)s(d)f(4,)k(this)f(is)h(a)g(Blum)f(prime,)g(and)g(th)m(us) -58 4349 y Fl(\000)p FI(1)j(do)s(es)f(not)g(lie)h(in)g Fu(G)p FI(.)83 4462 y(W)-8 b(e)44 b(can)e(de\014ne)f(the)i(follo)m (wing)g(extractor,)h(for)e(an)m(y)g Fw(x)j Fl(2)g Fu(G)p FI(:)d(if)g Fw(y)47 b Fl(\024)e Fw(q)s FI(,)d(then)g Fw(f)10 b FI(\()p Fw(y)s FI(\))44 b(=)h Fw(f)3383 4476 y FH(1)3422 4462 y FI(\()p Fw(y)s FI(\))g(=)g Fw(y)s FI(,)d(else)-58 4575 y Fw(f)10 b FI(\()p Fw(y)s FI(\))37 b(=)g Fw(f)305 4589 y FH(2)344 4575 y FI(\()p Fw(y)s FI(\))h(=)f Fw(p)25 b Fl(\000)g Fw(y)s FI(.)37 b(Since)h Fl(\000)p FI(1)f(is)h(not)g(in)f Fu(G)p FI(,)h(and)f Fw(p)25 b Fl(\000)f Fw(y)40 b FI(=)d Fl(\000)p Fw(y)j FI(=)d(\()p Fl(\000)p FI(1\))26 b Fl(\002)f Fw(y)j FI(mo)s(d)c Fw(p)p FI(,)38 b Fw(f)3339 4589 y FH(1)3415 4575 y FI(maps)g Fu(G)f FI(to)h Fu(G)-58 4688 y FI(\(the)33 b(iden)m(tit)m(y)h (function\))e(and)g Fw(f)1091 4702 y FH(2)1162 4688 y FI(maps)f Fu(G)h FI(to)h Fu(Z)1678 4702 y Ft(p)1718 4688 y Fl(n)p Fu(G)p FI(.)f(Therefore,)h Fw(f)41 b FI(is)32 b(an)g(injectiv)m(e)i(mapping)e(and)g(for)g Fw(y)f Fl(2)d Fu(G)p FI(,)-58 4801 y Fw(f)-13 4815 y FH(1)26 4801 y FI(\()p Fw(y)s FI(\))p Fw(;)15 b(f)229 4815 y FH(2)269 4801 y FI(\()p Fw(y)s FI(\))31 b(are)g(in)f Fu(Z)737 4815 y Ft(q)774 4801 y FI(.)h(A)f(simple)h(coun)m(ting)g(argumen)m(t)g (pro)m(v)m(es)g(that)g(this)f(is)g(a)h(bijection.)720 b Fl(u)-61 b(t)83 4984 y FI(The)26 b(follo)m(wing)i(lemma)f(analyzes)h (the)e(securit)m(y)h(when)f(truncation)h(is)f(used)g(in)g(order)g(to)h (get)g Fw(`)f FI(bits)h(uniformly)-58 5097 y(distributed.)32 b(W)-8 b(e)35 b(assume)e(that)g(the)g(distance)h(b)s(et)m(w)m(een)g Fw(q)i FI(and)c(the)h(smaller)h(and)e(closest)j(p)s(o)m(w)m(er)e(of)g (t)m(w)m(o)h(is)g(not)-58 5210 y(to)s(o)d(large,)h(sa)m(y)f(2)551 5177 y Ft(`=)p FH(2)685 5210 y FI(if)g(w)m(e)f(w)m(an)m(t)i(to)f (extract)h Fw(`)e FI(bits.)g(The)g(pro)s(of)g(of)g(the)h(lemma)g(is)f (done)h(in)f(app)s(endix)f(F.)-58 5371 y Fz(Lemma)35 b(14.)46 b Fx(L)-5 b(et)39 b(us)g(denote)g(by)g Fl(U)1258 5385 y Ft(q)1335 5371 y Fx(the)g(uniform)h(distribution)g(on)f(the)g (sp)-5 b(ac)g(e)41 b Fu(Z)2937 5385 y Ft(q)3013 5371 y Fx(and)f(by)f Fl(U)3378 5393 y FH(2)3413 5374 y Fn(`)3486 5371 y Fx(the)g(uniform)-58 5495 y(distribution)34 b(on)f(the)g(sp)-5 b(ac)g(e)34 b Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1167 5462 y Ft(`)1227 5495 y Fl(\030)25 b(f)p FI(0)p Fw(;)15 b(:)g(:)g(:)j(;)d FI(2)1661 5462 y Ft(`)1715 5495 y Fl(\000)20 b FI(1)p Fl(g)p Fx(.)33 b(Then)g(the)g(statistic)-5 b(al)35 b(distanc)-5 b(e)33 b(is)g(b)-5 b(ounde)g(d)34 b(by)f FI(2)p Fw(=)3755 5413 y Fl(p)p 3831 5413 79 4 v 82 x FI(2)3876 5469 y Ft(`)3910 5495 y Fx(.)1905 5744 y FI(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop -58 -83 a Fz(Corollary)35 b(15.)46 b Fx(Sinc)-5 b(e)26 b(the)h(statistic)-5 b(al)28 b(distanc)-5 b(e)27 b(b)-5 b(etwe)g(en)27 b(the)f(uniform)h(distribution)g(on)g Fl(U)3182 -68 y Ft(`)3241 -83 y Fx(and)g Fh(T)-8 b(runc)3631 -68 y Ft(`)3664 -83 y FI(\()p Fw(f)10 b FI(\()p Fu(G)p FI(\)\))p Fx(,)-58 30 y(wher)-5 b(e)35 b Fw(f)43 b Fx(is)34 b(the)g(pr)-5 b(evious)35 b(bije)-5 b(ction,)34 b Fl(j)p Fw(q)s Fl(j)28 b FI(=)f Fw(`)34 b Fx(and)h Fl(j)p Fw(q)24 b Fl(\000)d FI(2)1988 -3 y Ft(`)2021 30 y Fl(j)28 b(\024)f FI(2)2217 -3 y Ft(`=)p FH(2)2321 30 y Fx(,)34 b(is)g(upp)-5 b(er)35 b(b)-5 b(ounde)g(d)36 b(by)d FI(2)p Fw(=)3290 -52 y Fl(p)p 3367 -52 79 4 v 3367 30 a FI(2)3412 4 y Ft(`)3479 30 y Fx(ac)-5 b(c)g(or)g(ding)36 b(to)-58 143 y(lemma)e(14,)f(the)g(mapping)h Fe(Tr)n(unc)1196 158 y Ft(`)1249 143 y Fl(\016)21 b Fw(f)41 b Fx(is)33 b(a)g(go)-5 b(o)g(d)34 b(deterministic)g(r)-5 b(andomness)35 b(extr)-5 b(actor.)83 373 y FI(Therefore,)22 b(the)g(truncation)g(of)g Fw(f)31 b FI(giv)m(es)23 b(a)f(deterministic)h(randomness)d(extractor)j (from)f Fu(G)f FI(on)m(to)i Fu(Z)3512 387 y Ft(q)3550 373 y FI(.)f(Ho)m(w)m(ev)m(er,)-58 486 y(this)37 b(requires)f(the)h (use)f(of)h(a)g(safe)g(prime,)g(and)f(th)m(us)g(quite)h(large)h(exp)s (onen)m(ts:)f(1023)h(bits)f(instead)g(of)g(160)h(bits,)-58 598 y(whic)m(h)f(mak)m(es)h(an)m(y)f(Di\016e-Hellman)i(k)m(ey)e (agreemen)m(t)i(unpractical.)f(In)e(the)h(next)g(subsection,)g(w)m(e)h (describ)s(e)e(an)-58 711 y(e\016cien)m(t)c(deterministic)f(randomness) e(extraction.)-58 1016 y Fz(5.3)105 b(The)35 b('Twist-A)m(Ugmen)m(ted') f(T)-9 b(ec)m(hnique)-58 1237 y FI(In)34 b(the)g(early)h(90's)g (Kaliski)g([33])h(used)d(elliptic)j(curv)m(es)e(and)g(their)g(t)m (wists)h(for)f(making)h(a)f(random)g(p)s(erm)m(utation)-58 1350 y(from)g(a)h(random)f(function.)h(This)e(construction)j(can)e(b)s (e)g(used)g(to)i(mak)m(e)f(a)g(uniform)f(distribution)g(in)g Fu(Z)3666 1364 y FH(2)p Ft(q)3773 1350 y FI(from)-58 1463 y(p)s(oin)m(ts)23 b(uniformly)g(distributed)f(on)h(a)h(curv)m(e)g (or)f(its)h(quadratic)g(t)m(wist,)g(b)s(oth)f(on)g(the)g(\014nite)h (\014eld)f Fu(F)3313 1477 y Ft(q)3350 1463 y FI(.)h(More)g(recen)m(tly) -8 b(,)-58 1576 y(quadratic)29 b(t)m(wists)g(ha)m(v)m(e)h(also)f(b)s (een)f(used)f(in)h(the)h(con)m(text)h(of)e(passw)m(ord-authen)m (ticated)i(k)m(ey)f(exc)m(hange)h([16].)g(The)-58 1689 y(goal)d(w)m(as)f(to)g(mak)m(e)h(the)e(Bello)m(vin)j(et)e(al.'s)g (encrypted)f(k)m(ey)h(exc)m(hange)h(proto)s(col)g([6])f(imm)m(une)f(to) h(partition)h(attac)m(ks)-58 1802 y(but)g(did)f(not)i(explain)f(ho)m(w) h(to)g(sp)s(ecify)f(the)g(k)m(ey-deriv)-5 b(ation)30 b(function.)d(It)g(has)g(also)i(b)s(een)d(applied)h(to)h(the)g(con)m (text)-58 1915 y(of)j(public-k)m(ey)g(encryption)f([15].)83 2036 y(W)-8 b(e)25 b(can)f(tak)m(e)h(adv)-5 b(an)m(tage)26 b(of)e(elliptic)h(curv)m(es)f(and)f(their)h(quadratic)g(t)m(wists,)h (as)f(done)f(b)m(y)h(Kaliski)g([33],)h(to)g(come)-58 2149 y(up)36 b(with)g(a)h(tec)m(hnique)h(not)f(requiring)f(stronger)h (assumptions.)f(This)g(tec)m(hnique,)i(called)g('Twist-A)m(Ugmen)m (ted')-58 2262 y(\()p Fs(T)-8 b(A)m(U)p FI(\),)31 b(uses)e(the)h(fact)g (that)h(a)f(random)f(p)s(oin)m(t)h(on)f(a)h(curv)m(e)g(o)m(v)m(er)h Fu(F)2303 2276 y Ft(p)2372 2262 y FI(has)f(an)f(abscissa)i(uniformly)d (distributed)h(in)-58 2375 y(a)k(set)h Fw(E)k FI(and)32 b(that)i(a)f(random)f(p)s(oin)m(t)h(o)m(v)m(er)h(its)f(t)m(wisted)h (has)f(an)f(abscissa)i(uniformly)e(distributed)g(in)g(the)h(set)3907 2352 y(~)3886 2375 y Fw(E)-58 2488 y FI(as)j(w)m(ell,)h Fx(i.e.)d FI(it)i(is)g(the)g(complemen)m(tary)g(set)g(of)g Fw(E)41 b FI(in)35 b Fu(F)1961 2502 y Ft(p)2000 2488 y FI(.)h(Therefore)f(b)m(y)h(c)m(ho)s(osing)g(one)g(of)f(the)h(t)m(w)m (o)h(abscissae)-58 2601 y(at)31 b(random,)f(w)m(e)g(will)h(get)g(an)f (elemen)m(t)i(almost)f(uniformly)e(distributed)g(in)h Fu(F)2664 2615 y Ft(p)2703 2601 y FI(.)h(F)-8 b(or)31 b(w)m(ell-c)m(hosen)h(\014elds,)e(w)m(e)g(th)m(us)-58 2714 y(e\016cien)m(tly)35 b(get)g(an)e(almost)h(uniformly)e (distributed)h(bit-string,)g(whic)m(h)g(ma)m(y)h(b)s(e)f(256-bit)i (long:)f(it)g(is)f(enough)g(to)-58 2827 y(deriv)m(e)h(t)m(w)m(o)h(k)m (eys)f(\(for)f(priv)-5 b(acy)33 b(and)g(for)g(authen)m(tication\))j (without)d(an)m(y)h(pseudo-random)e(function)h(b)m(y)g(simply)-58 2940 y(splitting)e(this)f(bit-string.)-58 3244 y Fz(Quadratic)38 b(Twist)f(of)i(an)f(Elliptic)h(Curv)m(e.)49 b FI(Let)34 b Fw(p)c(>)g FI(3)k(b)s(e)e(a)i(prime)f(n)m(um)m(b)s(er.)f(An)h (elliptic)i(curv)m(e)f(is)f(a)h(set)-58 3357 y(of)g(p)s(oin)m(ts)g Fu(E)d FI(=)f Fu(E)580 3372 y Ft(a;b)702 3357 y FI(=)h Fl(f)p FI(\()p Fw(x;)15 b(y)s FI(\))33 b(:)e Fw(y)1196 3324 y FH(2)1266 3357 y FI(=)g Fw(x)1420 3324 y FH(3)1482 3357 y FI(+)22 b Fw(ax)h FI(+)f Fw(b)p Fl(g)h([)f(f1)2117 3371 y Fd(E)2166 3357 y Fl(g)p FI(,)34 b(where)g Fw(a)g FI(and)f Fw(b)h FI(are)g(elemen)m(ts)h(of)f Fu(F)3565 3371 y Ft(p)3638 3357 y FI(and)g Fl(1)3910 3371 y Fd(E)-58 3470 y FI(is)d(a)h(sym)m(b)s(ol)e(for)h(the)g(p)s(oin)m(t)g(at)h (in\014nit)m(y)-8 b(.)32 b(It)f(is)g(w)m(ell)h(kno)m(wn)e(that)i(an)f (elliptic)i(curv)m(e)e Fu(E)f FI(can)i(b)s(e)e(equipp)s(ed)g(with)g(a) -58 3583 y(group)h(la)m(w)h({)g(the)f(so-called)j(c)m(hord)d(and)g (tangen)m(t)h(group)f(la)m(w)h({)g(suc)m(h)f(that)h(the)g (computational)h(and)e(decisional)-58 3696 y(Di\016e-Hellman)h (problems)e(are)h(b)s(eliev)m(ed)g(to)g(b)s(e)f(hard)f(problems)h(in)g (general.)83 3817 y(Let)36 b Fw(c)f FI(b)s(e)g(a)g(quadratic)h (non-residue)e(in)h Fu(F)1603 3831 y Ft(p)1642 3817 y FI(,)h(and)e(de\014ne)g(the)i Fz(quadratic)k(t)m(wist)34 b FI(of)i Fu(E)3214 3832 y Ft(a;b)3340 3817 y FI(to)g(b)s(e)e(the)i (curv)m(e)-58 3930 y(giv)m(en)c(b)m(y)e(the)g(follo)m(wing)i(equation:) 1250 3907 y(~)1243 3930 y Fu(E)1304 3945 y Ft(a;b)1420 3930 y FI(=)25 b Fl(f)p FI(\()p Fw(x;)15 b(y)s FI(\))26 b(:)g Fw(cy)1935 3897 y FH(2)2000 3930 y FI(=)f Fw(x)2148 3897 y FH(3)2207 3930 y FI(+)20 b Fw(ax)h FI(+)e Fw(b)p Fl(g)i([)f(f1)2835 3943 y FH(~)2831 3960 y Fd(E)2880 3930 y Fl(g)p FI(.)83 4061 y(The)j(c)m(hange)i(of)e(v)-5 b(ariables)25 b Fw(x)1076 4028 y Fj(0)1124 4061 y FI(=)g Fw(cx)f FI(and)f Fw(y)1553 4028 y Fj(0)1601 4061 y FI(=)i Fw(c)1736 4028 y FH(2)1776 4061 y Fw(y)h FI(transforms)d(the)g (equation)i(of)2912 4038 y(~)2904 4061 y Fu(E)2965 4076 y Ft(a;b)3080 4061 y FI(in)m(to)f Fw(y)3305 4028 y Fj(0)p FH(2)3389 4061 y FI(=)h Fw(x)3537 4028 y Fj(0)p FH(3)3602 4061 y FI(+)6 b Fw(ac)3766 4028 y FH(2)3806 4061 y Fw(x)3858 4028 y Fj(0)3887 4061 y FI(+)-58 4174 y Fw(bc)20 4141 y FH(3)60 4174 y FI(.)28 b(This)e(demonstrates)i(that)1073 4151 y(~)1065 4174 y Fu(E)1126 4189 y Ft(a;b)1245 4174 y FI(is)f(isomorphic)h(to)g(an)g(elliptic)h(curv)m(e)f(and)e(can)i (therefore)g(b)s(e)f(equipp)s(ed)f(with)-58 4287 y(a)35 b(group)f(la)m(w.)i(The)e(main)h(in)m(terest)g(of)g(the)g(in)m(tro)s (duction)g(of)f(the)h(quadratic)g(t)m(wist)h(here)e(follo)m(ws)i (directly)f(from)-58 4400 y(the)g(de\014nition:)f(if)h Fw(x)f FI(is)h(not)g(the)f(abscissa)i(of)e(a)h(p)s(oin)m(t)g(of)g Fu(E)2080 4415 y Ft(a;b)2171 4400 y FI(,)f(then)h Fw(x)2494 4367 y FH(3)2556 4400 y FI(+)23 b Fw(ax)g FI(+)f Fw(b)35 b FI(is)f(not)h(a)g(square)f(in)h Fu(F)3738 4414 y Ft(p)3811 4400 y FI(and)-58 4513 y(therefore)d(\()p Fw(x)412 4480 y FH(3)473 4513 y FI(+)21 b Fw(ax)g FI(+)f Fw(b)p FI(\))p Fw(=c)33 b FI(is)f(a)g(square)f(in)g Fu(F)1588 4527 y Ft(p)1628 4513 y FI(.)g(Then)g(it)h(is)g(the)g(abscissa)g(of)f(a)h(p)s (oin)m(t)g(of)3144 4490 y(~)3137 4513 y Fu(E)3198 4528 y Ft(a;b)3289 4513 y FI(.)g(The)f(con)m(v)m(erse)i(is)-58 4626 y(also)e(true.)-58 4930 y Fz(Cardinalities.)49 b FI(Hasse-W)-8 b(eil's)36 b(theorem)d(giv)m(es)i(go)s(o)s(d)e(b)s(ound)e (on)i(the)g(group)g(order)g(of)g(an)g(elliptic)i(curv)m(e)e([46].)-58 5043 y(Let)c(us)e(write)i Fw(q)f FI(=)d(#)p Fu(E)f FI(=)h Fw(p)16 b FI(+)f(1)i Fl(\000)e Fw(t)p FI(,)28 b(then)g(w)m(e)h(ha)m(v)m (e)g Fl(j)p Fw(t)p Fl(j)d Fw(<)f FI(2)2046 4987 y Fl(p)p 2122 4987 46 4 v 56 x Fw(p)p FI(.)j(W)-8 b(e)30 b(could)e(apply)g(the)g (same)h(result)f(to)3611 5020 y(~)3604 5043 y Fu(E)o FI(,)h(but)e(in)-58 5156 y(fact)34 b(the)f(n)m(um)m(b)s(er)e(of)i(p)s (oin)m(ts)g(of)g(a)g(curv)m(e)g(and)f(its)h(t)m(wist)h(are)f(far)g (from)f(b)s(eing)g(indep)s(enden)m(t.)g(Starting)h(with)g(the)-58 5269 y(fact)f(that)f(a)g(scalar)g(is)g(either)g(a)g(p)s(oin)m(t)g(on)f Fu(E)g FI(or)h(a)g(p)s(oin)m(t)f(on)2093 5246 y(~)2086 5269 y Fu(E)o FI(,)h(it)g(is)g(easy)g(to)g(deriv)m(e)h(that)38 b(~)-52 b Fw(q)28 b FI(=)e(#)3412 5246 y(~)3404 5269 y Fu(E)e FI(=)i Fw(p)20 b FI(+)g(1)h(+)f Fw(t)p FI(.)-58 5382 y(F)-8 b(or)29 b(maximal)f(securit)m(y)-8 b(,)30 b(it)e(is)g(desirable)g(that)h(the)f(group)f(orders)g(are)h(prime)g(n)m (um)m(b)s(ers.)e(In)i(particular,)g(since)g Fw(p)g FI(is)-58 5495 y(o)s(dd,)i(this)g(implies)h(that)g Fw(t)f FI(is)g(o)s(dd.)g(Then) f(b)s(oth)h Fw(q)j FI(and)j(~)-51 b Fw(q)33 b FI(are)d(o)s(dd.)1905 5744 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop -58 -83 a Fz(Choice)37 b(of)g(the)g(Prime)g (Field.)48 b FI(W)-8 b(e)33 b(ha)m(v)m(e)g(restricted)g(ourselv)m(es)g (to)g(curv)m(es)f(de\014ned)f(o)m(v)m(er)i(prime)f(\014elds.)f(The)-58 30 y(notion)f(of)f(quadratic)g(t)m(wist)h(of)f(an)g(elliptic)h(curv)m (e)g(also)g(exists)f(for)g(more)g(general)h(\014nite)f(\014elds)f(and)h (in)f(particular)-58 143 y(for)f(\014elds)f(of)h(c)m(haracteristic)i (2.)e(Ho)m(w)m(ev)m(er,)i(they)e(are)g(of)g(less)g(in)m(terest)h(in)e (our)g(con)m(text)j(where)d(w)m(e)h(w)m(an)m(t)h(to)f(use)g(the)-58 256 y(prop)s(ert)m(y)f(that)i(the)f(abscissae)h(of)f(the)g(p)s(oin)m (ts)g(of)g(the)h(groups)e(w)m(e)h(are)h(dealing)f(with)g(co)m(v)m(er)i (the)e(whole)g(\014nite)g(\014eld.)-58 369 y(In)j(c)m(haracteristic)j (2,)d(all)i(the)e(non-sup)s(er-singular)e(curv)m(es)j(ha)m(v)m(e)g(a)g (group)f(order)f(that)i(is)f(divisible)h(b)m(y)f(\(at)h(least\))-58 482 y(2.)h(Hence)f(k)m(eeping)h(the)f(co)m(v)m(ering)i(prop)s(ert)m(y)d (w)m(ould)g(imply)h(to)g(w)m(ork)g(with)g(non-prime)f(order)g(groups.)h (Ev)m(en)g(if)f(it)-58 595 y(lo)s(oks)24 b(feasible)h(to)g(patc)m(h)f (the)g(proto)s(col)h(for)e(that)i(situation,)f(it)h(is)f(certainly)h (less)f(elegan)m(t)i(than)d(using)g(prime-order)-58 707 y(group)30 b(with)g(curv)m(es)h(o)m(v)m(er)g(prime)f(\014elds.)83 820 y(T)-8 b(o)37 b(ac)m(hiev)m(e)i(our)d(goal,)i(w)m(e)f(need)g(that)g (the)f(abscissa)i(of)e(a)h(p)s(oin)m(t)g(tak)m(en)g(randomly)f(in)g Fu(E)h FI(or)f(in)3560 797 y(~)3552 820 y Fu(E)g FI(b)s(eha)m(v)m(es) -58 933 y(lik)m(e)c(a)f(random)f(bit-string)h(of)g(length)g Fw(`)p FI(.)f(Since)h(all)h(the)e(elemen)m(ts)i(of)f Fu(F)2447 947 y Ft(p)2517 933 y FI(are)g(obtainable)h(as)f(abscissae)g (of)g(p)s(oin)m(ts)-58 1046 y(of)k Fu(E)f FI(and)334 1023 y(~)326 1046 y Fu(E)p FI(,)h(w)m(e)g(will)g(b)s(e)f(able)i(to)f (sho)m(w)g(that)g(the)g(random)f(abscissa)h(in)g Fu(E)f FI(or)2809 1023 y(~)2802 1046 y Fu(E)g FI(giv)m(es)i(a)f(random)f (elemen)m(t)i(in)-58 1159 y Fu(F)-2 1173 y Ft(p)74 1159 y FI(\(see)h(Lemma)f(16)h(in)f(App)s(endix)f(F.\))i(T)-8 b(o)36 b(con)m(v)m(ert)i(this)e(elemen)m(t)i(to)f(a)g(bit-string)f(of)h (length)f Fw(`)g FI(without)g(an)m(y)-58 1272 y(further)29 b(device)h(and)f(k)m(eeping)i(the)f(randomness)f(un)m(biased,)g(it)i (is)e(necessary)i(to)f(ha)m(v)m(e)h Fw(p)f FI(v)m(ery)g(close)h(to)g(2) 3630 1239 y Ft(`)3663 1272 y FI(.)f(Hence)-58 1385 y(w)m(e)j(prop)s (ose)f(to)h(use)f(a)h(prime)e Fw(p)h FI(whic)m(h)h(can)f(b)s(e)g (written)g Fw(p)d FI(=)f(2)2200 1352 y Ft(`)2255 1385 y Fl(\000)21 b Fw(")p FI(,)33 b(where)f Fw(")h FI(is)f(an)h(in)m(teger) g(less)g(than)f(2)22 b Fl(\001)g FI(2)3854 1352 y Ft(`=)p FH(2)-58 1498 y FI(\(see)31 b(Lemma)g(14.\))83 1611 y(This)38 b(extra-condition)i(on)e Fw(p)g FI(is)h(not)g(a)f(practical)i(incon)m (v)m(enience.)h(In)d(fact,)h(the)g(primes)f(that)h(are)f(used)g(in)-58 1724 y(practice)k(are)f(almost)g(alw)m(a)m(ys)h(of)f(this)f(form,)g(b)s (ecause)g(they)h(allo)m(w)h(a)f(faster)f(arithmetic)i(than)e(more)h (general)-58 1837 y(primes.)29 b(F)-8 b(or)30 b(instance,)g(the)g(curv) m(es)f(prop)s(osed)f(b)m(y)h(the)h(NIST)e(are)i(de\014ned)e(o)m(v)m(er) i(\014nite)g(\014eld)f(with)f(primes)h(whic)m(h)-58 1949 y(are)i(often)g(suitable)g(to)g(our)f(case)h(\(the)g(prime)f(\014eld,)g (not)h(the)f(curv)m(es!\).)-58 2206 y Ff(T)-8 b(A)m(U)32 b Fz(is)g(a)g(Go)s(o)s(d)h(Randomness)g(Extractor.)43 b FI(No)m(w,)29 b(w)m(e)g(sho)m(w)e(that)i(the)f(distribution)f(of)h (the)h(master)f(secret)-58 2319 y(k)m(ey)j Fw(K)36 b FI(if)30 b(w)m(e)g(tak)m(e)h(it)g(at)f(random)f(either)h(on)g(the)g (curv)m(e)g Fu(E)f FI(or)2155 2295 y(~)2147 2319 y Fu(E)h FI(is)f(statistically)k(almost)e(uniformly)e(distributed)-58 2432 y(on)45 b Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)303 2399 y Ft(`)339 2432 y FI(.)45 b(On)g(the)g(one)h(hand,)e(w)m(e)i(pro)m (v)m(e)g(that)g(it)g(is)f(statistically)k(indistinguishable)c(from)f (the)i(uniform)-58 2545 y(distribution)37 b(on)h Fl(f)p FI(0)p Fw(;)15 b(:)g(:)g(:)j(;)d(p)25 b Fl(\000)g FI(1)p Fl(g)39 b FI(and)f(then)f(that)i(the)f(latter)i(distribution)d(is)h (statistically)j(indistinguishable)-58 2658 y(from)d(the)h(uniform)e (distribution)h(on)g Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1537 2625 y Ft(`)1611 2658 y FI(b)m(y)38 b(using)g(lemma)h(14)h(b)m(y)e (replacing)h Fw(q)i FI(b)m(y)e Fw(p)p FI(.)f(The)g(pro)s(of)g(of)h(the) -58 2771 y(follo)m(wing)32 b(lemmas)f(are)g(done)f(in)g(app)s(endix)f (F.)83 2883 y(Let)i(us)f(denote)h(b)m(y)f Fl(D)j FI(the)e(distribution) e(of)i Fw(K)7 b FI(:)-16 3098 y Fl(D)28 b FI(=)d Fl(f)p Fw(b)306 3047 y Ft(R)288 3098 y Fl( )g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)p Fw(;)g Fz(R)742 3112 y FH(0)828 3047 y Ft(R)809 3098 y Fl( )26 b Fu(E)p Fw(;)15 b Fz(R)1105 3112 y FH(1)1188 3047 y Ft(R)1170 3098 y Fl( )1293 3075 y FI(~)1286 3098 y Fu(E)25 b FI(:)g Fw(K)32 b FI(=)25 b([)p Fz(R)1730 3113 y Ft(b)1765 3098 y FI(])1790 3113 y Fk(abs)1892 3098 y Fl(g)h FI(=)f Fl(f)p Fw(b)2187 3047 y Ft(R)2168 3098 y Fl( )g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)p Fw(;)g(x)2596 3112 y FH(0)2682 3047 y Ft(R)2664 3098 y Fl( )25 b FI([)p Fu(E)p FI(])2891 3113 y Fk(abs)2993 3098 y Fw(;)15 b(x)3085 3112 y FH(1)3168 3047 y Ft(R)3150 3098 y Fl( )25 b FI([)3299 3075 y(~)3291 3098 y Fu(E)p FI(])3377 3113 y Fk(abs)3504 3098 y FI(:)g Fw(K)32 b FI(=)25 b Fw(x)3811 3113 y Ft(b)3845 3098 y Fl(g)p Fw(:)-58 3294 y Fz(Lemma)35 b(16.)46 b Fx(The)33 b(distribution)g Fl(D)j Fx(is)c(statistic)-5 b(al)5 b(ly)35 b(close)e(to)g(the)g (uniform)g(distribution)h Fl(U)3220 3308 y Ft(p)3292 3294 y Fx(in)f Fu(F)3460 3308 y Ft(p)3524 3294 y Fl(\030)25 b Fu(Z)3681 3308 y Ft(p)3720 3294 y Fx(:)1015 3570 y Fw(\016)k FI(=)1196 3484 y Fg(X)1180 3681 y Ft(x)p Fj(2)p Fd(F)1308 3689 y Fn(p)1359 3411 y Fg(\014)1359 3466 y(\014)1359 3520 y(\014)1359 3575 y(\014)1359 3629 y(\014)1448 3570 y FI(Pr)1389 3666 y Ft(K)1466 3628 y Fn(R)1454 3666 y Fj( )o(U)1568 3674 y Fn(p)1604 3570 y FI([)p Fw(K)j FI(=)25 b Fw(x)p FI(])c Fl(\000)67 b FI(Pr)2023 3666 y Ft(K)2099 3628 y Fn(R)2088 3666 y Fj( )n(D)2214 3570 y FI([)p Fw(K)32 b FI(=)25 b Fw(x)p FI(])2521 3411 y Fg(\014)2521 3466 y(\014)2521 3520 y(\014)2521 3575 y(\014)2521 3629 y(\014)2577 3570 y Fl(\024)2683 3509 y FI(2)2728 3433 y Fl(p)p 2804 3433 46 4 v 76 x FI(2)p 2683 3549 167 4 v 2689 3567 a Fl(p)p 2765 3567 79 4 v 83 x FI(2)2810 3623 y Ft(`)2860 3570 y Fw(:)-58 3862 y Fz(Corollary)35 b(17.)46 b Fx(The)29 b(statistic)-5 b(al)31 b(distanc)-5 b(e)31 b(b)-5 b(etwe)g(en)29 b(the)h(uniform)f(distribution)h(on)g Fl(U)3005 3877 y Ft(`)3067 3862 y Fx(and)g(the)f Fs(T)-8 b(A)m(U)29 b Fx(te)-5 b(chnique)-58 3986 y(if)32 b Fl(j)p Fw(p)21 b Fl(\000)f FI(2)258 3953 y Ft(`)291 3986 y Fl(j)25 b(\024)g FI(2)482 3953 y Ft(`=)p FH(2)586 3986 y Fx(,)33 b(is)f(upp)-5 b(er)34 b(b)-5 b(ounde)g(d)34 b(by)f FI(2)p Fw(=)1549 3904 y Fl(p)p 1625 3904 V 82 x FI(2)1670 3960 y Ft(`)1724 3986 y FI(+)1825 3949 y FH(2)1860 3894 y Fj(p)p 1919 3894 36 3 v 55 x FH(2)p 1825 3965 130 4 v 1828 3975 a Fj(p)p 1886 3975 66 3 v 1886 4035 a FH(2)1921 4016 y Fn(`)1997 3986 y Fx(ac)-5 b(c)g(or)g(ding)35 b(to)e(lemma)g(16)h(and)g (14.)-58 4253 y Fz(Finding)41 b(a)g(Suitable)g(Elliptic)g(Curv)m(e)g (and)g(Twist.)51 b FI(The)35 b(basic)i(approac)m(h)f(for)f (construction)h(a)g(curv)m(e)g Fu(E)-58 4366 y FI(o)m(v)m(er)30 b Fu(F)191 4380 y Ft(p)259 4366 y FI(suc)m(h)e(that)h(b)s(oth)f Fw(q)j FI(and)k(~)-52 b Fw(q)31 b FI(are)e(primes)f(is)h(to)g(pic)m(k)g (random)f(curv)m(es,)h(coun)m(t)g(their)f(cardinalities)i(with)f(the) -58 4479 y(SEA)f(algorithm,)h(and)f(k)m(eep)h(only)f(the)h(go)s(o)s(d)f (ones.)h(With)f(this)g(strategy)-8 b(,)31 b(if)d(n)m(um)m(b)s(er)f(of)h (p)s(oin)m(ts)g(w)m(ere)h(completely)-58 4592 y(indep)s(enden)m(t)k (and)g(b)s(eha)m(v)m(ed)h(lik)m(e)g(random)f(n)m(um)m(b)s(ers)g(in)g (the)h(Hasse-W)-8 b(eil)36 b(in)m(terv)-5 b(al,)35 b(w)m(e)g(w)m(ould)e (exp)s(ect)h(to)h(ha)m(v)m(e)-58 4705 y(to)e(ha)m(v)m(e)h(to)f(build)e Fw(O)s FI(\(log)839 4668 y FH(2)894 4705 y Fw(p)p FI(\))h(curv)m(es)h (b)s(efore)f(\014nding)f(a)i(go)s(o)s(d)f(one.)h(If)f(log)17 b Fw(p)29 b Fl(\031)f FI(200,)34 b(it)f(means)g(that)g(w)m(e)f(ha)m(v)m (e)i(to)-58 4818 y(run)29 b(the)i(SEA)e(algorithm)j(ab)s(out)e(20000)j (times)d(to)i(construct)e(a)h(go)s(o)s(d)f(curv)m(e,)h(whic)m(h)f(is)h (prohibitiv)m(e.)83 4930 y(F)-8 b(ortunately)g(,)35 b(the)f(SEA)e (algorithm)i([40])g(is)f(suited)g(for)g(this)g(kind)f(of)h(searc)m(h,)h (since)f(it)h(computes)f(the)g(order)-58 5043 y(of)27 b Fu(E)g FI(mo)s(dulo)f(small)i(primes)f(and)f(recom)m(bine)i(the)f (group)g(order)f(b)m(y)h(Chinese)g(Remainder.)g(Hence)h(as)f(so)s(on)g (as)g(w)m(e)-58 5156 y(kno)m(w)33 b(the)g(order)f(of)h Fu(E)f FI(mo)s(dulo)g(a)h(small)g(prime)f Fw(`)p FI(,)h(w)m(e)g(ab)s (ort)g(the)f(computation)i(if)f(this)f(is)h(zero.)h(F)-8 b(urthermore,)-58 5269 y(the)29 b(group)f(order)h(of)699 5246 y(~)691 5269 y Fu(E)g FI(mo)s(dulo)f Fw(`)g FI(is)h(readily)g (deduced)f(from)h(#)p Fu(E)24 b FI(mo)s(d)h Fw(`)p FI(,)k(and)f (similar)h(ab)s(ortion)g(can)g(b)s(e)f(pla)m(y)m(ed)-58 5382 y(also)38 b(with)g(the)f(t)m(wist.)i(As)e(a)h(consequence,)g(most) g(of)f(the)h(curv)m(es)g(are)f(v)m(ery)h(quic)m(kly)g(detected)h(as)f (bad)e(curv)m(es,)-58 5495 y(b)s(ecause)30 b(either)h(the)g(curv)m(e)g (of)f(its)h(t)m(wist)g(has)f(a)h(non-prime)f(group)f(order.)1905 5744 y(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 83 -83 a FI(In)30 b(fact,)h(the)f(situation)h (is)f(more)g(tric)m(ky)-8 b(,)32 b(since)f(the)f(order)f(of)i(the)f (curv)m(e)g(and)g(the)g(order)f(of)i(its)f(t)m(wist)h(are)g(not)-58 30 y(indep)s(enden)m(t.)f(F)-8 b(or)31 b(instance,)g(imagine)g(that)g Fw(p)25 b Fl(\021)g FI(2)h(mo)s(d)f(3,)31 b(then)f(the)g(condition)h(#) p Fu(E)25 b Fl(\021)g FI(0)h(mo)s(d)e(3)31 b(is)f(equiv)-5 b(alen)m(t)-58 143 y(to)35 b Fw(t)d Fl(\021)g FI(0)26 b(mo)s(d)f(3,)35 b(whic)m(h)f(in)g(turn)g(is)g(equiv)-5 b(alen)m(t)36 b(to)g(#)1913 119 y(~)1905 143 y Fu(E)31 b Fl(\021)h FI(0)26 b(mo)s(d)e(3.)36 b(A)e(rigorous)h(estimation)h(of)f (the)g(running)-58 256 y(time)28 b(of)f(the)g(SEA)f(algorithm)i(equipp) s(ed)d(with)h(the)h(early-ab)s(ort)h(strategy)g(is)f(out)g(of)g(the)g (scop)s(e)g(of)g(this)f(w)m(ork.)i(W)-8 b(e)-58 369 y(just)30 b(prop)s(ose)h(some)g(n)m(umerical)g(exp)s(erimen)m(ts)g(to)h(justify)e (the)h(claim)h(that)g(the)f(construction)g(of)g(secure)g(pairs)g(of)-58 482 y(curv)m(e)g(and)f(t)m(wist)h(is)f(easily)i(feasible)f(on)f(a)h (reasonable)g(computer.)83 595 y(W)-8 b(e)31 b(pic)m(k)m(ed)g(randomly) f(ab)s(out)g(30000)i(200-bit)f(primes,)f(and)f(for)h(eac)m(h)h(of)g (them)f(w)m(e)g(pic)m(k)m(ed)h(a)f(random)g(curv)m(e)-58 707 y(and)d(computed)g(its)g(cardinalit)m(y)h(and)f(the)g(cardinalit)m (y)i(of)e(its)g(t)m(wist.)i(In)d(the)h(follo)m(wing)i(table,)f(w)m(e)g (summarize)f(the)-58 820 y(p)s(ercen)m(tage)32 b(of)e(the)h(curv)m(es)g (for)f(whic)m(h)g(b)s(oth)f(n)m(um)m(b)s(er)h(of)g(p)s(oin)m(ts)g(are)h (not)g(divisible)f(b)m(y)g(all)i(primes)d(up)h(to)h Fw(P)3774 834 y Ft(max)3918 820 y FI(.)p 581 908 2739 4 v 579 1021 4 113 v 828 987 a Fw(P)886 1001 y Ft(max)p 1275 1021 V 1379 987 a FI(1)p 1526 1021 V 183 w(2)p 1731 1021 V 160 w(3)p 1936 1021 V 173 w(5)p 2166 1021 V 185 w(7)p 2396 1021 V 163 w(11)p 2627 1021 V 140 w(13)p 2857 1021 V 140 w(17)p 3087 1021 V 141 w(19)p 3318 1021 V 581 1024 2739 4 v 579 1137 4 113 v 593 1103 a(remaining)f(curv)m(es)p 1275 1137 V 23 w(100)17 b(\045)p 1526 1137 V 23 w(33)f(\045)p 1731 1137 V 23 w(12)g(\045)p 1936 1137 V 23 w(7.2)g(\045)p 2166 1137 V 23 w(4.9)h(\045)p 2397 1137 V 23 w(3.9)f(\045)p 2627 1137 V 23 w(3.3)g(\045)p 2857 1137 V 23 w(3.0)h(\045)p 3088 1137 V 23 w(2.7)f(\045)p 3318 1137 V 581 1141 2739 4 v 83 1276 a(F)-8 b(rom)30 b(this)g(data,)h(w)m(e)f(see)g(that)h(for)e (97)p Fw(:)p FI(3)15 b(\045)31 b(of)f(the)g(curv)m(es,)g(the)g(SEA)f (algorithm)i(will)f(b)s(e)f(stopp)s(ed)g(at)h(a)g(v)m(ery)-58 1388 y(early)35 b(stage,)i(th)m(us)d(sp)s(ending)f(only)i(a)g(tin)m(y)g (fraction)h(of)f(the)g(running)d(time)k(of)f(the)g(whole)f (computation.)i(With)-58 1501 y(usual)e(reasonable)i(heuristics,)f(it)g (is)g(exp)s(ected)g(that)h(ab)s(out)e(500)i(full)f(computations)g(are)h (required)d(on)i(a)m(v)m(erage)-58 1614 y(b)s(efore)d(\014nding)f(a)i (go)s(o)s(d)g(pair)f(of)h(curv)m(e)f(and)g(t)m(wist.)i(A)f(single)g (SEA)f(computation)h(tak)m(es)h(ab)s(out)e(20)i(seconds)e(for)-58 1727 y(this)i(size)h(on)e(a)h(p)s(ersonal)g(computer,)g(hence)g(in)f (ab)s(out)h(3)g(hours,)f(w)m(e)h(exp)s(ect)h(to)f(build)f(go)s(o)s(d)h (parameters)g(for)f(a)-58 1840 y(k)m(ey-size)f(of)f(200)h(bits.)e(An)g (example)h(curv)m(e)g(is)f(giv)m(en)i(in)e(App)s(endix)e(G.)83 1953 y(If)23 b(there)g(is)g(a)g(need)g(to)g(construct)h(the)f(curv)m (es)g(in)f(constrain)m(t)i(en)m(vironmen)m(t,)g(then)f(it)g(is)g (probably)f(a)h(b)s(etter)g(idea)-58 2066 y(to)30 b(use)g(the)g(theory) f(of)h(Complex)g(Multiplication.)i(W)-8 b(e)30 b(will)g(not)g(giv)m(e)h (the)f(details)h(here,)e(since)h(the)g(construction)-58 2179 y(is)j(w)m(ell)h(describ)s(ed)d(b)s(oth)i(in)f(the)h(literature)h (and)e(in)h(the)g(standards.)f(F)-8 b(or)33 b(our)g(purp)s(ose,)e(it)i (su\016ces)g(to)h(c)m(ho)s(ose)f(a)-58 2292 y(group)d(order)g(and)g(a)g (t)m(wisted)i(group)d(order)h(whic)m(h)g(are)h(b)s(oth)f(primes.)-58 2538 y Fy(6)112 b(The)38 b('Twist-A)m(Ugmen)m(ted')g(Authen)m(ticated)g (Di\016e-Hellman)h(Proto)s(col)-58 2731 y Fz(6.1)105 b(Description)-58 2890 y FI(Using)31 b(the)f(prop)s(erties)g(of)h ('Twist-A)m(Ugmen)m(ted')i(deterministic)e(randomness)e(extractor,)j(w) m(e)f(then)f(con)m(v)m(ert)i(an)m(y)-58 3003 y(Di\016e-Hellman-lik)m(e) e(proto)s(col,)d(whic)m(h)f(pro)m(vides)g(a)g(random)f(elemen)m(t)j(in) e(a)g(cyclic)i(group,)e(in)m(to)h(a)f(proto)s(col)h(whic)m(h)-58 3116 y(pro)m(vides)j(a)h(random)f(bit-string,)h(without)f(an)m(y)h (additional)g(assumptions.)f(See)h(\014gure)f(2)g(for)g(the)h (description.)-58 3359 y Fz(6.2)105 b(Seman)m(tic)35 b(Securit)m(y)-58 3519 y FI(On)30 b(Figure)g(2,)h(w)m(e)g(presen)m(t)f (the)h Fs(T)-8 b(A)m(U)o FI(-enhancemen)m(t)32 b(of)e Fw(\006)2015 3533 y FH(0)2054 3519 y FI(:)h(some)f(\015o)m(ws)h(are)f (doubled,)g(on)g(eac)m(h)h(curv)m(e.)g(During)-58 3631 y(his)26 b(k)m(ey-con\014rmation)i(phase,)f(Bob)g(randomly)f(c)m(ho)s (oses)i(the)f(curv)m(e)g(whic)m(h)f(will)h(b)s(e)g(used)e(for)i(the)g (Di\016e-Hellman)-58 3744 y(computation.)36 b(This)e(proto)s(col)i(ac)m (hiev)m(es)h(the)f(prop)s(ert)m(y)e(of)h(seman)m(tic)h(securit)m(y)g (under)e(the)h(elliptic-curv)m(e)i(deci-)-58 3857 y(sional)c (Di\016e-Hellman)i(assumption)d(and)g(do)s(es)g(not)h(use)f(ideal-hash) h(functions.)f(In)g(order)g(to)h(pro)m(v)m(e)g(this)g(claim)-58 3970 y(\(the)39 b(full)f(pro)s(of)g(is)h(p)s(ostp)s(one)e(to)j(the)e (app)s(endix)f(C\))i(w)m(e)g(consider)f(games)i(that)f(ha)m(v)m(e)g (distances)h(that)f(can)f(b)s(e)-58 4083 y(measured)c(easily)-8 b(.)37 b(W)-8 b(e)35 b(use)g(Shoup's)e(lemma)i(to)g(b)s(ound)e(the)i (probabilit)m(y)g(of)g(ev)m(en)m(ts)h(in)e(successiv)m(e)i(games)f ([43,)-58 4196 y(45].)28 b(The)d(\014rst)g(game)i Fz(G)790 4210 y FH(1)856 4196 y FI(allo)m(ws)g(us)f(to)h(a)m(v)m(oid)g(activ)m (e)h(attac)m(ks)h(so)d(that)h(in)e(the)i(follo)m(wing)g(games)g(w)m(e)g (only)f(ha)m(v)m(e)h(to)-58 4309 y(w)m(orry)c(ab)s(out)g(repla)m(y)h (attac)m(ks.)i(Pro)m(ving)e(the)f(claim)i(b)s(oils)e(do)m(wn)g(to)h (coming)g(up)e(with)h(the)h(appropriate)f(games)h Fz(G)3918 4323 y FH(2)-58 4422 y FI(through)h Fz(G)363 4436 y FH(5)403 4422 y FI(.)h(In)f(these)h(games)h(w)m(e)f(obtain)g(a)h(random)e (master)h(k)m(ey)g Fw(K)33 b FI(uniformly)24 b(distributed)h(in)h Fl(f)p FI(0)p Fw(;)15 b(:)g(:)g(:)i(;)e FI(2)3740 4389 y Ft(`)3785 4422 y Fl(\000)c FI(1)p Fl(g)-58 4535 y FI(whic)m(h)31 b(corrects)h(the)f(uncertain)m(ties)i(of)e(previous)g(pro)s(ofs.)f(The) h(games)h Fz(G)2550 4549 y FH(6)2621 4535 y FI(and)e Fz(G)2880 4549 y FH(7)2951 4535 y FI(are)h(easy)h(to)g(come)g(up)e (with)-58 4648 y(and)h(therefore)g(the)g(pro)s(of)f(of)i(the)f(claim)h (easily)g(follo)m(ws.)g(In)f(the)g(last)h(game)g Fz(G)2742 4662 y FH(7)2781 4648 y FI(,)f(the)h(adv)m(ersary)f(has)g(clearly)h(no) -58 4761 y(means)e(to)i(get)f(an)m(y)g(information)f(ab)s(out)h(the)f (random)g(bit)g(in)m(v)m(olv)m(ed)i(in)e(the)h Fs(T)-8 b(est)p FI(-query)30 b(except)i(to)f(\015ip)e(a)i(coin.)-58 4932 y Fz(Theorem)k(18.)46 b Fx(F)-7 b(or)33 b(any)f(adversary)h Fl(A)e Fx(running)h(within)h(time)e(b)-5 b(ound)33 b Fw(t)p Fx(,)e(with)h(less)g(than)h Fw(q)3214 4946 y Ft(s)3282 4932 y Fx(di\013er)-5 b(ent)32 b(sessions)32 5140 y Fs(Adv)183 5102 y Fk(ak)n(e)183 5163 y(T)-6 b(A)n(U)323 5140 y FI(\()p Fl(A)p FI(\))25 b Fl(\024)g FI(4)c Fl(\001)f Fs(Succ)877 5102 y Fk(euf)5 b Fj(\000)p Fk(cma)877 5169 y(A)n(UTH)1151 5140 y FI(\()p Fw(t;)15 b(q)1300 5154 y Ft(s)1337 5140 y Fw(;)g(q)1418 5154 y Ft(s)1455 5140 y FI(\))20 b(+)g(2)h Fl(\001)f Fs(Adv)1863 5102 y Fk(ecddh)1863 5167 y Fq(P)p Ft(;)p Fj(h)p Fq(P)p Fj(i)2053 5140 y FI(\()p Fw(t)2121 5102 y Fj(0)2144 5140 y FI(\))h(+)f(2)g Fl(\001)h Fs(Adv)2553 5102 y Fk(ecddh)2553 5167 y Fq(Q)p Ft(;)p Fj(h)p Fq(Q)p Fj(i)2753 5140 y FI(\()p Fw(t)2821 5102 y Fj(0)2845 5140 y FI(\))f(+)g(2)p Fw(q)3077 5154 y Ft(s)3114 5140 y Fs(Adv)3265 5096 y Fk(p)n(rf)3265 5168 y Fj(F)3354 5140 y FI(\()p Fw(t;)15 b FI(2\))22 b(+)3665 5078 y(10)p Fw(q)3796 5092 y Ft(s)p 3665 5119 169 4 v 3672 5137 a Fl(p)p 3747 5137 79 4 v 3747 5219 a FI(2)3792 5193 y Ft(`)3843 5140 y Fw(;)-58 5364 y Fx(wher)-5 b(e)40 b Fw(t)238 5331 y Fj(0)296 5364 y Fl(\024)35 b Fw(t)25 b FI(+)f(8)g Fl(\002)g Fw(q)760 5378 y Ft(s)797 5364 y Fw(T)850 5378 y Ft(m)916 5364 y Fx(,)38 b(and)i Fw(T)1218 5378 y Ft(m)1323 5364 y Fx(is)e(an)h(upp)-5 b(er-b)g(ound)40 b(on)e(the)h(time)f(to)h(c)-5 b(ompute)40 b(the)e(multiplic)-5 b(ation)41 b(of)d(a)-58 5477 y(p)-5 b(oint)34 b(by)f(a)g(sc)-5 b(alar.)1905 5744 y FI(14)p eop end %%Page: 15 15 TeXDict begin 15 14 bop -11 628 3923 4 v -11 4452 4 3824 v 1228 796 a Fp(Alice)p 1228 809 169 4 v 922 w(Bob)p 2318 809 136 4 v 1223 984 a FF(Common)26 b(t)n(wisted)h(curv)n(es)21 b(:)g Fo(E)g FF(=)g FD(h)p FC(P)p FD(i)p FB(;)2404 965 y FF(~)2399 984 y Fo(E)g FF(=)g FD(h)p FC(Q)p FD(i)1449 1075 y FF(of)27 b(resp)r(ectiv)n(e)f(prime)f(orders)i FB(q)s(;)18 b FF(~)-43 b FB(q)1579 1167 y FF(o)n(v)n(er)26 b(the)f(\014nite)g(\014eld)h Fo(F)2285 1175 y Fn(p)808 1349 y FF(Signing)g(Key)21 b(:)h FE(sk)1347 1357 y Fn(A)2318 1349 y FF(Signing)k(Key)21 b(:)h FE(sk)2857 1357 y Fn(B)666 1441 y FF(V)-6 b(eri\014cation)25 b(Key)c(:)h FE(vk)1347 1449 y Fn(A)2318 1441 y FF(V)-6 b(eri\014cation)26 b(Key)21 b(:)h FE(vk)2999 1449 y Fn(B)928 1532 y FE(accept)f FD( )h FE(false)922 b(accept)21 b FD( )h FE(false)829 1623 y(terminate)f FD( )h FE(false)922 b(terminate)22 b FD( )f FE(false)273 1827 y FB(s)346 1784 y Fn(R)331 1827 y FD( )g(f)p FF(0)p FB(;)14 b FF(1)p FD(g)616 1795 y Fn(?)652 1827 y FB(;)g(x)731 1835 y FG(0)801 1784 y Fn(R)786 1827 y FD( )21 b Fo(Z)934 1835 y Fn(q)968 1827 y FB(;)13 b(X)1065 1835 y FG(0)1122 1827 y FF(=)21 b FB(x)1247 1835 y FG(0)1298 1827 y FD(\001)c FC(P)681 1940 y FB(x)725 1948 y FG(1)795 1897 y Fn(R)780 1940 y FD( )k Fo(Z)933 1948 y FG(~)-35 b Fn(q)962 1940 y FB(;)13 b(X)1059 1948 y FG(1)1116 1940 y FF(=)21 b FB(x)1241 1948 y FG(1)1292 1940 y FD(\001)c FC(Q)260 2078 y FB(\033)304 2086 y Fn(A)376 2078 y FF(=)k FE(A)n(UTH)p FB(:)p FE(Sign)q FF(\()p FE(sk)923 2086 y Fn(A)973 2078 y FF(;)13 b(\()p FB(s;)g(X)1170 2086 y FG(0)1205 2078 y FB(;)g(X)1302 2086 y FG(1)1337 2078 y FF(\)\))1542 2027 y Fp(Alice)q FB(;)g(s;)g(X)1878 2035 y FG(0)1913 2027 y FB(;)g(X)2010 2035 y FG(1)2045 2027 y FB(;)g(\033)2123 2035 y Fn(A)1474 2078 y FD(\000)-35 b(\000)-18 b(\000)h(\000)g(\000)f (\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h (\000)g(\000)-34 b(!)76 b FF(Chec)n(k)26 b FB(\033)2593 2086 y Fn(A)2318 2190 y FB(y)2356 2198 y FG(0)2427 2148 y Fn(R)2412 2190 y FD( )21 b Fo(Z)2560 2198 y Fn(q)2594 2190 y FB(;)14 b(Y)2674 2198 y FG(0)2729 2190 y FF(=)21 b FB(y)2848 2198 y FG(0)2900 2190 y FD(\001)c FC(P)2318 2303 y FB(y)2356 2311 y FG(1)2427 2260 y Fn(R)2412 2303 y FD( )k Fo(Z)2565 2311 y FG(~)-35 b Fn(q)2594 2303 y FB(;)14 b(Y)2674 2311 y FG(1)2729 2303 y FF(=)21 b FB(y)2848 2311 y FG(1)2900 2303 y FD(\001)c FC(Q)2318 2415 y FB(\014)2402 2373 y Fn(R)2387 2415 y FD( )k(f)p FF(0)p FB(;)14 b FF(1)p FD(g)2318 2507 y FB(K)2383 2516 y Fn(\014)2446 2507 y FF(=)21 b([)p FB(y)2586 2516 y Fn(\014)2645 2507 y FD(\001)c FB(X)2746 2516 y Fn(\014)2788 2507 y FF(])2809 2516 y Fc(abs)2887 2507 y FB(;)c(k)2961 2515 y Fn(m)3041 2507 y FF(=)21 b FE(MacKey)q FF(\()p FB(K)3478 2516 y Fn(\014)3519 2507 y FF(\))2318 2598 y FB(\033)2362 2606 y Fn(B)2436 2598 y FF(=)g FE(A)n(UTH)p FB(:)p FE(Sign)r FF(\()p FE(sk)2983 2606 y Fn(B)3036 2598 y FF(;)13 b(\()p FB(s;)g(X)3233 2606 y FG(0)3268 2598 y FB(;)g(X)3365 2606 y FG(1)3400 2598 y FB(;)g(Y)3479 2606 y FG(0)3513 2598 y FB(;)h(Y)3593 2606 y FG(1)3627 2598 y FF(\)\))1510 2686 y Fp(Bob)p FB(;)f(s;)g(Y)1794 2694 y FG(0)1828 2686 y FB(;)g(Y)1907 2694 y FG(1)1942 2686 y FB(;)g(\033)2020 2694 y Fn(B)2072 2686 y FB(;)h(\026)2153 2694 y Fn(B)1474 2736 y FD( )-35 b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g (\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)-34 b(\000)76 b FB(\026)2364 2744 y Fn(B)2439 2736 y FF(=)21 b FE(MA)n(C)p FB(:)p FE(Sign)p FF(\()p FB(k)2915 2744 y Fn(m)2974 2736 y FF(;)13 b(\()p FE(\\1")q FB(;)g(s;)g Fp(Bob)q FF(\)\))1050 2849 y FB(d)1126 2806 y Fn(R)1111 2849 y FD( )21 b(f)p FF(0)p FB(;)14 b FF(1)p FD(g)262 2940 y FB(K)27 b FF(=)21 b([)p FB(x)500 2949 y Fn(d)553 2940 y FD(\001)c FB(Y)636 2949 y Fn(d)672 2940 y FF(])693 2949 y Fc(abs)770 2940 y FB(;)d(k)845 2948 y Fn(m)925 2940 y FF(=)21 b FE(MacKey)q FF(\()p FB(K)5 b FF(\))p 212 3059 4 92 v 226 3031 a(T)-6 b(ry)24 b(to)i(c)n(hec)n(k)f FB(\026)717 3039 y Fn(B)792 3031 y FF(:)c(in)26 b(case)g(of)h(failure)p 212 3150 V 302 3123 a FB(d)21 b FF(=)g(1)d FD(\000)e FB(d;)d(K)27 b FF(=)21 b([)p FB(x)888 3132 y Fn(d)941 3123 y FD(\001)d FB(Y)1025 3132 y Fn(d)1060 3123 y FF(])1081 3132 y Fc(abs)p 212 3241 V 302 3214 a FB(k)342 3222 y Fn(m)422 3214 y FF(=)j FE(MacKey)q FF(\()p FB(K)5 b FF(\))937 3305 y(Chec)n(k)25 b FB(\026)1213 3313 y Fn(B)1266 3305 y FB(;)13 b(\033)1344 3313 y Fn(B)232 3397 y FB(\026)278 3405 y Fn(A)350 3397 y FF(=)21 b FE(MA)n(C)p FB(:)p FE(Sign)q FF(\()p FB(k)827 3405 y Fn(m)885 3397 y FB(;)13 b FF(\()p FE(\\0")r FB(;)g(s;)g Fp(Alice)p FF(\)\))943 3515 y FE(accept)21 b FD( )g FE(true)1710 3465 y FB(s;)13 b(\033)1824 3473 y Fn(A)1874 3465 y FB(;)g(\026)1954 3473 y Fn(A)1474 3515 y FD(\000)-35 b(\000)-18 b(\000)h(\000)g(\000)f (\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h (\000)g(\000)-34 b(!)76 b FF(Chec)n(k)26 b FB(\026)2595 3523 y Fn(A)2318 3607 y FE(accept)21 b FD( )h FE(true)844 3698 y(terminate)f FD( )g FE(true)921 b(terminate)22 b FD( )f FE(true)453 3881 y(sk)i FF(=)g FE(SessionKey)r FF(\()p FB(K)5 b FF(\))433 3972 y FE(sid)23 b FF(=)g FB(s;)13 b Fp(Alice)q FB(;)g Fp(Bob)p FB(;)g(X)1131 3980 y FG(0)1166 3972 y FB(;)h(X)1264 3980 y FG(1)1299 3972 y FB(;)f(Y)1378 3980 y FG(0)1412 3972 y FB(;)g(Y)1491 3980 y FG(1)1525 3972 y FB(;)g(\033)1603 3980 y Fn(A)1653 3972 y FB(;)h(\033)1732 3980 y Fn(B)1784 3972 y FB(;)f(\026)1864 3980 y Fn(A)1915 3972 y FB(;)g(\026)1995 3980 y Fn(B)298 4217 y FF(where)132 b FE(SessionKey)r FF(\()p FB(K)5 b FF(\))22 b(=)f FE(PRF)1357 4225 y Fn(K)1415 4217 y FF(\(0\))p FB(;)14 b FE(MacKey)q FF(\()p FB(K)5 b FF(\))21 b(=)g FE(PRF)2184 4225 y Fn(K)2243 4217 y FF(\(1\))626 4308 y([)p FC(R)p FF(])734 4317 y Fc(abs)838 4308 y FF(is)26 b(the)g(abscisse)h(of)f(the)f(p)r(oin)n(t)h FC(R)g FF(in)f Fo(F)1982 4316 y Fn(p)626 4399 y FF(and)h(when)f(a)h(c)n(hec)n(k)f (fails)j(whithout)d(b)r(eing)h(caugh)n(t,)g(one)g(stops)g(the)f (execution:)h FE(terminate)21 b FD( )g FE(true)p 3908 4452 4 3824 v -11 4455 3923 4 v 346 4598 a FC(Fig.)13 b(2.)26 b FF(An)f(honest)g(execution)h(of)g(the)g('Twist-A)n(Ugmen)n (ted')g(Authen)n(ticated)e(Di\016e-Hellman)i(proto)r(col.)1905 5744 y FI(15)p eop end %%Page: 16 16 TeXDict begin 16 15 bop -58 -83 a Fy(Conclusion)-58 124 y FI(This)31 b(pap)s(er)g(sho)m(ws)g(that)h(it)g(is)g(imp)s(ortan)m(t)g (to)g(pro)m(v)m(e)h(the)f(securit)m(y)g(of)g(a)g(whole)g(proto)s(col)h (and)e(not)h(to)g(mak)m(e)h(the)-58 237 y(pro)s(of)e(in)g(sev)m(eral)h (and)f(indep)s(enden)m(t)f(w)m(orks.)i(Some)f(gaps)h(ma)m(y)g(indeed)f (app)s(ear,)g(unless)f(theorems)i(are)g(applied,)-58 350 y(with)i(clear)h(assumptions)e(and)g(conclusions.)h(O)m(AEP)g(is)g (also)h(a)f(go)s(o)s(d)g(example,)g(where)g(the)g(seman)m(tic)h (securit)m(y)-58 463 y(against)f(adaptiv)m(e)g(c)m(hosen-ciphertext)g (attac)m(ks)h(w)m(as)e(widely)f(assumed,)h(without)f(a)h(global)h (securit)m(y)f(pro)s(of,)g(but)-58 576 y(only)j(t)m(w)m(o)h(unrelated)f (results)f(\(O)m(AEP)h(is)g(IND-CP)-8 b(A)36 b(and)f(P)-8 b(A94)37 b([13],)h(and)d(IND-CP)-8 b(A)36 b(com)m(bined)g(with)f(P)-8 b(A98)-58 688 y(implies)31 b(IND-CCA2)g([9]\),)h(as)e(noticed)h(b)m(y)g (Shoup)d(in)i([43].)83 801 y(Finally)-8 b(,)33 b(w)m(e)e(w)m(an)m(t)h (to)g(stress)e(that)i(next)f(v)m(ersions)g(of)g(IKE)f(should)g (precisely)i(refer)e(to)i(PRF)f(or)g(randomness)-58 914 y(extractor)36 b(and)d(not)i(use)f(the)g(same)h(acron)m(ym)f(for)g(the) h(t)m(w)m(o)g(di\013eren)m(t)g(goals:)h(randomness)d(extraction)i(and)f (k)m(ey)-58 1027 y(deriv)-5 b(ation.)-58 1287 y Fy(Ac)m(kno)m (wledgemen)m(t)-58 1494 y FI(The)23 b(w)m(ork)g(describ)s(ed)e(in)i (this)g(pap)s(er)f(has)g(b)s(een)h(supp)s(orted)e(in)h(part)h(b)m(y)g (the)g(Europ)s(ean)f(Commission)g(through)h(the)-58 1607 y(IST)28 b(Programme)h(under)e(Con)m(tract)j(IST-2002-507932)j(ECR)-8 b(YPT.)28 b(The)g(\014rst)g(author)h(is)g(supp)s(orted)d(b)m(y)j(the)g (Di-)-58 1720 y(rector,)c(O\016ce)e(of)h(Science,)h(O\016ce)e(of)h(Adv) -5 b(anced)23 b(Scien)m(ti\014c)i(Computing)e(Researc)m(h,)h (Mathematical)j(Information)-58 1833 y(and)32 b(Computing)g(Sciences)g (Division,)i(of)e(the)h(U.S.)f(Departmen)m(t)i(of)e(Energy)g(under)f (Con)m(tract)j(No.)f(DE-A)m(C03-)-58 1946 y(76SF00098.)27 b(This)d(do)s(cumen)m(t)g(is)g(rep)s(ort)f(LBNL-54709.)k(Disclaimer)f (a)m(v)-5 b(ailable)26 b(at)f Fv(http://www-)t(library.lbl.)-58 2059 y(gov/disclaimer)p FI(.)-58 2319 y Fy(References)-19 2503 y FF(1.)46 b(M.)30 b(Ab)r(dalla,)g(M.)g(Bellare,)h(and)e(P)-6 b(.)29 b(Roga)n(w)n(a)n(y)-6 b(.)46 b(The)30 b(Oracle)g (Di\016e-Hellman)f(Assumptions)g(and)g(an)h(Analysis)f(of)h(DHIES.)44 b(In)86 2594 y FA(CT)27 b({)h(RSA)f('01)p FF(,)f(LNCS)f(2020,)j(pages)e (143{158.)j(Springer-V)-6 b(erlag,)26 b(Berlin,)h(2001.)-19 2684 y(2.)46 b(W.)22 b(Aiello,)h(S.)f(M.)h(Bello)n(vin,)g(M.)g(Blaze,)h (J.)f(Ioannidis,)f(O.)h(Reingold,)f(R.)g(Canetti,)h(A.)f(D.)g(Kerom)n (ytis.)29 b(E\016cien)n(t,)22 b(DoS-resistan)n(t,)86 2775 y(Secure)j(Key)g(Exc)n(hange)h(for)g(In)n(ternet)f(Proto)r(cols.) 37 b(In)24 b FA(Pr)l(o)l(c.)k(of)g(the)g(9th)g(CCS)p FF(,)e(pages)h(48{58.)h(A)n(CM)e(Press,)h(New)e(Y)-6 b(ork,)25 b(2002.)-19 2865 y(3.)46 b(W.)24 b(Aiello,)i(S.)f(M.)g(Bello) n(vin,)h(M.)f(Blaze,)h(J.)f(Ioannidis,)g(O.)g(Reingold,)g(R.)f (Canetti,)i(A.)e(D.)h(Kerom)n(ytis.)32 b(Just)25 b(F)-6 b(ast)25 b(Keying:)f(Key)86 2956 y(Agreemen)n(t)j(In)h(A)f(Hostile)i (In)n(ternet.)40 b(In)27 b FA(A)n(CM)j(T)-6 b(r)l(ansactions)31 b(on)f(Information)g(and)g(System)h(Se)l(curity)p FF(,)e(V)-6 b(ol.)29 b(7,)f(No.)g(2,)h(pages)86 3048 y(1{30.)e(A)n(CM)f(Press,)h (Ma)n(y)f(2004.)-19 3138 y(4.)46 b(B.)32 b(Barak)g(and)f(S.)g(Halevi.) 52 b(An)30 b(arc)n(hitecture)i(for)g(robust)f(pseudo-random)g (generation)i(and)e(applications)h(to)g Fb(/dev/random)p FF(.)86 3229 y(Av)l(ailable)26 b(at)g Fb(http://eprint.iacr.org/)p FF(.)-19 3319 y(5.)46 b(B.)31 b(Barak,)i(R.)e(Shaltiel)g(and)g(E.)h(T) -6 b(romer.)51 b(T)-6 b(rue)31 b(Random)g(Num)n(b)r(er)f(Generators)i (Secure)f(in)g(a)h(Changing)g(En)n(vironmen)n(t.)49 b(In)86 3410 y FA(CHES)27 b('03)p FF(,)f(pages)h(166{180.)h(LNCS)e(2779,)h (2003.)-19 3500 y(6.)46 b(S.)34 b(M.)h(Bello)n(vin)g(and)f(M.)h (Merritt.)60 b(Encrypted)33 b(Key)h(Exc)n(hange:)g(P)n(assw)n (ord-Based)j(Proto)r(cols)f(Secure)e(against)i(Dictionary)86 3591 y(A)n(ttac)n(ks.)d(In)25 b FA(Pr)l(o)l(c.)j(of)g(the)g(Symp)l (osium)g(on)g(Se)l(curity)h(and)f(Privacy)p FF(,)e(pages)h(72{84.)h (IEEE,)e(1992.)-19 3681 y(7.)46 b(M.)24 b(Bellare,)i(R.)d(Canetti)h (and)g(H.)f(Kra)n(w)n(czyk.)31 b(Keying)23 b(Hash)h(F)-6 b(unctions)23 b(for)h(Message)i(Authen)n(tication.)k(In)23 b FA(Crypto)k('96)p FF(,)d(LNCS)86 3773 y(1109,)j(pages)g(1{15.)g (Springer-V)-6 b(erlag,)26 b(Berlin,)h(1996.)-19 3863 y(8.)46 b(M.)30 b(Bellare,)i(R.)e(Canetti)h(and)e(H.)h(Kra)n(w)n(czyk.) 47 b(Pseudorandom)30 b(F)-6 b(unctions)30 b(Revisited:)g(The)g(Cascade) i(Construction)e(and)g(Its)86 3954 y(Concrete)37 b(Securit)n(y.)66 b(In)36 b FA(Pr)l(o)l(c.)i(of)f(the)i(37th)f(A)n(nnual)g(IEEE)f(Symp)l (osium)h(on)g(F)-6 b(oundations)39 b(of)e(Computer)i(Scienc)l(e)p FF(,)f(pages)86 4045 y(514{523,)28 b(1996.)-19 4135 y(9.)46 b(M.)18 b(Bellare,)h(A.)f(Desai,)g(D.)f(P)n(oin)n(tc)n(hev)l(al,)h(and) f(P)-6 b(.)18 b(Roga)n(w)n(a)n(y)-6 b(.)21 b(Relations)d(among)h (Notions)e(of)i(Securit)n(y)d(for)j(Public-Key)d(Encryption)86 4226 y(Sc)n(hemes.)34 b(In)25 b FA(Crypto)k('98)p FF(,)d(LNCS)f(1462,)i (pages)g(26{45.)h(Springer-V)-6 b(erlag,)26 b(Berlin,)h(1998.)-58 4316 y(10.)47 b(M.)26 b(Bellare)i(and)d(P)-6 b(.)26 b(Roga)n(w)n(a)n(y) -6 b(.)35 b(Random)25 b(Oracles)i(Are)e(Practical:)j(a)e(P)n(aradigm)h (for)g(Designing)f(E\016cien)n(t)g(Proto)r(cols.)37 b(In)25 b FA(Pr)l(o)l(c.)86 4408 y(of)i(the)h(1st)h(CCS)p FF(,)d(pages)g (62{73.)i(A)n(CM)e(Press,)h(New)f(Y)-6 b(ork,)25 b(1993.)-58 4498 y(11.)47 b(M.)24 b(Bellare)i(and)e(P)-6 b(.)24 b(Roga)n(w)n(a)n(y) -6 b(.)32 b(En)n(tit)n(y)23 b(Authen)n(tication)h(and)f(Key)h (Distribution.)32 b(In)23 b FA(Crypto)k('93)p FF(,)e(LNCS)e(773,)j (pages)f(232{249.)86 4589 y(Springer-V)-6 b(erlag,)26 b(Berlin,)h(1994.)-58 4679 y(12.)47 b(M.)27 b(Bellare)h(and)e(P)-6 b(.)27 b(Roga)n(w)n(a)n(y)-6 b(.)37 b(Pro)n(v)l(ably)26 b(Secure)g(Session)h(Key)f(Distribution:)h(the)f(Three)h(P)n(art)n(y)f (Case.)38 b(In)26 b FA(Pr)l(o)l(c.)j(of)f(the)h(27th)86 4770 y(STOC)p FF(.)c(A)n(CM)h(Press,)h(New)f(Y)-6 b(ork,)25 b(1995.)-58 4860 y(13.)47 b(M.)23 b(Bellare)i(and)e(P)-6 b(.)23 b(Roga)n(w)n(a)n(y)-6 b(.)30 b(Optimal)23 b(Asymmetric)g (Encryption)f({)h(Ho)n(w)g(to)h(Encrypt)e(with)h(RSA.)28 b(In)23 b FA(Eur)l(o)l(crypt)k('94)p FF(,)c(LNCS)86 4951 y(950,)k(pages)f(92{111.)j(Springer-V)-6 b(erlag,)26 b(Berlin,)g(1995.)-58 5041 y(14.)47 b(D.)26 b(Boneh.)36 b(The)27 b(Decision)g(Di\016e-Hellman)f(problem.)36 b(In)26 b FA(Pr)l(o)l(c.)i(of)g(Thir)l(d)g(Numb)l(er)h(The)l(ory)g(Symp)l (osium)p FF(,)e(LNCS)f(1423,)i(pages)86 5133 y(48{63.)g(Springer-V)-6 b(erlag,)26 b(Berlin,)g(1998.)-58 5222 y(15.)47 b(B.)21 b(M\177)-38 b(oller.)28 b(A)20 b(Public-Key)f(Encryption)h(Sc)n(heme)h (with)f(Pseudo-Random)h(Ciphertexts.)26 b(In)19 b FA(ESORICS)k('04)p FF(,)d(LNCS)h(3193,)h(pages)86 5314 y(335{351.)28 b(Springer-V)-6 b(erlag,)26 b(Berlin,)h(2004.)-58 5404 y(16.)47 b(C.)26 b(Bo)n(yd,)g(P)-6 b(.)26 b(Mon)n(tague,)g(and)g(K.)f(Nguy)n(en.)33 b(Elliptic)27 b(Curv)n(e)e(Based)i(P)n(assw)n(ord)g(Authen)n(ticated)d (Key)h(Exc)n(hange)h(Proto)r(cols.)36 b(In)86 5495 y FA(A)n(CISP)27 b('01)p FF(,)f(LNCS)f(2119,)i(pages)g(487{501.)i (Springer-V)-6 b(erlag,)26 b(Berlin,)h(2001.)1905 5744 y FI(16)p eop end %%Page: 17 17 TeXDict begin 17 16 bop -58 -83 a FF(17.)47 b(R.)32 b(Canetti,)i(Y.)f (Do)r(dis,)g(S.)g(Halevi,)g(E.)g(Kushilevitz)g(and)f(A.)h(Sahai.)56 b(Exp)r(osure-Resilien)n(t)33 b(F)-6 b(unctions)32 b(and)h (All-Or-Nothing)86 8 y(T)-6 b(ransforms.)36 b(In)25 b FA(Eur)l(o)l(crypt)30 b('00)p FF(,)25 b(LNCS)h(1807,)h(pages)g (453{469.)i(Springer-V)-6 b(erlag,)26 b(Berlin,)g(2000.)-58 111 y(18.)47 b(R.)23 b(Canetti)h(and)f(H.)g(Kra)n(w)n(czyk.)30 b(Univ)n(ersally)24 b(Comp)r(osable)h(Notions)e(of)i(Key)d(Exc)n(hange) i(and)f(Secure)g(Channels.)31 b(In)22 b FA(Eur)l(o)l(crypt)86 203 y('02)p FF(,)k(LNCS)f(2332,)i(pages)g(337{351.)i(Springer-V)-6 b(erlag,)26 b(Berlin,)g(2002.)-58 305 y(19.)47 b(R.)29 b(Canetti)g(and)g(H.)g(Kra)n(w)n(czyk.)44 b(Securit)n(y)28 b(Analysis)i(of)g(IKE's)f(Signature-based)g(Key-Exc)n(hange)f(Proto)r (col.)46 b(In)29 b FA(Crypto)j('02)p FF(,)86 397 y(LNCS)25 b(2442,)j(pages)e(143{161.)j(Springer-V)-6 b(erlag,)26 b(Berlin,)h(2002.)36 b(Cryptology)26 b(ePrin)n(t)g(Arc)n(hiv)n(e)e (2002/120.)29 b(F)-6 b(ull)26 b(V)-6 b(ersion.)86 488 y(Av)l(ailable)26 b(at)g Fb(http://eprint.iacr.org/)p FF(.)-58 591 y(20.)47 b(W.)30 b(Di\016e)g(and)g(M.)g(E.)h(Hellman.)47 b(New)30 b(Directions)h(in)f(Cryptograph)n(y.)47 b FA(IEEE)31 b(T)-6 b(r)l(ansactions)34 b(on)d(Information)h(The)l(ory)p FF(,)f(IT{)86 682 y(22\(6\):644{654,)f(No)n(v)n(em)n(b)r(er)25 b(1976.)-58 785 y(21.)47 b(Y.)25 b(Do)r(dis.)35 b(Exp)r(osure-Resilien) n(t)26 b(Cryptograph)n(y.)34 b FA(PhD)27 b(Thesis)p FF(,)g(MIT,)f (August)g(2000.)-58 888 y(22.)47 b(Y.)27 b(Do)r(dis,)h(R.)e(Gennaro,)i (J.)g(H)-10 b(\027)-48 b(astad,)28 b(H.)f(Kra)n(w)n(czyk,)g(and)g(T.)g (Rabin.)39 b(Randomness)27 b(Extraction)g(and)g(Key)f(Deriv)l(ation)i (Using)86 979 y(the)d(CBC,)i(Cascade)g(and)f(HMA)n(C)f(Mo)r(des.)36 b(In)25 b FA(Crypto)j('04)p FF(,)e(LNCS,)g(pages)g(494{510.)j (Springer-V)-6 b(erlag,)26 b(Berlin,)h(2004.)-58 1082 y(23.)47 b(Y.)29 b(Do)r(dis,)i(A.)e(Sahai,)i(A.)f(Smith.)46 b(On)29 b(p)r(erfect)h(and)f(adaptiv)n(e)h(securit)n(y)g(in)f(exp)r (osure-resilien)n(t)i(cryptograph)n(y.)45 b(In)29 b FA(Eur)l(o)l(crypt) 86 1174 y('01)p FF(,)d(LNCS)f(2405,)i(pages)g(301{324.)i(Springer-V)-6 b(erlag,)26 b(Berlin,)g(2001.)-58 1276 y(24.)47 b(T.)19 b(El)g(Gamal.)24 b(A)18 b(Public)g(Key)g(Cryptosystem)g(and)g(a)h (Signature)g(Sc)n(heme)f(Based)h(on)f(Discrete)h(Logarithms.)24 b FA(IEEE)d(T)-6 b(r)l(ansactions)86 1368 y(on)27 b(Information)h(The)l (ory)p FF(,)f(IT{31\(4\):469{472,)k(July)25 b(1985.)-58 1471 y(25.)47 b(R.)26 b(Gennaro,)i(H.)e(Kra)n(w)n(czyk,)h(and)g(T.)g (Rabin.)37 b(Secure)27 b(Hashed)f(Di\016e-Hellman)h(o)n(v)n(er)g (Non-DDH)e(Groups.)38 b(In)26 b FA(Eur)l(o)l(crypt)31 b('04)p FF(,)86 1562 y(LNCS)25 b(3027,)j(pages)e(361{381.)j(Springer-V) -6 b(erlag,)26 b(Berlin,)h(2004.)-58 1665 y(26.)47 b(O.)25 b(Goldreic)n(h.)36 b(F)-6 b(oundations)25 b(of)i(Cryptograph)n(y)e(\(F) -6 b(ragmen)n(ts)26 b(of)g(a)g(Bo)r(ok\).)35 b(1995.)-58 1768 y(27.)47 b(S.)29 b(Goldw)n(asser,)j(S.)e(Micali,)i(and)d(R.)g(Riv) n(est.)46 b(A)29 b(Digital)i(Signature)f(Sc)n(heme)f(Secure)h(Against)g (Adaptativ)n(e)f(Chosen-Message)86 1859 y(A)n(ttac)n(ks.)k FA(SIAM)27 b(Journal)i(of)e(Computing)p FF(,)f(17\(2\):281{308,)k (April)c(1988.)-58 1962 y(28.)47 b(D.)25 b(Harkins)h(and)f(D.)h (Carrel.)35 b(The)26 b(In)n(ternet)f(Key)g(Exc)n(hange)h(\(IKE\).)33 b(RF)n(C)26 b(2409,)h(No)n(v)n(em)n(b)r(er)e(1998.)-58 2065 y(29.)47 b(J.)23 b(H)-10 b(\027)-48 b(astad,)24 b(R.)f(Impagliazzo,)i(L.)e(Levin,)g(and)g(M.)h(Lub)n(y)-6 b(.)28 b(A)23 b(Pseudorandom)g(Generator)h(from)g(an)n(y)e(One-W)-6 b(a)n(y)22 b(F)-6 b(unction.)29 b FA(SIAM)86 2156 y(Journal)f(of)f (Computing)p FF(,)g(28\(4\):1364{1396,)k(1999.)-58 2259 y(30.)47 b(IETF.)35 b(Arc)n(hiv)n(e)24 b(of)j(IETF-IPSEC.)35 b(Av)l(ailable)26 b(at)g Fb(http://www.vpnc.org/ietf-)t(ipsec)q(/)p FF(.)-58 2362 y(31.)47 b(I.)26 b(Impagliazzo,)j(L.)d(Levin,)g(and)g(M.) h(Lub)n(y)-6 b(.)35 b(Pseudo-Random)26 b(Generation)h(from)h(One-W)-6 b(a)n(y)24 b(F)-6 b(unctions.)36 b(In)26 b FA(Pr)l(o)l(c.)j(of)f(the)h (21st)86 2453 y(STOC)p FF(,)c(pages)i(12{24.)h(A)n(CM)e(Press,)h(New)e (Y)-6 b(ork,)26 b(1989.)-58 2556 y(32.)47 b(I.)25 b(Impagliazzo)i(and)e (D.)g(Zuc)n(k)n(erman.)33 b(Ho)n(w)25 b(to)g(Recycle)g(Random)g(Bits.) 35 b(In)24 b FA(Pr)l(o)l(c.)k(of)e(the)i(30th)g(A)n(nnual)g(IEEE)e (Symp)l(osium)i(on)86 2647 y(F)-6 b(oundations)29 b(of)e(Computer)i (Scienc)l(e)p FF(,)e(pages)f(248{253,)j(1989.)-58 2750 y(33.)47 b(B.)26 b(Kaliski.)35 b(One-W)-6 b(a)n(y)24 b(P)n(erm)n(utations)j(on)e(Elliptic)i(Curv)n(es.)35 b FA(Journal)28 b(of)f(Cryptolo)l(gy)p FF(,)h(3\(3\):187{199,)h(1991.) -58 2853 y(34.)47 b(J.)23 b(Kamp)f(and)g(D.)h(Zuc)n(k)n(erman.)28 b(Deterministic)c(Extractors)f(for)g(Bit-Fixing)g(Sources)g(and)f(Exp)r (osure-Resilien)n(t)h(Cryptograph)n(y.)86 2944 y(In)i FA(Pr)l(o)l(c.)j(of)f(the)h(44th)h(A)n(nnual)f(IEEE)f(Symp)l(osium)g (on)h(F)-6 b(oundations)29 b(of)f(Computer)g(Scienc)l(e)p FF(,)f(2003.)-58 3047 y(35.)47 b(C.)36 b(Kaufman.)64 b(The)35 b(In)n(ternet)g(Key)f(Exc)n(hange)i(\(IKEv2\))f(Proto)r(col.) 65 b(INTERNET-DRAFT)34 b(draft-ietf-ipsec-ik)n(ev2-17.txt,)86 3139 y(Septem)n(b)r(er)25 b(23,)h(2004.)i(Av)l(ailable)e(at)g Fb(http://www.ietf.org/internet-)5 b(draft)q(s/dr)q(aft-)g(ietf)q(-)t (ips)q(ec-)g(ikev2)q(-)t(17.)q(txt)-58 3241 y FF(36.)47 b(H.)18 b(Kra)n(w)n(czyk.)k(The)d(SIGMA)f(F)-6 b(amily)18 b(of)h(Key-Exc)n(hange)f(Proto)r(cols.)25 b(Av)l(ailable)18 b(at)h Fb(http://www.ee.technion.ac.il/)q(~hugo)q(/)86 3333 y(sigma.html)p FF(.)-58 3436 y(37.)47 b(H.)32 b(Kra)n(w)n(czyk.)56 b(SIGMA:)32 b(The)h('SIGn-and-MAc')f(Approac)n(h)g(to)h(Authen)n (ticated)e(Di\016e-Hellman)i(and)g(Its)f(Use)h(in)g(the)f(IKE)86 3527 y(Proto)r(cols.)41 b(In)27 b FA(Crypto)j('03)p FF(,)d(LNCS)g (2729,)i(pages)g(400{425.)h(Springer-V)-6 b(erlag,)27 b(Berlin,)i(2003.)41 b(Extended)26 b(v)n(ersion)h(a)n(v)l(ailable)i(at) 86 3618 y Fb(http://www.ee.technion.ac.il/~)q(hugo/)q(sigm)q(a.htm)q(l) p FF(.)-58 3721 y(38.)47 b(M.)23 b(Naor)g(and)g(O.)g(Reingold.)30 b(F)-6 b(rom)23 b(Unpredictabilit)n(y)f(to)h(Indistinguishabilit)n(y:)h (A)e(Simple)h(Construction)h(of)f(Pseudo-Random)86 3813 y(F)-6 b(unctions)25 b(from)i(MA)n(Cs.)34 b(In)25 b FA(Crypto)k('98)p FF(,)d(LNCS)f(1462.)j(Springer-V)-6 b(erlag,)26 b(Berlin,)h(1998.)-58 3915 y(39.)47 b(M.)28 b(San)n(tha)f(and)g(U.)h(V.)f(V)-6 b(azirani.)41 b(Generating)29 b(quasi-random)e(sequences)h(from)g (semi-random)g(sources.)42 b(In)27 b FA(J.)i(of)g(Computer)86 4007 y(and)f(System)g(Scienc)l(es)p FF(,)g(63:612{626,)h(1986.)-58 4110 y(40.)47 b(R.)24 b(Sc)n(ho)r(of.)34 b(Coun)n(ting)25 b(P)n(oin)n(ts)g(on)g(Elliptic)g(Curv)n(es)g(o)n(v)n(er)g(Finite)g (Fields.)33 b(In)24 b FA(J.)j(Th)n(\023)-37 b(eor.)27 b(Nombr)l(es)h(Bor)l(de)l(aux)p FF(,)e(7:219{254,)j(1995.)-58 4212 y(41.)47 b(R.)27 b(Shaltiel.)40 b(Recen)n(t)26 b(dev)n(elopmen)n (ts)h(in)g(Extractors.)40 b(In)27 b FA(Bul)t(letin)i(of)f(the)i(Eur)l (op)l(e)l(an)h(Asso)l(ciation)f(for)f(The)l(or)l(etic)l(al)i(Computer) 86 4304 y(Scienc)l(e)p FF(,)e(V)-6 b(olume)27 b(77,)i(June)e(2002,)j (pages)e(67{95.)42 b(Av)l(ailable)28 b(at)g Fb (http://www.wisdom.weizmann.ac)q(.il/~)q(rone)q(ns/p)q(apers)q(/)86 4395 y(survey.ps)p FF(,)g(2002.)-58 4498 y(42.)47 b(V.)25 b(Shoup.)34 b(A)25 b(Prop)r(osal)i(for)g(an)e(ISO)g(Standard)g(for)i (Public-Key)e(Encryption,)g(decem)n(b)r(er)h(2001.)36 b(ISO/IEC)25 b(JTC)i(1/SC27.)-58 4601 y(43.)47 b(V.)25 b(Shoup.)34 b(O)n(AEP)25 b(Reconsidered.)35 b(In)24 b FA(Crypto)29 b('01)p FF(,)d(LNCS)f(2139,)j(pages)e(239{259.)j (Springer-V)-6 b(erlag,)26 b(Berlin,)h(2001.)-58 4704 y(44.)47 b(V.)24 b(Shoup.)31 b(A)24 b(Computational)i(In)n(tro)r (duction)d(to)i(Num)n(b)r(er)e(Theory)h(Algebra.)33 b(In)24 b FA(Cambridge)j(University)g(Pr)l(ess)p FF(,)f(2005.)34 b(F)-6 b(reely)86 4795 y(a)n(v)l(ailable)26 b(at)g Fb (http://www.shoup.net/ntb/)p FF(.)-58 4898 y(45.)47 b(V.)25 b(Shoup.)34 b(Sequences)25 b(of)h(Games:)h(A)e(T)-6 b(o)r(ol)27 b(for)g(T)-6 b(aming)26 b(Complexit)n(y)g(in)g(Securit)n(y)e(Pro)r (ofs.)86 4989 y(Av)l(ailable)i(at)g Fb(http://www.shoup.net/papers/)p FF(,)32 b(2004.)-58 5092 y(46.)47 b(J.)24 b(H.)f(Silv)n(erman.)31 b FA(The)26 b(A)n(rithmetic)g(of)f(El)t(liptic)g(Curves)p FF(,)g(v)n(olume)e(106)h(of)h FA(Gr)l(aduate)i(T)-6 b(exts)27 b(in)e(Mathematics)p FF(.)32 b(Springer-V)-6 b(erlag,)86 5183 y(1986.)-58 5286 y(47.)47 b(T.)26 b(Dierks)g(and)f(C.)h(Allen.)35 b(The)26 b(TLS)f(Proto)r(col)j(V)-6 b(ersion)26 b(1.0.)35 b(RF)n(C)26 b(2246,)h(Jan)n(uary)f(1999.)36 b(Op)r(enSSL.)24 b(v)n(ersion)i(0.9.7e)-58 5389 y(48.)47 b(L.)32 b(T)-6 b(revisan)32 b(and)g(S.)g(V)-6 b(adhan.)53 b(Extracting)32 b(Randomness)g(from)h(Samplable)g(Distributions.)53 b(In)32 b FA(Pr)l(o)l(c.)i(of)f(the)h(41st)h(A)n(nnual)86 5481 y(IEEE)27 b(Symp)l(osium)h(on)f(F)-6 b(oundations)30 b(of)d(Computer)i(Scienc)l(e)p FF(,)d(2000.)1905 5744 y FI(17)p eop end %%Page: 18 18 TeXDict begin 18 17 bop -58 -83 a Fy(A)112 b(Authen)m(ticated)37 b(Key)h(Exc)m(hange)-58 137 y FI(An)g(algorithm)h(for)e(k)m(ey)i(exc)m (hange)h(is)e(an)g(in)m(teractiv)m(e)i(proto)s(col)f(b)s(et)m(w)m(een)g (t)m(w)m(o)g(pla)m(y)m(ers)g Fw(A)f FI(\(for)g(Alice\))i(and)d Fw(B)-58 250 y FI(\(for)31 b(Bob\))h(at)g(the)f(end)f(of)i(whic)m(h)e (they)h(b)s(oth)g(share)g(a)g(session)g(k)m(ey)h Fs(sk)p FI(.)f(Eac)m(h)h(of)f(the)h(pla)m(y)m(ers)g(ma)m(y)f(ha)m(v)m(e)h(sev)m (eral)-58 363 y Fx(instanc)-5 b(es)45 b FI(in)m(v)m(olv)m(ed)38 b(in)e(distinct,)h(p)s(ossibly)f(concurren)m(t,)h(executions)g(of)g (the)f(proto)s(col.)i(Instances)e(of)h(part)m(y)g Fw(A)-58 476 y FI(\(resp.)i Fw(B)5 b FI(\))40 b(are)f(mo)s(deled)g(b)m(y)h (oracles)g([11,)17 b(12],)41 b(denoted)e Fw(\005)2099 443 y Ft(i)2092 503 y(A)2188 476 y FI(\(resp.)g Fw(\005)2533 432 y Ft(j)2526 505 y(B)2586 476 y FI(\),)h(or)g(b)m(y)f Fw(\005)46 b FI(when)38 b(w)m(e)i(consider)f(an)m(y)-58 589 y(pla)m(y)m(er's)32 b(instance.)-58 859 y Fz(A.1)105 b(The)35 b(Comm)m(unication)g(Mo)s(del)-58 1046 y FI(During)42 b(executions)h(of)f(this)g(proto)s(col,)h(the)f(adv)m(ersary)g(has)g (the)g(en)m(tire)h(con)m(trol)h(of)e(the)g(net)m(w)m(ork,)h(and)e (tries)-58 1159 y(to)k(break)g(the)g(priv)-5 b(acy)44 b(of)h(the)g(k)m(ey)g(\()p Fx(semantic)i(se)-5 b(curity)8 b FI(\))45 b(or)g(the)g(authen)m(tication)i(of)d(the)h(pla)m(y)m(ers)h (\()p Fx(mutual)-58 1272 y(authentic)-5 b(ation)7 b FI(\).)30 b(T)-8 b(o)27 b(mo)s(del)g(the)g(v)-5 b(arious)26 b(capabilities)j(of)e (the)g(adv)m(ersary)-8 b(,)28 b(sev)m(eral)g(queries)f(are)g(a)m(v)-5 b(ailable)29 b(to)f(the)-58 1385 y(latter:)10 1570 y Fz({)46 b Fs(Execute)q FI(\()p Fw(A;)15 b(i;)g(B)5 b(;)15 b(j)5 b FI(\):)35 b(This)c(query)g(mo)s(dels)h(passiv)m(e)g(attac)m (ks,)j(where)c(the)h(adv)m(ersary)g(gets)h(access)g(to)g(honest)108 1683 y(executions)f(of)e(the)h(proto)s(col)g(b)s(et)m(w)m(een)g(the)g Fw(i)p FI(-th)f(instance)h(of)g Fw(A)f FI(\()p Fw(\005)2526 1650 y Ft(i)2519 1710 y(A)2576 1683 y FI(\))h(and)f(the)g Fw(j)5 b FI(-th)31 b(instance)g(of)g Fw(B)k FI(\()p Fw(\005)3844 1639 y Ft(j)3837 1711 y(B)3897 1683 y FI(\),)108 1796 y(b)m(y)30 b(ea)m(v)m(esdropping)i(for)e(example.)10 1910 y Fz({)46 b Fs(Reveal)p FI(\()p Fw(U;)15 b(i)p FI(\):)33 b(This)e(query)g(mo)s(dels)g(the)h(misuse)f(of)h(the)g(session)f(k)m (ey)i(b)m(y)e(the)h Fw(i)p FI(-th)g(instance)g(of)g Fw(U)41 b FI(\(either)33 b Fw(A)108 2023 y FI(or)f Fw(B)5 b FI(\).)31 b(Our)g(mo)s(del)g(th)m(us)g(encompasses)h(the)g(so-called)h Fx(known-key)h(attacks)p FI(.)f(The)e(query)g(is)h(only)f(a)m(v)-5 b(ailable)108 2136 y(to)28 b(the)f(adv)m(ersary)g(if)g(the)g(attac)m(k) m(ed)i(instance)f(actually)g(\\holds")f(a)h(session)e(k)m(ey)-8 b(.)29 b(It)e(then)f(releases)i(the)f(latter.)108 2249 y(During)32 b(the)f(proto)s(col,)i(the)f(instance)g(will)g(claim)h (that)f(it)g(actually)i(holds)d(a)h(session)g(k)m(ey)g(when)f(it)h (\015ips)f(the)108 2362 y(\015ag)k Fs(accept)e FI(to)h Fs(true)p FI(.)f(This)f(ma)m(y)i(nev)m(er)f(happ)s(en)e(if)i(the)g (instance)h(detects)g(that)f(the)h(other)f(part)m(y)g(do)s(es)g(not)108 2475 y(b)s(eha)m(v)m(e)i(honestly:)g(it)g(then)f(terminates)h(without)f (accepting)i(\(the)f(\015ag)h Fs(terminate)e FI(c)m(hanges)h(to)g Fs(true)p FI(,)g(while)108 2588 y(the)c(\015ag)h Fs(accept)f FI(remains)f(to)h Fs(false)p FI(.\))f(A)h Fs(Reveal)p FI(-query)f(ask)m(ed)h(to)g(suc)m(h)f(a)h(pla)m(y)m(er)g(is)f(answ)m (ered)h(b)m(y)f Fl(?)p FI(.)-58 2858 y Fz(A.2)105 b(Session)36 b(Key)f(Priv)-6 b(acy)-58 3045 y FI(The)31 b(\014rst)f(goal)j(of)e(an)g (adv)m(ersary)g(is)g(to)h(break)f(the)g(priv)-5 b(acy)32 b(of)f(the)g(session)g(k)m(ey)h(\(a.k.a.,)h(seman)m(tic)g(securit)m (y\):)f(it)-58 3158 y(w)m(an)m(ts)25 b(to)f(learn)g(some)g(information) g(ab)s(out)g(it.)g(Suc)m(h)f(a)h(securit)m(y)h(notion)f(is)g(mo)s (deled)f(b)m(y)h(the)g(game)g Fz(Game)3687 3121 y Fk(ak)n(e)3789 3158 y FI(\()p Fl(A)p FI(\),)-58 3270 y(in)30 b(whic)m(h)f(one)i(more)f (query)f(is)h(a)m(v)-5 b(ailable)32 b(to)f(the)f(adv)m(ersary)g Fl(A)p FI(:)g(the)g Fs(T)-8 b(est)p FI(-query)g(.)30 b(This)f(query)h Fs(T)-8 b(est)p FI(\()p Fw(U;)15 b(i)p FI(\))31 b(can)f(b)s(e)-58 3383 y(ask)m(ed)c(at)g(most)g(once,)h(on)e (an)h(instance)g(of)f(an)m(y)h(part)m(y)g(whic)m(h)f(actually)i(holds)e (a)h Fx(fr)-5 b(esh)34 b FI(session)25 b(k)m(ey)-8 b(.)27 b(The)e(freshness)-58 3496 y(notion)34 b(\(whic)m(h)f(will)g(b)s(e)g (de\014ned)f(more)h(precisely)h(later,)g(with)f(the)g(partnering)g (relation\))h(roughly)f(means)g(that)-58 3609 y(the)40 b(session)g(k)m(ey)g(is)g(not)g(\\ob)m(viously")h(kno)m(wn)e(to)h(the)g (adv)m(ersary)-8 b(.)41 b(This)e(query)g(is)g(answ)m(ered)h(as)g(follo) m(ws:)h(one)-58 3722 y(\015ips)31 b(a)h(\(priv)-5 b(ate\))33 b(coin)g Fw(b)f FI(and)f(forw)m(ards)g Fs(sk)h FI(\(the)h(v)-5 b(alue)32 b Fs(Reveal)p FI(\()p Fw(U;)15 b(i)p FI(\))33 b(w)m(ould)f(output\))g(if)g Fw(b)c FI(=)f(1,)33 b(or)e(a)i(uniformly) -58 3835 y(distributed)d(random)f(v)-5 b(alue)31 b(if)f Fw(b)c FI(=)f(0.)83 3949 y(When)k(pla)m(ying)g(this)g(game,)h(the)f (goal)h(of)f(the)g(adv)m(ersary)g(is)g(to)g(guess)g(the)g(bit)g Fw(b)f FI(in)m(v)m(olv)m(ed)j(in)d(the)h Fs(T)-8 b(est)p FI(-query)g(,)-58 4062 y(b)m(y)33 b(outputting)h(its)f(guess)g Fw(b)938 4029 y Fj(0)962 4062 y FI(.)g(W)-8 b(e)34 b(denote)g(the)f Fz(AKE)38 b(adv)-6 b(an)m(tage)33 b FI(against)i(a)e(proto)s(col)h Fw(P)46 b FI(as)34 b(the)f(probabilit)m(y)-58 4175 y(that)e Fl(A)f FI(correctly)i(guesses)e(the)h(v)-5 b(alue)31 b(of)f Fw(b)p FI(.)h(More)g(precisely)-8 b(,)32 b(w)m(e)f(de\014ne)e Fs(Adv)2695 4138 y Fk(ak)n(e)2695 4198 y Ft(P)2797 4175 y FI(\()p Fl(A)p FI(\))c(=)g(2)15 b(Pr[)p Fw(b)26 b FI(=)f Fw(b)3444 4142 y Fj(0)3467 4175 y FI(])c Fl(\000)f FI(1.)-58 4445 y Fz(A.3)105 b(Activ)m(e)35 b(Adv)m(ersaries)-58 4632 y FI(Classical)j(attac)m(ks)h(in)d(k)m(ey)i(exc)m(hange)g(proto)s (cols)f(are)g(the)g(so-called)i(\\man-in-the-middle")f(attac)m(ks.)h (They)d(do)-58 4745 y(not)28 b(in)m(v)m(olv)m(e)i(a)f(simple)f(passiv)m (e)g(adv)m(ersary)-8 b(,)29 b(but)f(an)f(adv)m(ersary)i(whic)m(h)e(in)m (tercepts,)j(repla)m(ys,)e(mo)s(di\014es)f(or)h(creates)-58 4858 y(\015o)m(ws)i(from/to)i(Alice)f(to/from)h(Bob.)e(W)-8 b(e)32 b(th)m(us)e(consider)g(the)h(p)s(o)m(w)m(erful)f(query)10 5043 y Fz({)46 b Fs(Send)p FI(\()p Fw(U;)15 b(i;)g(m)p FI(\):)47 b(this)e(allo)m(ws)h(the)f(adv)m(ersary)g Fl(A)g FI(to)g(send)g(a)g(message)h(to)g(the)f Fw(i)p FI(-th)g(instance)h(of)f Fw(U)10 b FI(.)45 b(The)108 5156 y(adv)m(ersary)27 b Fl(A)e FI(gets)i(bac)m(k)g(the)f(resp)s(onse)g(this)g(instance)g (generates)i(in)e(pro)s(cessing)f(the)i(message)g Fw(m)f FI(according)108 5269 y(to)g(the)f(proto)s(col)h(and)e(its)h(curren)m (t)g(state.)h(A)f(query)f Fs(Send)p FI(\()p Fw(A;)15 b(i;)g Fv(Start)q FI(\))25 b(initiates)h(a)f(k)m(ey)h(exc)m(hange)g (execution,)108 5382 y(and)k(th)m(us)g(the)g(adv)m(ersary)g(receiv)m (es)i(the)f(initial)g(\015o)m(w)g(the)f(pla)m(y)m(er)h Fw(A)g FI(should)e(send)g(out)i(to)g(the)f(pla)m(y)m(er)h Fw(B)k FI(\(w)m(e)108 5495 y(assume)30 b(here)h(that)g(Alice)g(is)g (the)f(initiator.\))1905 5744 y(18)p eop end %%Page: 19 19 TeXDict begin 19 18 bop 83 -83 a FI(When)42 b(considering)g(activ)m(e)j (adv)m(ersaries,)e(the)f Fs(Execute)p FI(-query)h(b)s(ecomes)g (useless,)f(since)h(using)e(the)i Fs(Send)p FI(-)-58 30 y(query)-8 b(,)40 b(and)g(rela)m(ying)h(the)f(\015o)m(ws,)h(the)f (adv)m(ersary)g(has)g(the)g(abilit)m(y)i(to)f(carry)f(out)g(honest)g (executions)h(among)-58 143 y(parties.)d(W)-8 b(e)38 b(can)f(th)m(us)g(forget)h(the)f(former)g(one)g(in)g(our)f(mo)s(del.)h (Note)i(ho)m(w)m(ev)m(er)f(that)g Fs(Execute)p FI(-queries)g(are)g(of) -58 256 y(ma)5 b(jor)24 b(in)m(terest)h(when)e(dealing)i(with)f(passw)m (ord-based)f(authen)m(tication.)j(In)d(suc)m(h)h(a)g(case,)i(it)e(is)g (indeed)g(imp)s(ortan)m(t)-58 369 y(to)31 b(distinguish)f(passiv)m(e)h (and)f(activ)m(e)i(attac)m(ks.)-58 641 y Fz(A.4)105 b(Authen)m (tication)-58 831 y FI(Another)36 b(goal)h(for)f(an)f(adv)m(ersary)h (ma)m(y)g(also)h(b)s(e)e(to)i(break)e(the)h(authen)m(tication)i(of)e (the)g(pla)m(y)m(ers)g(\(imp)s(ersonate)-58 944 y(a)h(pla)m(y)m(er,)g (or)f(simply)g(mak)m(e)h(a)g(pla)m(y)m(er)g(to)g(share)f(a)h(k)m(ey)g (with)e(nob)s(o)s(dy)g(|unkno)m(wn-k)m(ey)h(attac)m(ks|,)i(or)f(a)f (non-)-58 1056 y(in)m(tended)27 b(partner)g(|miss-binding)f(iden)m(tit) m(y)i(attac)m(ks|\).)i(The)d Fx(mutual)j(authentic)-5 b(ation)36 b FI(is)27 b(the)h(formal)f(securit)m(y)-58 1169 y(notion)k(whic)m(h)f(prev)m(en)m(ts)h(all)g(these)g(kinds)e(of)h (attac)m(ks.)j(More)e(precisely)-8 b(,)32 b(a)e(k)m(ey)i(exc)m(hange)f (sc)m(heme)g(ac)m(hiev)m(es)i(m)m(u-)-58 1282 y(tual)j(authen)m (tication)h(if)d(an)m(y)i(part)m(y)f(who)f(terminates)i(has)f(an)f (accepting)j(partner.)d(Com)m(bined)h(with)f(seman)m(tic)-58 1395 y(securit)m(y)39 b(whic)m(h)e(roughly)h(means)g(that)h(nob)s(o)s (dy)d(except)j(the)f(in)m(tended)g(partners)f(kno)m(ws)h(the)g(k)m(ey) -8 b(,)39 b(it)g(guaran-)-58 1508 y(tees)g(an)m(y)f(terminating)h(part) m(y)f(that)g(the)g(in)m(tended)g(partner)f(actually)i(kno)m(ws)f(the)g (k)m(ey)-8 b(,)39 b(and)e(nob)s(o)s(dy)f(else)j(has)-58 1621 y(an)m(y)34 b(information)g(ab)s(out)f(it.)h(This)f(is)h(usually)f (ac)m(hiev)m(ed)i(b)m(y)f(additional)g(rounds)e(in)h(whic)m(h)h (parties)f(pro)m(v)m(e)i(their)-58 1734 y(kno)m(wledge)d(of)e(the)h(k)m (ey)g(material)h(to)f(their)f(partners:)g(k)m(ey)h(con\014rmation)g (rounds.)83 1849 y(Note)36 b(ho)m(w)m(ev)m(er)g(that)g(ev)m(en)f(if)g (one)g(is)f(only)h(in)m(terested)h(in)e(the)h(priv)-5 b(acy)35 b(of)g(the)g(k)m(eys)g(under)e(activ)m(e)k(attac)m(ks,)-58 1962 y(pla)m(y)m(ers)f(ha)m(v)m(e)f(to)g(authen)m(ticate)i(themselv)m (es)f(in)e(some)h(w)m(a)m(y)-8 b(.)36 b(Otherwise,)e(it)h(w)m(ould)g(b) s(e)f(easy)h(for)f(the)h(adv)m(ersary)-58 2075 y(to)d(imp)s(ersonate)g (Bob)f(to)i(Alice,)g(and)d(th)m(us)i(\014nally)f(share)g(a)h(k)m(ey)g (with)f(Alice,)i(while)f(the)f(latter)i(has)e(no)g(partner)-58 2188 y(\(except)e(the)f(adv)m(ersary\).)g(Since)g(the)g(adv)m(ersary)g (kno)m(ws)f(the)h(k)m(ey)-8 b(,)29 b(he)e(de\014nitely)h(can)g (distinguish)f(it)h(in)f(the)h Fs(T)-8 b(est)p FI(-)-58 2300 y(query)34 b(ask)m(ed)g(to)h(Alice.)h(Therefore,)e(while)g(seman)m (tic)h(securit)m(y)g(do)s(es)e(not)i(guaran)m(tee)g(a)f(strong)h (authen)m(tication)-58 2413 y(\(a.k.a.)30 b(explicit)f(authen)m (tication\))i(it)e(still)f(ensures)g(an)f(implicit)i(one:)g(when)e (Alice)i(accepts)h(a)e(k)m(ey)-8 b(,)30 b(it)e(can)g(also)h(b)s(e)-58 2526 y(kno)m(wn)h(to)h(Bob)g(only)f(\(but)g(to)h(nob)s(o)s(dy)e(else,)j (and)d(ma)m(yb)s(e)i(Bob)f(neither.\))-58 2799 y Fz(A.5)105 b(F)-9 b(reshness)36 b(and)f(P)m(artnering)-58 2988 y FI(W)-8 b(e)45 b(restricted)f(the)f Fs(T)-8 b(est)p FI(-query)43 b(on)g Fx(fr)-5 b(esh)52 b FI(k)m(eys.)44 b(Indeed,)e(if)i Fw(\005)2285 2955 y Ft(i)2278 3015 y(A)2377 2988 y FI(and)f Fw(\005)2650 2944 y Ft(j)2643 3017 y(B)2746 2988 y FI(agreed)h(on)g(a)f (session)h(k)m(ey)g Fs(sk)p FI(,)f(a)-58 3101 y(query)29 b Fs(Reveal)p FI(\()p Fw(A;)15 b(i)p FI(\))31 b(pro)m(vides)f(this)g (session)f(k)m(ey)i Fs(sk)f FI(to)g(the)g(adv)m(ersary)-8 b(.)31 b(Thereafter,)f(a)g Fs(T)-8 b(est)p FI(\()p Fw(B)5 b(;)15 b(j)5 b FI(\))31 b(\(or)f Fx(a)i(fortiori)-58 3214 y Fs(T)-8 b(est)q FI(\()p Fw(A;)15 b(i)p FI(\)\))45 b(w)m(ould)f(immediately)h(leak)g(all)g(the)f(information)g(ab)s(out)g (the)g(bit)g Fw(b)p FI(.)g(This)f(is)h(ho)m(w)m(ev)m(er)i(the)e(only) -58 3327 y(restriction:)32 b(a)e(k)m(ey)h(is)f(said)h(to)f(b)s(e)g Fx(fr)-5 b(esh)38 b FI(if)30 b(neither)g(the)h(instance)g(or)f(its)g (partner)g(has)g(b)s(een)f(ask)m(ed)i(for)f(a)h Fs(Reveal)p FI(-)-58 3440 y(query)-8 b(.)83 3555 y(Therefore,)37 b(a)h(new)e(notion)i(of)f Fx(p)-5 b(artnership)46 b FI(app)s(ears.)36 b(W)-8 b(e)38 b(sa)m(y)g(that)g(t)m(w)m(o)g(instances)g(are)f Fx(p)-5 b(artners)47 b FI(if)37 b(they)-58 3668 y(ha)m(v)m(e)k(b)s(een) e(in)m(v)m(olv)m(ed)j(in)d(the)h(same)g(session)g(of)g(the)g(proto)s (col,)h(whic)m(h)e(is)h(named)f(b)m(y)h(its)g Fz(session)47 b(ID)39 b FI(or)h Fs(sid)p FI(,)-58 3781 y(de\014ned)35 b(as)i(the)f(\(common\))h(view)g(of)f(the)g(execution:)i(the)e (concatenation)j(of)d(the)h Fx(crucial)46 b FI(\015o)m(ws.)36 b(The)g Fx(crucial)-58 3894 y FI(\015o)m(ws)30 b(are)h(the)g(required)e (\015o)m(ws)i(for)f(ac)m(hieving)i(acceptance)g(from)e(b)s(oth)g (sides.)-58 4169 y Fy(B)112 b(Securit)m(y)37 b(Notions)h(and)g (Computational)h(Assumptions)-58 4392 y FI(In)h(this)g(section)i(w)m(e) f(review)g(the)g(cryptographic)g(primitiv)m(es)g(\(Signatures,)g (Message)h(Authen)m(tication)g(Co)s(des)-58 4505 y(\(MA)m(Cs\)\))32 b(and)e(the)g(Di\016e-Hellman)j(in)m(tractabilit)m(y)g(assumptions.)-58 4777 y Fz(B.1)105 b(Signature)35 b(Sc)m(hemes)-58 4967 y FI(A)c(signature)f(sc)m(heme)h Fs(SIG)25 b FI(=)g(\()p Fs(SIG)p Fw(:)p Fs(Key)r Fw(;)15 b Fs(SIG)p Fw(:)p Fs(Sign)o Fw(;)g Fs(SIG)p Fw(:)p Fs(V)m(erify)r FI(\))30 b(is)h(de\014ned)e(b)m (y)h(the)h(three)f(follo)m(wing)i(algorithms:)10 5154 y Fz({)46 b FI(The)23 b Fx(key)j(gener)-5 b(ation)28 b(algorithm)33 b Fs(SIG)p Fw(:)p Fs(Key)q FI(.)24 b(On)f(input)g(1)2070 5121 y Ft(k)2113 5154 y FI(,)h(the)g(algorithm)g Fs(SIG)p Fw(:)p Fs(Key)h FI(pro)s(duces)e(a)h(pair)f(\()p Fs(pk)q Fw(;)15 b Fs(sk)q FI(\))108 5267 y(of)31 b(matc)m(hing)g(public)f(\(v)m (eri\014cation\))j(and)c(priv)-5 b(ate)31 b(\(signing\))g(k)m(eys.)10 5382 y Fz({)46 b FI(The)36 b Fx(signing)i(algorithm)46 b Fs(SIG)p Fw(:)p Fs(Sign)o FI(.)37 b(Giv)m(en)h(a)f(message)h Fw(m)e FI(and)g(a)h(pair)g(of)g(matc)m(hing)g(public)f(and)g(priv)-5 b(ate)108 5495 y(k)m(eys)31 b(\()p Fs(pk)q Fw(;)15 b Fs(sk)q FI(\),)31 b Fs(SIG)p Fw(:)p Fs(Sign)e FI(pro)s(duces)g(a)i (signature)g Fw(\033)s FI(.)f(The)g(signing)h(algorithm)g(migh)m(t)g(b) s(e)f(probabilistic.)1905 5744 y(19)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 10 -83 a Fz({)46 b FI(The)40 b Fx(veri\014c)-5 b(ation)43 b(algorithm)50 b Fs(SIG)p Fw(:)p Fs(V)m(erify)q FI(.)41 b(Giv)m(en)g(a)g(signature)g Fw(\033)s FI(,)g(a)g(message)h Fw(m)e FI(and)g(a)h(public)f(k)m(ey)h Fs(pk)q FI(,)108 30 y Fs(SIG)p Fw(:)p Fs(V)m(erify)31 b FI(tests)g(whether)f Fw(\033)k FI(is)c(a)h(v)-5 b(alid)31 b(signature)f(of)h Fw(m)f FI(with)g(resp)s(ect)g(to)h Fs(pk)q FI(.)-58 228 y(Sev)m(eral)26 b(securit)m(y)g(notions)f(ha)m(v)m (e)h(b)s(een)e(de\014ned)g(ab)s(out)g(signature)h(sc)m(hemes,)h(mainly) f(based)g(on)f(the)h(seminal)h(w)m(ork)-58 341 y(of)i(Goldw)m(asser)g Fx(et)i(al)38 b FI([27].)29 b(It)f(is)g(no)m(w)g(classical)h(to)g(ask)f (for)f(the)h(imp)s(ossibilit)m(y)g(of)g(existen)m(tial)i(forgeries,)f (ev)m(en)f(for)-58 454 y(adaptiv)m(e)k(c)m(hosen-message)g(adv)m (ersaries:)10 658 y Fz({)46 b FI(An)28 b Fx(existential)j(for)-5 b(gery)37 b FI(is)28 b(a)g(new)f(message-signature)j(pair,)e(v)-5 b(alid)28 b(and)f(generated)i(b)m(y)f(the)g(adv)m(ersary)-8 b(.)28 b(The)108 771 y(corresp)s(onding)i(securit)m(y)h(lev)m(el)h(is)e (called)i Fx(existential)h(unfor)-5 b(ge)g(ability)40 b FI(\()p Fs(EUF)p FI(\).)10 890 y Fz({)46 b FI(The)c(v)m (eri\014cation)j(k)m(ey)e(is)g(public,)g(including)f(to)i(the)f(adv)m (ersary)-8 b(.)43 b(But)g(more)g(information)g(ma)m(y)h(also)f(b)s(e) 108 1002 y(a)m(v)-5 b(ailable.)23 b(The)d(strongest)h(kind)f(of)h (information)g(is)f(de\014nitely)h(formalized)g(b)m(y)f(the)h Fx(adaptive)k(chosen-message)108 1115 y(attacks)48 b FI(\()p Fs(CMA)p FI(\),)39 b(where)g(the)g(attac)m(k)m(er)j(can)e(ask)f (the)g(signer)g(to)h(sign)f(an)m(y)h(message)g(of)f(its)h(c)m(hoice,)h (in)e(an)108 1228 y(adaptiv)m(e)32 b(w)m(a)m(y)-8 b(.)-58 1426 y(As)37 b(a)f(consequence,)i(w)m(e)f(sa)m(y)g(that)g(a)g (signature)g(sc)m(heme)g(is)g(secure)f(if)h(it)g(prev)m(en)m(ts)g (existen)m(tial)i(forgeries,)e(ev)m(en)-58 1539 y(under)29 b(adaptiv)m(e)j(c)m(hosen-message)g(attac)m(ks.)-58 1832 y Fz(B.2)105 b(Message)36 b(Authen)m(tication)f(Co)s(des)-58 2042 y FI(A)46 b(Message)h(Authen)m(tication)g(Co)s(de)e Fs(MA)m(C)k FI(=)h(\()p Fs(MA)m(C)p Fw(:)p Fs(Sign)p Fw(;)15 b Fs(MA)m(C)p Fw(:)p Fs(V)m(erify)r FI(\))45 b(is)h(de\014ned)e(b)m(y)h(the)h(t)m(w)m(o)g(follo)m(wing)-58 2155 y(algorithms,)32 b(with)e(a)g(secret)i(k)m(ey)f Fs(sk)g FI(uniformly)e(distributed)g(in)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2438 2122 y Ft(`)2474 2155 y FI(:)10 2359 y Fz({)46 b FI(The)h Fx(MA)n(C)f(gener)-5 b(ation)49 b(algorithm)56 b Fs(MA)m(C)p Fw(:)p Fs(Sign)p FI(.)47 b(Giv)m(en)h(a)f(message)h Fw(m)f FI(and)f(secret)i(k)m(ey)g Fs(sk)53 b Fl(2)f(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)3897 2326 y Ft(`)3933 2359 y FI(,)108 2472 y Fs(MA)m(C)p Fw(:)p Fs(Sign)30 b FI(pro)s(duces)f(an)h(authen)m(ticator)j Fw(\026)p FI(.)d(This)g(algorithm)h(migh)m(t)g(b)s(e)f(probabilistic.) 10 2591 y Fz({)46 b FI(The)27 b Fx(MA)n(C)h(veri\014c)-5 b(ation)31 b(algorithm)36 b Fs(MA)m(C)p Fw(:)p Fs(V)m(erify)q FI(.)28 b(Giv)m(en)g(an)f(authen)m(ticator)i Fw(\026)p FI(,)e(a)h(message)g Fw(m)f FI(and)f(a)i(secret)108 2704 y(k)m(ey)j Fs(sk)q FI(,)f Fs(MA)m(C)p Fw(:)p Fs(V)m(erify)i FI(tests)f(whether)f Fw(\026)g FI(has)g(b)s(een)f(pro)s(duced)g(using)h Fs(MA)m(C)p Fw(:)p Fs(Sign)g FI(on)g(inputs)f Fw(m)i FI(and)e Fs(sk)q FI(.)-58 2902 y(As)i(for)g(signature)h(sc)m(hemes,)g (the)f(classical)i(securit)m(y)f(lev)m(el)h(for)e(MA)m(C)h(is)f(to)h (prev)m(en)m(t)f(existen)m(tial)j(forgeries,)e(ev)m(en)-58 3015 y(for)e(an)h(adv)m(ersary)f(whic)m(h)g(has)g(access)i(to)f(the)g (generation)g(and)f(the)h(v)m(eri\014cation)h(oracles.)-58 3308 y Fz(B.3)105 b(Authen)m(tication)35 b(Sc)m(hemes)-58 3518 y FI(In)j(this)h(section,)i(w)m(e)e(simply)g(unify)f(the)h(t)m(w)m (o)i(ab)s(o)m(v)m(e)f(primitiv)m(es,)g(so)f(that)h(analyses)f(in)g (this)g(pap)s(er)f(are)h(quite)-58 3631 y(general)c(\(in)g(the)f (symmetric)h(or)f(the)h(asymmetric)g(settings.\))g(W)-8 b(e)36 b(th)m(us)e(de\014ne)f(an)h(authen)m(tication)j(sc)m(heme)e(b)m (y)-58 3744 y(three)c(algorithms)g Fs(A)m(UTH)25 b FI(=)g(\()p Fs(A)m(UTH)p Fw(:)p Fs(Key)r Fw(;)15 b Fs(A)m(UTH)p Fw(:)p Fs(Sign)p Fw(;)g Fs(A)m(UTH)p Fw(:)p Fs(V)m(erify)r FI(\):)10 3948 y Fz({)46 b FI(The)30 b Fx(key)i(gener)-5 b(ation)34 b(algorithm)39 b Fs(A)m(UTH)p Fw(:)p Fs(Key)r FI(.)31 b(On)e(input)g(1)2225 3915 y Ft(k)2268 3948 y FI(,)i(the)f(algorithm)h Fs(A)m(UTH)p Fw(:)p Fs(Key)h FI(pro)s(duces)d(a)i(pair)108 4061 y(\()p Fs(vk)q Fw(;)15 b Fs(sk)q FI(\))30 b(of)h(matc)m(hing)g(v)m (eri\014cation)h(and)e(signing)h(k)m(eys)g(\(they)f(can)h(b)s(e)f (either)h(the)f(same)h(or)f(di\013eren)m(t.\))10 4180 y Fz({)46 b FI(The)22 b Fx(signing)j(algorithm)31 b Fs(A)m(UTH)p Fw(:)p Fs(Sign)p FI(.)23 b(Giv)m(en)g(a)g(message)g Fw(m)f FI(and)g(the)h(signing)f(k)m(ey)h Fs(sk)q FI(,)f Fs(A)m(UTH)p Fw(:)p Fs(Sign)g FI(pro)s(duces)108 4293 y(an)30 b(authen)m(ticator)j Fw(\033)s FI(.)10 4412 y Fz({)46 b FI(The)25 b Fx(veri\014c)-5 b(ation)29 b(algorithm)35 b Fs(A)m(UTH)p Fw(:)p Fs(V)m(erify)q FI(.)26 b(Giv)m(en)g(an)g(authen)m(ticator)h Fw(\033)s FI(,)f(a)g(message)g Fw(m)g FI(and)e(a)i(v)m(eri\014cation)108 4525 y(k)m(ey)31 b Fs(vk)q FI(,)f Fs(A)m(UTH)p Fw(:)p Fs(V)m(erify)i FI(tests)f(whether)f Fw(\033)j FI(is)e(a)f(v)-5 b(alid)31 b(authen)m(ticator)h(of)f Fw(m)f FI(with)g(resp)s(ect)h(to)g Fs(vk)p FI(.)-58 4723 y(Suc)m(h)40 b(an)h(authen)m(tication)i(sc)m (heme)f(is)e(said)h(to)h(b)s(e)e(secure)h(if)g(it)g(prev)m(en)m(ts)h (existen)m(tial)h(forgeries,)f(ev)m(en)f(for)g(an)-58 4836 y(adv)m(ersary)31 b(whic)m(h)f(has)g(access)i(to)f(the)f(signing)h (and)f(the)g(v)m(eri\014cation)i(oracles.)g(This)e(is)g(measured)g(b)m (y)11 5109 y Fs(Succ)189 5071 y Fk(euf)5 b Fj(\000)p Fk(cma)189 5138 y(A)n(UTH)464 5109 y FI(\()p Fl(A)p Fw(;)15 b(q)653 5123 y Ft(s)689 5109 y Fw(;)g(q)770 5123 y Ft(v)811 5109 y FI(\))26 b(=)f(Pr)1081 4981 y Fg(\024)1140 5054 y FI(\()p Fs(vk)q Fw(;)15 b Fs(sk)q FI(\))25 b Fl( )g Fs(A)m(UTH)p Fw(:)p Fs(Key)r FI(\(1)2057 5021 y Ft(k)2101 5054 y FI(\))p Fw(;)15 b FI(\()p Fw(m;)g(\033)s FI(\))27 b Fl( )e(A)2637 5021 y Fk(A)n(UTH)p Ft(:)p Fk(Sign)p FH(\()p Fk(sk)q FH(;)p Fj(\001)p FH(\))p Ft(;)p Fk(A)n(UTH)p Ft(:)p Fk(V)n(erify)p FH(\()p Fk(vk)q FH(;)p Fj(\001)p Ft(;)p Fj(\001)p FH(\))3764 5054 y FI(:)1948 5167 y Fs(A)m(UTH)p Fw(:)p Fs(V)m(erify)q FI(\()p Fs(vk)q FI(;)15 b Fw(m;)g(\033)s FI(\))26 b(=)f(1)3801 4981 y Fg(\025)3864 5109 y Fw(;)-58 5382 y FI(where)i(the)h(adv)m(ersary)g(can)g(ask)g(up)f(to)h Fw(q)1365 5396 y Ft(s)1429 5382 y FI(and)f Fw(q)1644 5396 y Ft(v)1712 5382 y FI(queries)h(to)g(the)g(signing)g(and)f(v)m (eri\014cation)i(oracles)g Fs(A)m(UTH)p Fw(:)p Fs(Sign)-58 5495 y FI(and)h Fs(A)m(UTH)p Fw(:)p Fs(V)m(erify)i FI(resp)s(ectiv)m (ely)-8 b(.)1905 5744 y(20)p eop end %%Page: 21 21 TeXDict begin 21 20 bop -58 -83 a Fz(B.4)105 b(Computational)35 b(Assumptions)-58 93 y FI(When)f(one)g(deals)g(with)f(k)m(ey)h(exc)m (hange,)i(the)e(classical)i(problem)d(whic)m(h)g(arises)h(is)g(the)g (problem)f(in)m(tro)s(duced)g(b)m(y)-58 206 y(Di\016e-Hellman)f(in)d (the)h(seminal)h(pap)s(er)d(ab)s(out)i(asymmetric)h(cryptograph)m(y)f ([20].)h(More)g(formally)-8 b(,)31 b(w)m(e)f(consider)-58 319 y(a)k(\014nite)f(cyclic)h(group)f Fu(G)g FI(of)g(prime)g(order)f Fw(q)k FI(with)d(a)h(generator)g Fw(g)s FI(,)g(whic)m(h)f(w)m(e)g (denote)h(m)m(ultiplicativ)m(ely)i(in)d(this)-58 431 y(de\014nition:)d Fu(G)25 b FI(=)g(\()p Fl(h)p Fw(g)s Fl(i)p Fw(;)15 b Fl(\002)p FI(\).)33 b(Tw)m(o)e(problems)e(are)i (usually)f(assumed)g(to)h(b)s(e)f(in)m(tractable,)i(in)e(w)m(ell-c)m (hosen)i(groups:)10 606 y Fz({)46 b FI(the)30 b Fx(Computational)35 b(Di\016e-Hel)5 b(lman)31 b(Pr)-5 b(oblem)p FI(,)31 b(in)e(whic)m(h)h (giv)m(en)g(random)f(elemen)m(ts)i Fw(g)3223 573 y Ft(x)3297 606 y FI(and)e Fw(g)3519 573 y Ft(y)3591 606 y FI(in)g Fu(G)p FI(,)h(one)108 719 y(w)m(an)m(ts)h(to)g(\014nd)e Fs(DH)p FI(\()p Fw(g)870 686 y Ft(x)915 719 y Fw(;)15 b(g)1001 686 y Ft(y)1044 719 y FI(\))25 b(=)g Fw(g)1246 686 y Ft(xy)1328 719 y FI(.)30 b(The)g(actual)i(in)m(tractabilit)m(y)h (is)e(measured,)f(for)g(an)m(y)h(adv)m(ersary)f Fl(A)p FI(,)g(b)m(y)980 942 y Fs(Succ)1158 905 y Fk(cdh)1158 965 y Ft(g)r(;)p Fd(G)1269 942 y FI(\()p Fl(A)p FI(\))c(=)f(Pr)o([)p Fw(x;)15 b(y)1841 891 y Ft(R)1822 942 y Fl( )25 b Fu(Z)1999 956 y Ft(q)2062 942 y FI(:)h Fs(DH)p FI(\()p Fw(g)2324 905 y Ft(x)2368 942 y Fw(;)15 b(g)2454 905 y Ft(y)2497 942 y FI(\))25 b Fl( )h(A)p FI(\()p Fw(g)2828 905 y Ft(x)2872 942 y Fw(;)15 b(g)2958 905 y Ft(y)3001 942 y FI(\)])p Fw(:)10 1140 y Fz({)46 b FI(the)36 b Fx(De)-5 b(cisional)38 b(Di\016e-Hel)5 b(lman)37 b(Pr)-5 b(oblem)p FI(,)37 b(in)e(whic)m(h)h (giv)m(en)h(random)d(elemen)m(ts)j Fw(g)3101 1107 y Ft(x)3182 1140 y FI(and)e Fw(g)3410 1107 y Ft(y)3487 1140 y FI(in)h Fu(G)p FI(,)f(and)g(a)108 1253 y(candidate)29 b Fw(g)566 1220 y Ft(z)634 1253 y FI(for)f(the)g(v)-5 b(alue)28 b Fs(DH)p FI(\()p Fw(g)1368 1220 y Ft(x)1413 1253 y Fw(;)15 b(g)1499 1220 y Ft(y)1542 1253 y FI(\),)28 b(one)g(should)f(guess)h (whether)g(this)f(is)h(the)h(actual)g(solution)f(or)g(not.)108 1366 y(The)i(actual)i(in)m(tractabilit)m(y)h(is)d(measured,)g(for)h(an) m(y)f(distinguisher)g Fl(D)s FI(,)g(b)m(y)319 1584 y Fs(Adv)469 1546 y Fk(ddh)469 1606 y Ft(g)r(;)p Fd(G)583 1584 y FI(\()p Fl(D)s FI(\))25 b(=)847 1479 y Fg(\014)847 1534 y(\014)847 1588 y(\014)878 1584 y FI(Pr)o([)p Fw(x;)15 b(y)1185 1532 y Ft(R)1166 1584 y Fl( )25 b Fu(Z)1343 1598 y Ft(q)1406 1584 y FI(:)g(1)h Fl( )f(D)s FI(\()p Fw(g)1797 1546 y Ft(x)1842 1584 y Fw(;)15 b(g)1928 1546 y Ft(y)1970 1584 y Fw(;)g(g)2056 1546 y Ft(xy)2138 1584 y FI(\)])21 b Fl(\000)f FI(Pr[)p Fw(x;)15 b(y)s(;)g(z)2704 1532 y Ft(R)2685 1584 y Fl( )25 b Fu(Z)2862 1598 y Ft(q)2925 1584 y FI(:)h(1)f Fl( )g(D)s FI(\()p Fw(g)3316 1546 y Ft(x)3361 1584 y Fw(;)15 b(g)3447 1546 y Ft(y)3489 1584 y Fw(;)g(g)3575 1546 y Ft(z)3616 1584 y FI(\)])3676 1479 y Fg(\014)3676 1534 y(\014)3676 1588 y(\014)3722 1584 y Fw(:)83 1799 y FI(In)29 b(the)h(follo)m(wing,)i(w)m(e)e(w)m(ork)g(on) g(elliptic)h(curv)m(es,)f(whic)m(h)g(groups)f(are)h(usually)g(denoted)g (in)f(an)h(additiv)m(e)h(w)m(a)m(y:)-58 1912 y Fu(G)e FI(=)g(\()p Fl(h)p Fz(P)p Fl(i)p Fw(;)15 b FI(+\).)35 b(The)e(latter)h(problem)e(can)i(b)s(e)e(stated)i(as)f(follo)m(ws)h(b)m (y)f(adapting)g(the)g(notations:)h(in)f(the)g Fx(El)5 b(liptic)-58 2025 y(Curve)28 b(De)-5 b(cisional)29 b(Di\016e-Hel)5 b(lman)27 b(Pr)-5 b(oblem)p FI(,)27 b(giv)m(en)f(random)f(elemen)m(ts)h Fw(x)10 b Fl(\001)g Fz(P)27 b FI(and)e Fw(y)13 b Fl(\001)d Fz(P)26 b FI(in)f(the)h(group)e(of)i(p)s(oin)m(ts)-58 2138 y Fu(G)p FI(,)j(of)h(order)f Fw(q)s FI(,)h(and)f(a)g(candidate)i Fw(z)22 b Fl(\001)d Fz(P)30 b FI(for)f(the)h(v)-5 b(alue)30 b Fs(ECDH)p FI(\()p Fw(x)19 b Fl(\001)g Fz(P)p Fw(;)c(y)22 b Fl(\001)c Fz(P)p FI(\),)31 b(one)f(should)e(guess)i(whether)e(this)i (is)-58 2251 y(the)j(actual)g(solution)g(or)g(not.)g(The)f(in)m (tractabilit)m(y)j(is)d(measured,)g(for)g(an)m(y)h(distinguisher)f Fl(D)s FI(,)g(b)m(y)g(the)h(adv)-5 b(an)m(tage)-58 2364 y Fs(Adv)93 2327 y Fk(ecddh)93 2387 y Fq(P)p Ft(;)p Fd(G)269 2364 y FI(\()p Fl(D)s FI(\))31 b(de\014ned)e(as)h(ab)s(o)m(v)m(e.)-58 2555 y Fx(Note)j(19.)46 b FI(W)-8 b(e)27 b(insist)f(here)f(on)h(the)g (w)m(ell-kno)m(wn)h(fact)g(that)f(the)g(in)m(tractabilit)m(y)j(of)d(an) m(y)g(decisional)h(Di\016e-Hellman)-58 2668 y(problem)32 b(just)g(means)h(that)g(the)g(Di\016e-Hellman)h(v)-5 b(alue)33 b(is)g(indistinguishable)f(from)g(a)h(random)f(elemen)m(t)i (in)f(the)-58 2781 y(cyclic)e(group.)d(It)h(do)s(es)f(not)h(mean)g (that)g(the)g(enco)s(ding)g(of)g(a)g(Di\016e-Hellman)i(v)-5 b(alue)29 b(is)g(indistinguishable)f(from)g(a)-58 2894 y(random)i(bit-string)g([42].)-58 3152 y Fz(B.5)105 b(Upp)s(er-Bounds) 37 b(for)e(Time-Constrained)f(Adv)m(ersaries)-58 3328 y FI(As)25 b(usual,)g(for)f(all)i(the)f(ab)s(o)m(v)m(e)h(success)f (probabilities)h(or)e(adv)-5 b(an)m(tages,)27 b(w)m(e)f(denote)f(b)m(y) g Fs(Succ)p FI(\()p Fw(t;)15 b(:)g(:)g(:)r FI(\))25 b(and)f Fs(Adv)q FI(\()p Fw(t;)15 b(:)g(:)g(:)r FI(\))-58 3441 y(the)31 b(maximal)g(probabilities)g(o)m(v)m(er)h(all)f(the)f(adv)m (ersaries)i(whic)m(h)e(running)e(time)j(is)g(b)s(ounded)d(b)m(y)i Fw(t)p FI(.)-58 3703 y Fy(C)112 b(Pro)s(of)37 b(of)h(Theorem)g(18)-58 3912 y FI(Let)29 b Fl(A)e FI(b)s(e)g(an)h(adv)m(ersary)-8 b(,)29 b(and)f(let)g Fz(G)1261 3926 y FH(0)1329 3912 y FI(b)s(e)f(the)h(original)i(AKE)d(attac)m(k)k(game.)e(Let)f Fw(b)g FI(and)g Fw(b)3136 3879 y Fj(0)3187 3912 y FI(b)s(e)f(as)h (de\014ned)f(in)h(the)-58 4025 y(securit)m(y)j(mo)s(del)f(\(see)i(app)s (endix)d(A\),)i(and)f(let)h Fw(S)1651 4039 y FH(0)1720 4025 y FI(b)s(e)f(the)h(ev)m(en)m(t)h(that)f Fw(b)25 b FI(=)g Fw(b)2637 3992 y Fj(0)2660 4025 y FI(.)-58 4138 y Fz(Game)30 b(G)322 4152 y FH(0)387 4138 y FI(:)h(This)e(is)h(the)h (real)f(proto)s(col.)i(In)d(this)h(game,)i(w)m(e)f(are)f(in)m(terested) h(in)f(the)h(ev)m(en)m(t)g Fw(S)3269 4152 y FH(0)3309 4138 y FI(,)f(whic)m(h)g(o)s(ccurs)g(if)-58 4251 y Fw(b)25 b FI(=)g Fw(b)141 4218 y Fj(0)194 4251 y FI(in)j(this)h(game,)i(where)d Fw(b)h FI(is)g(the)g(bit)h(in)m(v)m(olv)m(ed)g(in)f(the)g Fs(T)-8 b(est)p FI(-query)29 b(and)g Fw(b)2724 4218 y Fj(0)2776 4251 y FI(is)g(the)g(output)g(of)g(the)h(adv)m(ersary)-58 4364 y Fl(A)p FI(.)-58 4477 y Fz(Game)h(G)323 4491 y FH(1)389 4477 y FI(:)h(W)-8 b(e)32 b(mo)s(dify)e(the)i(oracle)g (instances)g(as)g(follo)m(ws.)g(If)f(the)g(adv)m(ersary)g(submits)g(a)g (new)g(authen)m(ticator)-58 4589 y(\()p Fw(\033)29 4603 y Ft(A)121 4589 y FI(or)k Fw(\033)289 4603 y Ft(B)349 4589 y FI(\))g(whic)m(h)g(has)f(not)h(b)s(een)f(previously)h(generated) g(b)m(y)g(an)g(oracle,)h(and)e(th)m(us)g(our)h(sim)m(ulation,)h(then)e (in)-58 4702 y(game)c Fz(G)260 4716 y FH(1)299 4702 y FI(,)f(w)m(e)g(reject)h(it)f(and)f(the)h(instance)g(w)m(e)g(are)g(sim)m (ulating)h(\(and)f(whic)m(h)f(receiv)m(es)i(suc)m(h)f(a)g Fx(for)-5 b(ge)g(d)39 b FI(message\),)-58 4815 y(stops:)31 b(it)g(terminates)g(without)f(accepting.)83 4928 y(Let)45 b Fw(F)318 4942 y FH(1)402 4928 y FI(b)s(e)e(the)h(ev)m(en)m(t)i(that)e (in)g(game)h Fz(G)1626 4942 y FH(1)1709 4928 y FI(an)f(authen)m (ticator)i(is)e(rejected)h(that)f(w)m(ould)g(not)g(ha)m(v)m(e)i(b)s (een)-58 5041 y(rejected)g(under)d(the)i(rules)f(of)h(game)g Fz(G)1424 5055 y FH(0)1464 5041 y FI(.)g(Since)g(these)g(t)m(w)m(o)h (games)f(pro)s(ceed)g(iden)m(tically)h(un)m(til)f Fw(F)3597 5055 y FH(1)3682 5041 y FI(o)s(ccurs,)-58 5154 y(w)m(e)38 b(ha)m(v)m(e)g(Pr)o([)p Fw(S)477 5168 y FH(0)541 5154 y Fl(^)25 b(:)p Fw(F)746 5168 y FH(1)785 5154 y FI(])37 b(=)f(Pr)o([)p Fw(S)1132 5168 y FH(1)1196 5154 y Fl(^)25 b(:)p Fw(F)1401 5168 y FH(1)1440 5154 y FI(],)38 b(and)e(applying)h (Lemma)g(1)g(of)h([43,)16 b(45])38 b(with)f(\()p Fw(S)3227 5168 y FH(0)3267 5154 y Fw(;)15 b(S)3363 5168 y FH(1)3402 5154 y Fw(;)g(F)3500 5168 y FH(1)3541 5154 y FI(\),)37 b(w)m(e)h(ha)m(v)m(e)-58 5267 y Fl(j)15 b FI(Pr[)p Fw(S)161 5281 y FH(0)200 5267 y FI(])21 b Fl(\000)f FI(Pr)o([)p Fw(S)515 5281 y FH(1)555 5267 y FI(])p Fl(j)25 b(\024)g FI(Pr[)p Fw(F)907 5281 y FH(1)947 5267 y FI(].)31 b(F)-8 b(rom)31 b(the)f(follo)m(wing)i(lemma,)f(one)g(immediately)h(gets:)1094 5466 y Fl(j)15 b FI(Pr[)p Fw(S)1313 5480 y FH(0)1352 5466 y FI(])20 b Fl(\000)g FI(Pr[)p Fw(S)1667 5480 y FH(1)1706 5466 y FI(])p Fl(j)26 b(\024)f FI(2)c Fl(\001)f Fs(Succ)2167 5427 y Fk(euf)6 b Fj(\000)p Fk(cma)2167 5495 y(A)n(UTH)2442 5466 y FI(\()p Fw(t;)15 b(q)2591 5480 y Ft(s)2628 5466 y Fw(;)g(q)2709 5480 y Ft(s)2746 5466 y FI(\))p Fw(:)1036 b FI(\(1\))1905 5744 y(21)p eop end %%Page: 22 22 TeXDict begin 22 21 bop -58 -83 a Fz(Lemma)35 b(20.)1361 37 y FI(Pr[)p Fw(F)1542 51 y FH(1)1582 37 y FI(])25 b Fl(\024)g FI(2)c Fl(\001)f Fs(Succ)2018 -1 y Fk(euf)5 b Fj(\000)p Fk(cma)2018 66 y(A)n(UTH)2292 37 y FI(\()p Fw(t;)15 b(q)2441 51 y Ft(s)2478 37 y FI(\))p Fw(:)-58 242 y Fx(Pr)-5 b(o)g(of.)47 b FI(W)-8 b(e)28 b(w)m(an)m(t)f(to)h(b)s (ound)c(Pr[)p Fw(F)1163 256 y FH(1)1203 242 y FI(].)j(This)f (probabilit)m(y)h(is)g(b)s(ounded)e(b)m(y)h(the)h(probabilit)m(y)g (that)g(an)g(adv)m(ersary)g Fl(A)3935 209 y Fj(0)-58 355 y FI(|running)j(in)h(exp)s(ected)h(time)h(nearly)f(t)m(wice)h(the)f (same)g(as)g(the)g(running)e(time)i(of)g(the)g(original)g(adv)m(ersary) g Fl(A)p FI(|)-58 468 y(can)j(forge)g(an)f(authen)m(ticator)j(under)c (a)h(c)m(hosen-message)j(attac)m(k.)g(In)d(this)g(case,)i Fl(A)2927 435 y Fj(0)2984 468 y FI(accesses)g(a)f(signing)f(oracle)-58 581 y(and)28 b(tries)h(to)h(forge)f(a)g(new)f(authen)m(ticator.)j(A)m (t)e(the)g(b)s(eginning,)f Fl(A)2294 548 y Fj(0)2346 581 y FI(pic)m(ks)h(at)g(random)f(a)h(bit)g Fw(b)f FI(and)g(according)i (to)-58 693 y(this)h(bit,)g(it)g(pla)m(ys)h(the)f(role)g(of)g(an)g(adv) m(ersary)g(against)h(either)f Fw(A)g FI(or)g Fw(B)k FI(authen)m (tication.)f(If)c Fw(b)c FI(=)g(0,)31 b(then)g Fl(A)3742 660 y Fj(0)3795 693 y FI(uses)-58 806 y(the)f(signing)f(oracle)i(to)f (sim)m(ulate)g Fw(A)g FI(authen)m(ticators,)h(but)e(kno)m(ws)g(the)g (signing)h(k)m(ey)g(of)f Fw(B)5 b FI(,)29 b(and)g(if)g Fw(b)c FI(=)g(1,)30 b Fl(A)3743 773 y Fj(0)3795 806 y FI(uses)-58 919 y(the)35 b(signing)g(oracle)h(to)f(sim)m(ulate)h Fw(B)j FI(authen)m(ticators,)d(but)e(kno)m(ws)g(the)h(signing)g(k)m(ey) g(of)g Fw(A)p FI(.)g(It)f(is)h(easy)g(to)g(c)m(hec)m(k)-58 1032 y(that)26 b(all)h(the)f Fs(Reveal)p FI(\()p Fw(U;)15 b(i)p FI(\),)27 b Fs(Send)o FI(\()p Fw(U;)15 b(i;)g(m)p FI(\))28 b(and)d Fs(T)-8 b(est)p FI(\()p Fw(U;)15 b(i)p FI(\))27 b(queries)e(will)h(b)s(e)f(p)s(erfectly)h(sim)m(ulated)g(and)f (there)h(is)g(no)-58 1145 y(w)m(a)m(y)i(for)f Fl(A)f FI(to)h(guess)g(whic)m(h)g(of)g(the)g(t)m(w)m(o)h(signing)f(k)m(eys)g (are)h(kno)m(wn,)e(and)g(th)m(us)h(whic)m(h)f(of)h(the)g(t)m(w)m(o)i (authen)m(tication)-58 1258 y(sc)m(hemes)37 b(w)m(e)g(try)g(to)g (break.)g(Consequen)m(tly)-8 b(,)38 b(if)e(the)h(ev)m(en)m(t)h Fw(F)2134 1272 y FH(1)2211 1258 y FI(happ)s(ens,)d(the)i(adv)m(ersary)f Fl(A)h FI(has)f(b)s(een)g(able)h(to)-58 1371 y(forge)28 b(an)f(authen)m(ticator)i(either)f(for)f Fw(A)g FI(or)h Fw(B)5 b FI(.)26 b(If)h(the)h(forgery)f(is)g(an)h(authen)m(ticator)h (under)c(the)j(unkno)m(wn)e(signing)-58 1484 y(k)m(ey)-8 b(,)39 b(then)f Fl(A)419 1451 y Fj(0)479 1484 y FI(can)g(win)f(the)h (game;)h(otherwise)g(he)e(cannot)i(do)e(an)m(ything)h(with)g(the)g (forgery)-8 b(.)38 b(On)f(a)m(v)m(erage,)k(b)m(y)-58 1597 y(running)31 b(t)m(wice)k(the)e(algorithm)h Fl(A)1170 1564 y Fj(0)1193 1597 y FI(,)f(he)g(will)g(forge)h(an)f(authen)m (ticator.)i(If)d Fl(A)h FI(mak)m(es)h Fw(q)3013 1611 y Ft(s)3082 1597 y Fs(Send)p FI(-queries)f(and)f(runs)-58 1710 y(within)h(time)g Fw(t)p FI(,)g(then)g Fl(A)811 1677 y Fj(0)867 1710 y FI(runs)e(in)i(the)g(same)h(time,)g(since)f (exactly)i(the)e(same)h(n)m(um)m(b)s(er)d(of)j(authen)m(ticators)h(ha)m (v)m(e)-58 1823 y(to)c(b)s(e)f(generated.)i(Therefore,)74 2034 y Fs(Succ)253 1995 y Fk(euf)5 b Fj(\000)p Fk(cma)253 2063 y(A)n(UTH)527 2034 y FI(\()p Fw(t;)15 b(q)676 2048 y Ft(s)713 2034 y Fw(;)g(q)794 2048 y Ft(s)831 2034 y FI(\))24 b Fl(\025)f Fs(Succ)p FI(\()p Fl(A)1270 1996 y Fj(0)1293 2034 y Fw(;)15 b(q)1374 2048 y Ft(s)1411 2034 y FI(\))25 b(=)g(Pr[)p Fl(A)1763 1996 y Fj(0)1816 2034 y FI(forges)q(])890 2171 y Fl(\025)e FI(Pr)o([)p Fl(A)1179 2134 y Fj(0)1233 2171 y FI(forges)30 b Fw(A)21 b Fl(^)f Fw(b)25 b FI(=)g(0])c(+)f(Pr)o([)p Fl(A)2200 2134 y Fj(0)2254 2171 y FI(forges)30 b Fw(B)25 b Fl(^)20 b Fw(b)25 b FI(=)g(1])890 2347 y Fl(\025)994 2286 y FI(1)p 994 2327 46 4 v 994 2410 a(2)1069 2347 y Fl(\001)c FI(Pr)o([)p Fl(A)1310 2310 y Fj(0)1364 2347 y FI(forges)30 b Fw(A)p FI(])21 b(+)1839 2286 y(1)p 1839 2327 V 1839 2410 a(2)1915 2347 y Fl(\001)f FI(Pr)o([)p Fl(A)2155 2310 y Fj(0)2209 2347 y FI(forges)31 b Fw(B)5 b FI(])25 b(=)2700 2286 y(1)p 2700 2327 V 2700 2410 a(2)2775 2347 y Fl(\001)c FI(Pr)o([)p Fl(A)30 b FI(forges)q(])25 b(=)3433 2286 y(1)p 3433 2327 V 3433 2410 a(2)3509 2347 y Fl(\001)20 b FI(Pr[)p Fw(F)3735 2361 y FH(1)3775 2347 y FI(])p Fw(:)3897 2559 y Fl(u)-61 b(t)-58 2764 y Fz(Game)35 b(G)327 2778 y FH(2)399 2764 y FI(:)g(In)f(this)g(game,)i(w)m(e)f(try)g(to)h(a)m(v)m (oid)g(the)f(use)f(of)h(the)g(discrete-log)i(of)e(the)f(elemen)m(ts)i Fw(X)3472 2778 y FH(0)3512 2764 y Fw(;)15 b(X)3627 2778 y FH(1)3667 2764 y Fw(;)g(Y)3760 2778 y FH(0)3800 2764 y Fw(;)g(Y)3893 2778 y FH(1)3933 2764 y FI(.)-58 2876 y(W)-8 b(e)28 b(th)m(us)e(in)m(tro)s(duce)g(t)m(w)m(o)i(random)d(DDH)j (triples)e(\()p Fw(X)r(;)15 b(Y)5 b(;)15 b(Z)7 b FI(\))28 b(and)e(\()2312 2853 y(~)2286 2876 y Fw(X)7 b(;)2423 2853 y FI(~)2408 2876 y Fw(Y)21 b(;)2541 2853 y FI(~)2522 2876 y Fw(Z)7 b FI(\):)27 b(the)f(\014rst)g(one)h(on)f(the)h(elliptic)h (curv)m(e)-58 2989 y Fu(E)38 b FI(and)g(the)h(second)f(on)h(the)g(t)m (wisted)g(curv)m(e)1574 2966 y(~)1567 2989 y Fu(E)o FI(.)g(Then,)f (using)g(the)h(classical)h(random)e(self-reducibilit)m(y)i(of)f(the)-58 3102 y(Di\016e-Hellman)30 b(problem,)e(one)h(can)f(in)m(tro)s(duce)g (the)h(ab)s(o)m(v)m(e)g(triples)f(in)g(all)h(the)g(sessions)f(whic)m(h) g(can)g(b)s(e)g(tested)h(b)m(y)-58 3215 y(the)i(adv)m(ersary)-8 b(.)31 b(W)-8 b(e)32 b(do)e(not)g(need)h(to)g(mo)s(dify)e(the)i(other)f (sessions.)83 3330 y(The)f(complete)h(b)s(eha)m(vior)g(of)f(our)f(sim)m (ulation)j(in)d(this)h(game)i(is)e(describ)s(ed)f(in)g(App)s(endix)g (D.)i(It)f(is)g(then)g(clear)-58 3443 y(that)f(games)f Fz(G)487 3457 y FH(1)554 3443 y FI(and)f Fz(G)809 3457 y FH(2)875 3443 y FI(are)h(equiv)-5 b(alen)m(t,)29 b(since)e(w)m(e)g (ha)m(v)m(e)h(consisten)m(tly)h(replaced)e(one)g(set)g(of)g(random)f(v) -5 b(ariables)-58 3556 y(b)m(y)30 b(another)h(set)g(of)f(iden)m (tically)j(distributed)c(random)h(v)-5 b(ariables.)31 b(In)f(particular,)h(Pr)o([)p Fw(S)3025 3570 y FH(1)3065 3556 y FI(])25 b(=)g(Pr[)p Fw(S)3390 3570 y FH(2)3429 3556 y FI(].)-58 3671 y Fz(Game)31 b(G)323 3685 y FH(3)387 3671 y FI(:)g(Game)g Fz(G)788 3685 y FH(3)858 3671 y FI(is)g(exactly)h(the)e(same)h(as)g(game)g Fz(G)2078 3685 y FH(2)2118 3671 y FI(,)f(except)i(that)f(in)f(all)h(the)g(rules,) f(w)m(e)h(use)f(a)h(random)-58 3784 y(triple)i(\()p Fw(X)r(;)15 b(Y)5 b(;)15 b(Z)7 b FI(\))34 b(coming)f(from)f(a)h(random)e (distribution)h(\()p Fw(x)22 b Fl(\001)g Fz(P)p Fw(;)15 b(y)25 b Fl(\001)d Fz(P)p Fw(;)15 b(z)26 b Fl(\001)c Fz(P)p FI(\),)34 b(instead)e(of)h(a)g(DDH)g(triple.)g(The)-58 3897 y(distance)39 b(b)s(et)m(w)m(een)g(the)f(t)m(w)m(o)h(games)g(is)g (clearly)g(b)s(ounded)d(b)m(y)i(the)g(adv)-5 b(an)m(tage)40 b(of)e(an)m(y)h(adv)m(ersary)f(against)i(the)-58 4010 y(DDH)32 b(\(see)f(App)s(endix)d(E\):)1146 4130 y Fl(j)15 b FI(Pr[)p Fw(S)1365 4144 y FH(2)1405 4130 y FI(])20 b Fl(\000)g FI(Pr[)p Fw(S)1720 4144 y FH(3)1759 4130 y FI(])p Fl(j)26 b(\024)f Fs(Adv)2082 4092 y Fk(ecddh)2082 4157 y Fq(P)p Ft(;)p Fj(h)p Fq(P)p Fj(i)2271 4130 y FI(\()p Fw(t)c FI(+)e(8)p Fw(q)2536 4144 y Ft(s)2573 4130 y Fw(T)2626 4144 y Ft(m)2693 4130 y FI(\))p Fw(:)1089 b FI(\(2\))-58 4307 y Fz(Game)26 b(G)318 4321 y FH(4)382 4307 y FI(:)g(The)f(mo)s (di\014cation)h(b)s(et)m(w)m(een)g(games)g Fz(G)1829 4321 y FH(4)1894 4307 y FI(and)f Fz(G)2148 4321 y FH(3)2213 4307 y FI(is)g(the)h(same)g(that)g(b)s(et)m(w)m(een)g Fz(G)3294 4321 y FH(3)3359 4307 y FI(and)f Fz(G)3613 4321 y FH(2)3652 4307 y FI(,)h(except)-58 4420 y(that)31 b(instead)g(of)f(replacing)h(a)g(DDH)g(triple)g(b)m(y)f(a)g(random)g (triple)h(on)f(the)g(elliptic)i(curv)m(e)f Fu(E)p FI(,)f(w)m(e)h(do)f (the)g(same)h(on)-58 4533 y(the)g(triple)f(on)h(the)f(t)m(wisted)948 4509 y(~)940 4533 y Fu(E)p FI(.)h(Hence,)g(w)m(e)g(ha)m(v)m(e)1141 4744 y Fl(j)15 b FI(Pr[)p Fw(S)1360 4758 y FH(3)1399 4744 y FI(])21 b Fl(\000)f FI(Pr)o([)p Fw(S)1714 4758 y FH(4)1753 4744 y FI(])p Fl(j)26 b(\024)f Fs(Adv)2076 4706 y Fk(ecddh)2076 4771 y Fq(Q)p Ft(;)p Fj(h)p Fq(Q)p Fj(i)2277 4744 y FI(\()p Fw(t)20 b FI(+)g(8)p Fw(q)2542 4758 y Ft(s)2579 4744 y Fw(T)2632 4758 y Ft(m)2699 4744 y FI(\))p Fw(:)1083 b FI(\(3\))-58 4957 y Fz(Game)28 b(G)320 4971 y FH(5)385 4957 y FI(:)g(In)f(this)h(game,)h(w)m(e)g(mo)s (dify)e(the)h(generation)h(of)f(the)g(master)h(k)m(ey)f Fw(K)35 b FI(in)27 b(eac)m(h)j(session)e(b)m(y)f(pic)m(king)i(at)-58 5070 y(random)h(in)g Fu(F)438 5084 y Ft(p)508 5070 y FI(instead)h(of)g(as)f([)p Fw(Z)7 b FI(])1156 5085 y Fk(abs)1258 5070 y FI(.)31 b(Gran)m(ted)g(to)g(the)g(random-self)f (reducibilit)m(y)i(prop)s(ert)m(y)e(used)f(in)i(game)g Fz(G)3918 5084 y FH(2)-58 5183 y FI(\(describ)s(ed)f(in)g(App)s(endix)e (D\),)k(the)e Fw(Z)7 b FI('s)30 b(are)h(random)f(elemen)m(ts)h(on)g (the)f(curv)m(es.)h(According)g(to)g(Lemma)g(16,)1358 5456 y Fl(j)15 b FI(Pr[)p Fw(S)1577 5470 y FH(4)1616 5456 y FI(])20 b Fl(\000)g FI(Pr[)p Fw(S)1931 5470 y FH(5)1970 5456 y FI(])p Fl(j)26 b(\024)f Fw(q)2183 5470 y Ft(s)2240 5456 y Fl(\002)2340 5395 y FI(2)2385 5319 y Fl(p)p 2462 5319 V 2462 5395 a FI(2)p 2340 5435 167 4 v 2346 5453 a Fl(p)p 2422 5453 79 4 v 83 x FI(2)2467 5509 y Ft(`)2517 5456 y Fw(:)1300 b FI(\(4\))1905 5744 y(22)p eop end %%Page: 23 23 TeXDict begin 23 22 bop -58 -83 a Fz(Game)28 b(G)320 -69 y FH(6)385 -83 y FI(:)g(In)f(this)h(game,)h(w)m(e)g(mo)s(dify)e (the)h(generation)h(of)f(the)g(master)h(k)m(ey)f Fw(K)35 b FI(in)27 b(eac)m(h)j(session)e(b)m(y)f(pic)m(king)i(at)-58 30 y(random)h(in)f Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)601 -3 y Ft(`)667 30 y FI(instead)30 b(of)g(as)h(random)e(in)h Fu(F)1690 44 y Ft(p)1729 30 y FI(.)h(This)e(is)h(done)g(indep)s(enden)m (tly)f(for)h(eac)m(h)i(session.)e(According)-58 143 y(to)h(Lemma)g(14,) 1364 296 y Fl(j)15 b FI(Pr[)p Fw(S)1583 310 y FH(5)1622 296 y FI(])21 b Fl(\000)f FI(Pr)o([)p Fw(S)1937 310 y FH(6)1977 296 y FI(])p Fl(j)25 b(\024)g Fw(q)2189 310 y Ft(s)2246 296 y Fl(\002)2401 235 y FI(2)p 2347 276 155 4 v 2347 294 a Fl(p)p 2422 294 79 4 v 2422 376 a FI(2)2467 350 y Ft(`)2511 296 y Fw(:)1306 b FI(\(5\))-58 518 y Fz(Game)36 b(G)328 532 y FH(7)403 518 y FI(:)g(In)f(this)h(game,) i(instead)e(of)h(using)e(the)i Fs(PRF)e FI(in)h(order)g(to)h(generate)g (the)g(MA)m(C)f(k)m(ey)h Fw(k)3546 532 y Ft(m)3649 518 y FI(and)f(the)-58 631 y(session)c(k)m(ey)h Fs(sk)p FI(,)f(w)m(e)g(pic) m(k)h(random)e(v)-5 b(alues)32 b(in)f Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1808 598 y Ft(n)1858 631 y FI(.)32 b(W)-8 b(e)33 b(use)e(a)h(classical)i(h)m(ybrid)d(argumen)m(t)h([26])h(in)f (order)f(to)-58 752 y(pro)m(v)m(e)f(that)f(the)g(di\013erence)g(b)s(et) m(w)m(een)g(game)h Fz(G)1608 766 y FH(6)1676 752 y FI(and)e Fz(G)1933 766 y FH(7)2001 752 y FI(is)h Fw(q)2132 766 y Ft(s)2185 752 y Fl(\002)17 b Fs(Adv)2424 708 y Fk(p)n(rf)2424 781 y Fj(F)2513 752 y FI(\()p Fl(A)p Fw(;)e FI(2\).)30 b(Hybrids)d(consist)j(of)e(a)h(sequence)-58 865 y(of)i(random)e(v)-5 b(ariables)31 b Fw(V)809 879 y Ft(i)837 865 y FI(,)g(1)26 b Fl(\024)f Fw(i)g Fl(\024)g Fw(q)1253 879 y Ft(s)1310 865 y FI(+)20 b(1,)31 b(suc)m(h)f(that)-8 1054 y(1.)46 b(the)40 b(random)e(v)-5 b(ariable)41 b Fw(V)1020 1068 y Ft(i)1087 1054 y FI(is)f(constructed)f(as)h(follo)m(ws)h(:)e(in)g (the)h(\014rst)f(\()p Fw(i)26 b Fl(\000)g FI(1\))41 b(sessions,)e(the)h (session)f(and)108 1167 y(MA)m(C)27 b(k)m(eys)g(are)g(generated)h (according)f(to)h(game)f Fz(G)1932 1181 y FH(7)1998 1167 y FI(and)f(in)g(the)h(\()p Fw(q)2502 1181 y Ft(s)2551 1167 y Fl(\000)12 b Fw(i)g FI(+)g(1\))28 b(sessions,)f(they)g(are)g (generated)108 1280 y(according)32 b(the)e Fz(G)756 1294 y FH(6)796 1280 y FI(;)-8 1395 y(2.)46 b(extreme)31 b(h)m(ybrids)e(\()p Fw(i)d FI(=)f(1\))31 b(and)f(\()p Fw(i)c FI(=)f Fw(q)1483 1409 y Ft(s)1540 1395 y FI(+)19 b(1\))32 b(collide)f(with)g Fz(G)2314 1409 y FH(6)2383 1395 y FI(and)f Fz(G)2642 1409 y FH(7)2712 1395 y FI(resp)s(ectiv)m(ely;)-8 1511 y(3.)46 b(random)30 b(v)-5 b(alues)31 b(of)f(eac)m(h)i(h)m(ybrid)d(can) i(b)s(e)f(pro)s(duced)f(b)m(y)h(a)h(probabilistic)g(p)s(olynomial)g (time)g(algorithm)g(and)108 1624 y(the)g(session)f(that)h(w)m(e)g(mo)s (dify)f(is)g(indep)s(enden)m(t)f(of)i(the)f(other)h(sessions;)-8 1739 y(4.)46 b(there)31 b(are)g(only)f(p)s(olynomially)h(man)m(y)f(h)m (ybrids.)-58 1926 y(The)37 b(h)m(ybrids)e(allo)m(w)j(us)f(to)g (de\014ne)f Fw(q)1258 1940 y Ft(s)1331 1926 y FI(di\013eren)m(t)i (games)g(and)e(in)g(eac)m(h)j(of)e(the)g(h)m(ybrids)e(w)m(e)i(only)g (ask)h(2)f(queries)-58 2039 y(to)45 b(the)f Fs(PRF)p FI(.)f(The)h(di\013erence)g(b)s(et)m(w)m(een)g(t)m(w)m(o)i(consecutiv)m (e)f(h)m(ybrid)e(games)i(can)f(b)s(e)f(sho)m(wn)g(to)i(b)s(e)e(less)h (than)-58 2152 y Fs(Adv)93 2108 y Fk(p)n(rf)93 2181 y Fj(F)182 2152 y FI(\()p Fl(A)p Fw(;)15 b FI(2\),)32 b(as)e(w)m(e)h(did) f(b)s(et)m(w)m(een)h(games)g Fz(G)1575 2166 y FH(2)1645 2152 y FI(and)e Fz(G)1903 2166 y FH(3)1943 2152 y FI(,)i(but)e(here)h (b)m(y)h(constructing)g(an)f(adv)m(ersary)g Fl(A)3621 2119 y Fj(0)3675 2152 y FI(against)-58 2265 y(the)h Fs(PRF)f FI(securit)m(y)h(game.)1216 2385 y Fl(j)15 b FI(Pr[)p Fw(S)1435 2399 y FH(6)1475 2385 y FI(])20 b Fl(\000)g FI(Pr[)p Fw(S)1790 2399 y FH(7)1829 2385 y FI(])p Fl(j)26 b(\024)f Fw(q)2042 2399 y Ft(s)2098 2385 y Fl(\002)20 b Fs(Adv)2340 2341 y Fk(p)n(rf)2340 2414 y Fj(F)2429 2385 y FI(\()p Fl(A)p Fw(;)15 b FI(2\))p Fw(:)1160 b FI(\(6\))83 2563 y(It)36 b(is)g(also)h(clear)g(that)g(in)e(game)i Fz(G)1334 2577 y FH(7)1374 2563 y FI(,)f(the)g(hidden)e(bit)i Fw(b)g FI(of)g(the)g Fs(T)-8 b(est)q FI(-query)35 b(in)h(indep)s(enden) m(t)f(of)h(all)g(v)-5 b(alues)-58 2676 y(directly)31 b(or)f(indirectly)h(accessible)h(to)f(the)f(adv)m(ersary)-8 b(.)31 b(Hence,)g(Pr[)p Fw(S)2372 2690 y FH(7)2411 2676 y FI(])26 b(=)f(1)p Fw(=)p FI(2.)32 b(Com)m(bined)d(with)h(Equations)g (\(1\),)-58 2789 y(\(2\),)i(\(3\),)g(\(4\),)f(\(5\))h(and)e(\(6\),)h (it)g(giv)m(es)h(the)e(exp)s(ected)h(result.)-58 3067 y Fy(D)112 b(Random)39 b(Self-Reducibilit)m(y)-58 3292 y FI(Game)30 b Fz(G)286 3306 y FH(2)354 3292 y FI(is)e(iden)m(tical)j (to)e(game)h Fz(G)1235 3306 y FH(1)1274 3292 y FI(,)f(except)h(that)f (w)m(e)g(apply)f(the)h(follo)m(wing)h(sp)s(ecial)f(rules)f(when)g (dealing)h(with)-58 3405 y(the)i Fs(Reveal)p FI(\()p Fw(U;)15 b(i)p FI(\),)31 b Fs(T)-8 b(est)q FI(\()p Fw(U;)15 b(i)p FI(\))31 b(and)f Fs(Send)p FI(\()p Fw(U;)15 b(i;)g(m)p FI(\))32 b(queries)e(:)-58 3619 y Fz(R1:)46 b FI(When)32 b(pro)s(cessing)f(a)h Fs(Send)p FI(\()p Fw(A;)15 b(i;)g Fv(Start)p FI(\))32 b(query)-8 b(,)31 b(the)h(sim)m(ulator)g(pic)m(ks)g (four)f(random)g(v)-5 b(alues)32 b Fw(a)3543 3633 y FH(0)3582 3619 y Fw(;)15 b(x)3674 3633 y FH(0)3760 3567 y Ft(R)3741 3619 y Fl( )27 b Fu(Z)3920 3633 y Ft(q)108 3760 y FI(and)34 b Fw(a)337 3774 y FH(1)377 3760 y Fw(;)15 b(x)469 3774 y FH(1)560 3708 y Ft(R)542 3760 y Fl( )32 b Fu(Z)731 3774 y FH(~)-40 b Ft(q)764 3760 y FI(,)35 b(computes)g Fw(X)1308 3774 y FH(0)1381 3760 y FI(=)d Fw(a)1532 3774 y FH(0)1595 3760 y Fl(\001)23 b Fw(X)31 b FI(+)23 b Fw(x)1895 3774 y FH(0)1958 3760 y Fl(\001)g Fz(P)35 b FI(and)g Fw(X)2369 3774 y FH(1)2441 3760 y FI(=)e Fw(a)2593 3774 y FH(1)2655 3760 y Fl(\001)2730 3737 y FI(~)2704 3760 y Fw(X)e FI(+)22 b Fw(x)2955 3774 y FH(1)3018 3760 y Fl(\001)i Fz(Q)p FI(,)34 b(and)g(stores)i(in)e(some)108 3873 y Fl(X)13 b FI(-table)32 b(\()p Fw(a)527 3887 y FH(0)567 3873 y Fw(;)15 b(x)659 3887 y FH(0)699 3873 y Fw(;)g(X)814 3887 y FH(0)854 3873 y FI(\))30 b(and)g(\()p Fw(a)1179 3887 y FH(1)1219 3873 y Fw(;)15 b(x)1311 3887 y FH(1)1351 3873 y Fw(;)g(X)1466 3887 y FH(1)1506 3873 y FI(\).)-58 3988 y Fz(R2:)46 b FI(When)30 b(pro)s(cessing)h(a)f Fs(Send)p FI(\()p Fw(B)5 b(;)15 b(j;)g FI(\()p Fw(s;)g(X)1530 4002 y FH(0)1572 3988 y Fw(;)g(X)1687 4002 y FH(1)1727 3988 y FI(\)\))31 b(query)-8 b(,)176 4109 y Fz({)46 b FI(if)39 b(the)f(t)m(w)m(o)i(elemen)m(ts)g Fw(X)1165 4123 y FH(0)1243 4109 y FI(and)e Fw(X)1503 4123 y FH(1)1581 4109 y FI(ha)m(v)m(e)h(b)s(een)f(computed)g(b)m(y)h(our)f(sim)m(ulator) h(and)f(th)m(us)g(ha)m(v)m(e)i(b)s(een)274 4221 y(stored)e(in)f(the)g Fl(X)13 b FI(-table,)39 b(then)e(it)h(generates)g(the)g(same)g(w)m(a)m (y)g(its)g(answ)m(er)f(b)m(y)g(c)m(ho)s(osing)h(four)f(random)274 4353 y(v)-5 b(alues)31 b Fw(b)584 4367 y FH(0)624 4353 y Fw(;)15 b(y)709 4367 y FH(0)792 4302 y Ft(R)773 4353 y Fl( )26 b Fu(Z)951 4367 y Ft(q)1019 4353 y FI(and)k Fw(b)1235 4367 y FH(1)1274 4353 y Fw(;)15 b(y)1359 4367 y FH(1)1443 4302 y Ft(R)1424 4353 y Fl( )26 b Fu(Z)1607 4367 y FH(~)-40 b Ft(q)1639 4353 y FI(,)31 b(it)g(computes)g Fw(Y)2244 4367 y FH(0)2308 4353 y FI(=)26 b Fw(b)2444 4367 y FH(0)2503 4353 y Fl(\001)21 b Fw(Y)40 b FI(+)20 b Fw(y)2778 4367 y FH(0)2837 4353 y Fl(\001)h Fz(P)31 b FI(and)f Fw(Y)3215 4367 y FH(1)3279 4353 y FI(=)c Fw(b)3415 4367 y FH(1)3474 4353 y Fl(\001)3534 4330 y FI(~)3520 4353 y Fw(Y)40 b FI(+)20 b Fw(y)3749 4367 y FH(1)3809 4353 y Fl(\001)g Fz(Q)p FI(,)274 4466 y(and)34 b(stores)i(in)e(some)h Fl(Y)7 b FI(-table)37 b(\()p Fw(b)1466 4480 y FH(0)1505 4466 y Fw(;)15 b(y)1590 4480 y FH(0)1630 4466 y Fw(;)g(Y)1723 4480 y FH(0)1762 4466 y FI(\))35 b(and)g(\()p Fw(b)2088 4480 y FH(1)2127 4466 y Fw(;)15 b(y)2212 4480 y FH(1)2252 4466 y Fw(;)g(Y)2345 4480 y FH(1)2384 4466 y FI(\).)36 b(It)f(can)g(no)m(w)g(compute)g Fw(Z)3383 4480 y FH(0)3455 4466 y FI(=)d Fw(a)3606 4480 y FH(0)3645 4466 y Fw(b)3684 4480 y FH(0)3747 4466 y Fl(\001)23 b Fw(Z)30 b FI(+)274 4579 y Fw(x)326 4593 y FH(0)366 4579 y Fw(b)405 4593 y FH(0)464 4579 y Fl(\001)21 b Fw(Y)40 b FI(+)20 b Fw(a)742 4593 y FH(0)781 4579 y Fw(y)826 4593 y FH(0)886 4579 y Fl(\001)g Fw(X)28 b FI(+)20 b Fw(x)1177 4593 y FH(0)1216 4579 y Fw(y)1261 4593 y FH(0)1320 4579 y Fl(\001)h Fz(P)30 b FI(and)g Fw(Z)1706 4593 y FH(1)1771 4579 y FI(=)25 b Fw(a)1915 4593 y FH(1)1954 4579 y Fw(b)1993 4593 y FH(1)2053 4579 y Fl(\001)2118 4556 y FI(~)2098 4579 y Fw(Z)i FI(+)20 b Fw(x)2330 4593 y FH(1)2369 4579 y Fw(b)2408 4593 y FH(1)2468 4579 y Fl(\001)2527 4556 y FI(~)2514 4579 y Fw(Y)40 b FI(+)20 b Fw(a)2746 4593 y FH(0)2785 4579 y Fw(y)2830 4593 y FH(1)2889 4579 y Fl(\001)2961 4556 y FI(~)2935 4579 y Fw(X)27 b FI(+)20 b Fw(x)3180 4593 y FH(1)3220 4579 y Fw(y)3265 4593 y FH(1)3324 4579 y Fl(\001)g Fz(Q)p FI(.)176 4695 y Fz({)46 b FI(if)29 b(one)g(of)g(the)g(elemen)m(ts)i Fw(X)1224 4709 y FH(0)1292 4695 y FI(or)e Fw(X)1477 4709 y FH(1)1546 4695 y FI(has)f(not)i(b)s (een)e(previously)g(computed)h(b)m(y)g(our)f Fw(A)p FI(-sim)m(ulation,) j(then)274 4808 y(it)g(pro)s(ceeds)f(as)h(in)f(the)g(game)i Fz(G)1431 4822 y FH(1)1470 4808 y FI(.)108 4928 y(In)25 b(the)g(\014rst)f(case,)j(the)e(sim)m(ulator)h(uses)f(the)g(k)m(ey)h Fw(Z)1871 4942 y FH(0)1936 4928 y FI(or)f Fw(Z)2104 4942 y FH(1)2169 4928 y FI(as)g(a)g(master)h(k)m(ey)g(according)g(to)g(b)s (e)e(bit)i Fw(\014)k FI(whereas)108 5041 y(in)g(the)h(second)f(case,)i (the)e(master)h(k)m(ey)g(will)g(b)s(e)f(calculated)i(as)f(in)f(the)g (previous)g(game.)-58 5156 y Fz(R3:)46 b FI(When)d(pro)s(cessing)f(a)h Fs(Send)p FI(\()p Fw(A;)15 b(i;)g FI(\()p Fw(s;)g(Y)1533 5170 y FH(0)1574 5156 y Fw(;)g(Y)1667 5170 y FH(1)1707 5156 y Fw(;)g(B)5 b(ob;)15 b(\033)1996 5170 y Ft(B)2057 5156 y Fw(;)g(\026)2152 5170 y Ft(B)2212 5156 y FI(\)\),)44 b(then)e(if)h(the)f(authen)m(ticator)j(is)d(correct,)i(w)m(e)108 5269 y(can)g(assume)f(that)h(the)g(corresp)s(onding)e(v)-5 b(alues)44 b(\()p Fw(X)1986 5283 y FH(0)2026 5269 y Fw(;)15 b(X)2141 5283 y FH(1)2182 5269 y Fw(;)g(Y)2275 5283 y FH(0)2314 5269 y Fw(;)g(Y)2407 5283 y FH(1)2447 5269 y Fw(;)g(Z)2549 5283 y FH(0)2589 5269 y Fw(;)g(Z)2691 5283 y FH(1)2731 5269 y FI(\))43 b(ha)m(v)m(e)i(b)s(een)e(computed)g(b) m(y)h(the)108 5382 y(sim)m(ulator:)34 b(w)m(e)g(can)g(compute)f(the)g (master)h(k)m(ey)-8 b(,)35 b(and)d(th)m(us)h(compute)g(and)g(c)m(hec)m (k)i(the)e(MA)m(C)h(to)g(determine)108 5495 y(the)d(bit)f Fw(d)p FI(,)h(if)f(it)h(exists.)1905 5744 y(23)p eop end %%Page: 24 24 TeXDict begin 24 23 bop -58 -83 a Fz(R4:)46 b FI(When)32 b(pro)s(cessing)g(a)g Fs(T)-8 b(est)q FI(\()p Fw(U;)15 b(i)p FI(\)-query)-8 b(,)33 b(w)m(e)g(kno)m(w)f(that)g(suc)m(h)g(a)g (query)g(can)g(only)g(b)s(e)g(ask)m(ed)g(on)g(accepting)108 30 y(instance,)i(and)e(accepting)j(session)e(can)g(only)g(happ)s(en)f (when)g(the)h(sim)m(ulator)h(kno)m(ws)f(the)g(correct)h(v)-5 b(alue)33 b Fw(Z)3917 45 y Ft(d)108 143 y FI(and)d(can)h(answ)m(er)f (suc)m(h)g(query)g(as)g(in)g(the)h(game)g Fz(G)1904 157 y FH(1)1944 143 y FI(.)-58 255 y Fz(R5:)46 b FI(When)38 b(pro)s(cessing)f(a)h Fs(Reveal)p FI(\()p Fw(U;)15 b(i)p FI(\)-query)-8 b(,)39 b(as)f(in)f(the)h(rule)f Fz(R4)p FI(,)h(the)g(sim)m(ulator)h(is)e(able)h(to)h(answ)m(er)e(suc)m(h)108 368 y(queries)30 b(as)h(in)f(the)h(previous)f(game.)-58 542 y(It)d(is)h(easy)g(to)g(see)g(that)f(in)g(the)h(second)f(case)h(of) g(rule)f Fz(R2)p FI(,)h(as)f(in)g(game)i Fz(G)2495 556 y FH(1)2534 542 y FI(,)f(the)f(adv)m(ersary)h(will)f(not)h(b)s(een)e (able)i(to)-58 655 y(forge)e(an)f(authen)m(ticator,)i(and)d(then)h(he)g (will)g(not)h(b)s(e)e(able)h(to)h(generate)h(a)e(correct)h(third)e (message.)j(Consequen)m(tly)-8 b(,)-58 768 y(the)24 b(session)g(will)h (not)f(b)s(e)f(accepted)j(b)m(y)d(an)m(y)i(part)m(y)f(and)f(so)i(the)f (adv)m(ersary)g(will)g(not)h(b)s(e)e(able)h(to)h(send)e(a)i Fs(T)-8 b(est)p FI(-query)-58 881 y(to)31 b(an)m(y)g(instance.)g (Hence,)h(the)e(sim)m(ulation)i(will)e(b)s(e)g(consisten)m(t.)-58 1142 y Fy(E)112 b(The)37 b(DDH)g(Distinguisher)-58 1349 y FI(W)-8 b(e)37 b(assume)e(that)g Fl(A)g FI(is)g(an)g(attac)m(k)m(er)k (that)c(breaks)g(the)h(AKE)f(securit)m(y)h(game)g(with)f(a)g (di\013eren)m(t)h(adv)-5 b(an)m(tage)37 b(in)-58 1462 y(Game)f Fz(G)292 1476 y FH(3)366 1462 y FI(than)e(in)h(Game)g Fz(G)1042 1476 y FH(2)1082 1462 y FI(,)g(then)f(w)m(e)h(construct)g(an) g(adv)m(ersary)g Fl(A)2516 1429 y Fj(0)2573 1462 y FI(whic)m(h)f(is)h (able)g(to)h(distinguish)e(triples)-58 1575 y(coming)d(from)g(either)g (a)f(DDH)i(or)f(a)g(random)e(distribution:)h(at)i(the)e(b)s(eginning)g (of)h(the)g(exp)s(erimen)m(t,)g Fl(A)3601 1542 y Fj(0)3654 1575 y FI(receiv)m(es)-58 1688 y(a)d(triple)f(\()p Fw(X)r(;)15 b(Y)5 b(;)15 b(Z)7 b FI(\))28 b(whic)m(h)f(is)g(a)g(DDH)h(triple)g(if)f Fw(b)e FI(=)g(0)i(or)g(a)h(random)e(triple)h(if)g Fw(b)f FI(=)f(1.)i(Then)f Fl(A)3234 1655 y Fj(0)3284 1688 y FI(runs)g(the)h(attac)m(k)m(er)-58 1801 y Fl(A)39 b FI(using)f(this)h (triple)g(to)h(sim)m(ulate)h(all)e(the)h(queries)f(as)g(in)g(the)g (previous)f(game)i(\(with)f(is)h(actually)g(either)g(the)-58 1914 y(previous)31 b(game)h(if)f Fw(b)c FI(=)f(0)31 b(or)h(the)f (curren)m(t)g(game)h(if)f Fw(b)c FI(=)f(1\)..)32 b(When)f(the)h Fs(T)-8 b(est)p FI(\()p Fw(U;)15 b(i)p FI(\)-query)32 b(happ)s(ens,)e Fl(A)3630 1881 y Fj(0)3684 1914 y FI(pic)m(ks)h(a)-58 2027 y(bit)c(at)h(random)e Fw(b)557 1994 y Fj(0)608 2027 y FI(and)g(sends)g(according)i(to)g Fw(b)1574 1994 y Fj(0)1625 2027 y FI(either)f(the)g(real)h(session)f(k)m(ey)h(if)f Fw(b)2782 1994 y Fj(0)2831 2027 y FI(=)e(0)i(or)g(a)h(random)e(session) h(k)m(ey)-8 b(.)-58 2140 y(Ev)m(en)m(tually)g(,)34 b Fl(A)d FI(will)h(reply)f(with)h(a)g(bit)g Fw(b)1393 2107 y Fj(00)1435 2140 y FI(.)g(Finally)-8 b(,)33 b(if)f Fw(b)1944 2107 y Fj(0)1995 2140 y FI(=)27 b Fw(b)2132 2107 y Fj(00)2174 2140 y FI(,)32 b(then)f Fl(A)2512 2107 y Fj(0)2567 2140 y FI(returns)f(a)i(bit)g Fw(b)3141 2107 y Ft(?)3208 2140 y FI(=)27 b(1,)32 b(else)h(it)f(returns)-58 2253 y Fw(b)-19 2220 y Ft(?)46 2253 y FI(=)25 b(0.)52 2465 y(Pr[)p Fw(b)214 2428 y Ft(?)279 2465 y FI(=)g Fw(b)p FI(])e(=)566 2404 y(1)p 566 2444 46 4 v 566 2527 a(2)642 2465 y Fl(\001)d FI(\()q(Pr)o([)p Fw(b)884 2428 y Ft(?)949 2465 y FI(=)25 b(0)p Fl(j)p Fw(b)h FI(=)f(0])c(+)f(Pr)o([)p Fw(b)1619 2428 y Ft(?)1684 2465 y FI(=)25 b(1)p Fl(j)p Fw(b)h FI(=)f(1]\))h(=) 2248 2404 y(1)p 2248 2444 V 2248 2527 a(2)2324 2465 y Fl(\001)2369 2391 y Fg(\000)2411 2465 y FI(Pr[)p Fw(b)2573 2428 y Fj(0)2621 2465 y FI(=)f Fw(b)2756 2428 y Fj(00)2799 2465 y Fl(j)p Fs(DDH)p FI(])20 b(+)g(Pr[)p Fw(b)3318 2428 y Fj(0)3366 2465 y Fl(6)p FI(=)25 b Fw(b)3501 2428 y Fj(00)3544 2465 y Fl(j)p Fs(Rand)o FI(])3790 2391 y Fg(\001)462 2681 y FI(=)566 2619 y(1)p 566 2660 V 566 2743 a(2)642 2681 y Fl(\001)687 2607 y Fg(\000)729 2681 y FI(Pr[)p Fw(b)891 2643 y Fj(0)939 2681 y FI(=)g Fw(b)1074 2643 y Fj(00)1117 2681 y Fl(j)p Fs(DDH)p FI(])20 b(+)g(1)h Fl(\000)f FI(Pr)o([)p Fw(b)1792 2643 y Fj(0)1841 2681 y FI(=)25 b Fw(b)1976 2643 y Fj(00)2018 2681 y Fl(j)p Fs(Rand)p FI(])2265 2607 y Fg(\001)2332 2681 y FI(=)2438 2619 y(1)p 2438 2660 V 2438 2743 a(2)2514 2681 y Fl(\001)20 b FI(\(Pr[)p Fw(S)2773 2695 y FH(2)2812 2681 y FI(])h(+)f(1)g Fl(\000)g FI(Pr[)p Fw(S)3284 2695 y FH(3)3323 2681 y FI(]\))c Fw(:)-58 2905 y FI(Note)29 b(that)g(the)f(running)e(time)j Fw(t)1082 2872 y Fj(0)1133 2905 y FI(of)f Fl(A)1307 2872 y Fj(0)1358 2905 y FI(is)g(the)g(same)g(as)g Fw(t)g FI(plus)f(the)h (time)h(for)f(the)g(computations)g(of)g(the)h(random)-58 3018 y(self-reducibilit)m(y:)j Fw(t)20 b FI(+)g(8)p Fw(q)837 3032 y Ft(s)874 3018 y Fw(T)927 3032 y Ft(m)993 3018 y FI(.)-58 3279 y Fy(F)113 b(Distribution)37 b(of)h(the)f(Preliminary)i (Secret)-58 3487 y FI(In)31 b(this)h(section)g(w)m(e)g(sho)m(w)g(that)g (the)g(distribution)f(of)h(the)f(preliminary)h(secret)g(k)m(ey)h Fw(K)38 b FI(is)31 b(statistically)k(indistin-)-58 3600 y(guishable)d(from)g(the)g(uniform)f(distribution)g(on)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1906 3567 y Ft(`)1942 3600 y FI(.)32 b(On)f(the)h(one)h(hand,)e(w)m(e)h(pro)m(v)m(e)h(that)g (it)g(is)f(statistically)-58 3713 y(indistinguishable)c(from)f(the)h (uniform)f(distribution)g(on)h Fl(f)p FI(0)p Fw(;)15 b(:)g(:)g(:)j(;)d(p)g Fl(\000)h FI(1)p Fl(g)28 b FI(and)g(then)f(that)i (the)f(latter)h(distribution)-58 3826 y(is)i(statistically)i (indistinguishable)d(from)g(the)g(uniform)g(distribution)f(on)i Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)2775 3793 y Ft(`)2810 3826 y FI(.)83 3938 y(Let)31 b(us)f(denote)h(b)m(y)f Fl(D)j FI(the)e(distribution)e(of)i Fw(K)7 b FI(:)-16 4155 y Fl(D)28 b FI(=)d Fl(f)p Fw(b)306 4103 y Ft(R)288 4155 y Fl( )g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)p Fw(;)g Fz(R)742 4169 y FH(0)828 4103 y Ft(R)809 4155 y Fl( )26 b Fu(E)p Fw(;)15 b Fz(R)1105 4169 y FH(1)1188 4103 y Ft(R)1170 4155 y Fl( )1293 4131 y FI(~)1286 4155 y Fu(E)25 b FI(:)g Fw(K)32 b FI(=)25 b([)p Fz(R)1730 4170 y Ft(b)1765 4155 y FI(])1790 4170 y Fk(abs)1892 4155 y Fl(g)h FI(=)f Fl(f)p Fw(b)2187 4103 y Ft(R)2168 4155 y Fl( )g(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)p Fw(;)g(x)2596 4169 y FH(0)2682 4103 y Ft(R)2664 4155 y Fl( )25 b FI([)p Fu(E)p FI(])2891 4170 y Fk(abs)2993 4155 y Fw(;)15 b(x)3085 4169 y FH(1)3168 4103 y Ft(R)3150 4155 y Fl( )25 b FI([)3299 4131 y(~)3291 4155 y Fu(E)p FI(])3377 4170 y Fk(abs)3504 4155 y FI(:)g Fw(K)32 b FI(=)25 b Fw(x)3811 4170 y Ft(b)3845 4155 y Fl(g)p Fw(:)-58 4412 y Fz(F.1)105 b(Pro)s(of)36 b(of)f(Lemma)f(16)-58 4587 y FI(In)d(this)g(pro)s(of,)g(w)m(e)g(note)h Fw(E)903 4601 y FH(0)969 4587 y FI(=)27 b([)p Fu(E)p FI(])1178 4602 y Fk(abs)1311 4587 y FI(and)j Fw(E)1555 4601 y FH(1)1622 4587 y FI(=)c([)1752 4563 y(~)1744 4587 y Fu(E)p FI(])1830 4602 y Fk(abs)1932 4587 y FI(.)31 b(Then,)f(w)m(e)i(ha)m(v)m(e)h Fu(F)2653 4601 y Ft(p)2719 4587 y FI(=)26 b Fw(E)2883 4601 y FH(0)2943 4587 y Fl([)21 b Fw(E)3092 4601 y FH(1)3131 4587 y FI(.)32 b(As)f(already)h(noticed,)-58 4699 y(#)p Fu(E)25 b FI(=)g Fw(p)9 b FI(+)g(1)g Fl(\000)g Fw(t)26 b FI(=)f Fw(q)j FI(and)c(#)948 4676 y(~)940 4699 y Fu(E)h FI(=)g Fw(p)9 b FI(+)g(1)g(+)g Fw(t)26 b FI(=)32 b(~)-52 b Fw(q)s FI(,)25 b(where)g Fw(t)g FI(is)g(less)g(than)g(2)2456 4643 y Fl(p)p 2532 4643 V 56 x Fw(p)p FI(.)g(Then)f(#)p Fw(E)3003 4713 y FH(0)3067 4699 y FI(=)h Fw(q)s(=)p FI(2)h(and)e(#)p Fw(E)3637 4713 y FH(1)3702 4699 y FI(=)32 b(~)-52 b Fw(q)s(=)p FI(2,)-58 4812 y(since)31 b(one)g(abscissa)f(corresp)s(onds)f(to)j(t)m (w)m(o)f(p)s(oin)m(ts)g(on)f(the)g(elliptic)i(curv)m(es.)f(W)-8 b(e)32 b(th)m(us)e(ha)m(v)m(e)14 5082 y Fw(\016)d FI(=)192 4995 y Fg(X)175 5192 y Ft(x)p Fj(2)p Fd(F)303 5200 y Fn(p)354 4922 y Fg(\014)354 4977 y(\014)354 5032 y(\014)354 5086 y(\014)354 5141 y(\014)443 5082 y FI(Pr)384 5177 y Ft(K)461 5139 y Fn(R)449 5177 y Fj( )o(U)563 5185 y Fn(p)599 5082 y FI([)p Fw(K)33 b FI(=)25 b Fw(x)p FI(])20 b Fl(\000)67 b FI(Pr)1018 5177 y Ft(K)1094 5139 y Fn(R)1083 5177 y Fj( )o(D)1209 5082 y FI([)p Fw(K)32 b FI(=)25 b Fw(x)p FI(])1516 4922 y Fg(\014)1516 4977 y(\014)1516 5032 y(\014)1516 5086 y(\014)1516 5141 y(\014)1572 5082 y FI(=)1684 4995 y Fg(X)1668 5192 y Ft(x)p Fj(2)p Fd(F)1796 5200 y Fn(p)1847 4922 y Fg(\014)1847 4977 y(\014)1847 5032 y(\014)1847 5086 y(\014)1847 5141 y(\014)1887 5020 y FI(1)p 1887 5061 V 1887 5144 a Fw(p)1963 5082 y Fl(\000)102 b FI(Pr)2054 5177 y Ft(b)2096 5139 y Fn(R)2084 5177 y Fj( f)p FH(0)p Ft(;)p FH(1)p Fj(g)2315 5082 y FI([)p Fw(x)2392 5096 y FH(0)2476 5030 y Ft(R)2457 5082 y Fl( )25 b Fw(E)2640 5096 y FH(0)2680 5082 y Fw(;)15 b(x)2772 5096 y FH(1)2856 5030 y Ft(R)2837 5082 y Fl( )25 b Fw(E)3020 5096 y FH(1)3085 5082 y FI(:)g Fw(x)h FI(=)f Fw(x)3361 5097 y Ft(b)3395 5082 y FI(])3420 4922 y Fg(\014)3420 4977 y(\014)3420 5032 y(\014)3420 5086 y(\014)3420 5141 y(\014)81 5412 y FI(=)196 5325 y Fg(X)175 5522 y Ft(x)p Fj(2)p Ft(E)314 5531 y FG(0)364 5253 y Fg(\014)364 5307 y(\014)364 5362 y(\014)364 5416 y(\014)364 5471 y(\014)404 5350 y FI(1)p 404 5391 V 404 5474 a Fw(p)480 5412 y Fl(\000)102 b FI(Pr)571 5508 y Ft(b)613 5469 y Fn(R)601 5508 y Fj( f)p FH(0)p Ft(;)p FH(1)p Fj(g)832 5412 y FI([)p Fw(x)909 5426 y FH(0)993 5360 y Ft(R)974 5412 y Fl( )25 b Fw(E)1157 5426 y FH(0)1197 5412 y Fw(;)15 b(x)1289 5426 y FH(1)1373 5360 y Ft(R)1354 5412 y Fl( )25 b Fw(E)1537 5426 y FH(1)1602 5412 y FI(:)g Fw(x)h FI(=)f Fw(x)1878 5427 y Ft(b)1912 5412 y FI(])1937 5253 y Fg(\014)1937 5307 y(\014)1937 5362 y(\014)1937 5416 y(\014)1937 5471 y(\014)1988 5412 y FI(+)2099 5325 y Fg(X)2079 5522 y Ft(x)p Fj(2)p Ft(E)2218 5531 y FG(1)2267 5253 y Fg(\014)2267 5307 y(\014)2267 5362 y(\014)2267 5416 y(\014)2267 5471 y(\014)2307 5350 y FI(1)p 2307 5391 V 2307 5474 a Fw(p)2383 5412 y Fl(\000)102 b FI(Pr)2474 5508 y Ft(b)2516 5469 y Fn(R)2504 5508 y Fj( f)p FH(0)p Ft(;)p FH(1)p Fj(g)2735 5412 y FI([)p Fw(x)2812 5426 y FH(0)2896 5360 y Ft(R)2877 5412 y Fl( )25 b Fw(E)3060 5426 y FH(0)3100 5412 y Fw(;)15 b(x)3192 5426 y FH(1)3276 5360 y Ft(R)3257 5412 y Fl( )25 b Fw(E)3440 5426 y FH(1)3505 5412 y FI(:)g Fw(x)h FI(=)f Fw(x)3781 5427 y Ft(b)3815 5412 y FI(])3840 5253 y Fg(\014)3840 5307 y(\014)3840 5362 y(\014)3840 5416 y(\014)3840 5471 y(\014)1905 5744 y FI(24)p eop end %%Page: 25 25 TeXDict begin 25 24 bop 81 -42 a FI(=)196 -129 y Fg(X)175 68 y Ft(x)p Fj(2)p Ft(E)314 77 y FG(0)364 -174 y Fg(\014)364 -120 y(\014)364 -65 y(\014)364 -11 y(\014)404 -104 y FI(1)p 404 -63 46 4 v 404 20 a Fw(p)480 -42 y Fl(\000)581 -104 y FI(1)p 581 -63 V 581 20 a(2)656 -42 y Fl(\002)20 b FI(Pr[)p Fw(x)922 -28 y FH(0)1005 -94 y Ft(R)987 -42 y Fl( )25 b Fw(E)1170 -28 y FH(0)1235 -42 y FI(:)g Fw(x)g FI(=)g Fw(x)1510 -28 y FH(0)1550 -42 y FI(])1575 -174 y Fg(\014)1575 -120 y(\014)1575 -65 y(\014)1575 -11 y(\014)1625 -42 y FI(+)1737 -129 y Fg(X)1716 68 y Ft(x)p Fj(2)p Ft(E)1855 77 y FG(1)1905 -174 y Fg(\014)1905 -120 y(\014)1905 -65 y(\014)1905 -11 y(\014)1945 -104 y FI(1)p 1945 -63 V 1945 20 a Fw(p)2021 -42 y Fl(\000)2122 -104 y FI(1)p 2122 -63 V 2122 20 a(2)2197 -42 y Fl(\002)20 b FI(Pr[)p Fw(x)2463 -28 y FH(1)2546 -94 y Ft(R)2527 -42 y Fl( )26 b Fw(E)2711 -28 y FH(1)2775 -42 y FI(:)g Fw(x)f FI(=)g Fw(x)3051 -28 y FH(1)3091 -42 y FI(])3116 -174 y Fg(\014)3116 -120 y(\014)3116 -65 y(\014)3116 -11 y(\014)81 251 y FI(=)186 190 y Fw(q)p 185 231 V 185 314 a FI(2)261 251 y Fl(\002)352 120 y Fg(\014)352 174 y(\014)352 229 y(\014)352 283 y(\014)392 190 y FI(1)p 392 231 V 392 314 a Fw(p)468 251 y Fl(\000)569 190 y FI(1)p 569 231 V 569 314 a(2)645 251 y Fl(\002)745 190 y FI(2)p 745 231 V 746 314 a Fw(q)801 120 y Fg(\014)801 174 y(\014)801 229 y(\014)801 283 y(\014)851 251 y FI(+)960 190 y(~)-52 b Fw(q)p 952 231 V 952 314 a FI(2)1028 251 y Fl(\002)1119 120 y Fg(\014)1119 174 y(\014)1119 229 y(\014)1119 283 y(\014)1159 190 y FI(1)p 1159 231 V 1159 314 a Fw(p)1235 251 y Fl(\000)1336 190 y FI(1)p 1336 231 V 1336 314 a(2)1411 251 y Fl(\002)1512 190 y FI(2)p 1512 231 V 1520 314 a(~)g Fw(q)1568 120 y Fg(\014)1568 174 y(\014)1568 229 y(\014)1568 283 y(\014)1623 251 y FI(=)1730 190 y Fw(q)p 1729 231 V 1729 314 a FI(2)1805 251 y Fl(\002)1896 123 y Fg(\022)1973 190 y FI(1)p 1973 231 V 1974 314 a Fw(q)2048 251 y Fl(\000)2149 190 y FI(1)p 2149 231 V 2149 314 a Fw(p)2205 123 y Fg(\023)2292 251 y FI(+)2400 190 y(~)h Fw(q)p 2393 231 V 2393 314 a FI(2)2468 251 y Fl(\002)2559 123 y Fg(\022)2636 190 y FI(1)p 2636 231 V 2636 314 a Fw(p)2712 251 y Fl(\000)2813 190 y FI(1)p 2813 231 V 2821 314 a(~)f Fw(q)2868 123 y Fg(\023)81 515 y FI(=)175 387 y Fg(\022)252 453 y FI(1)p 252 494 V 252 577 a(2)328 515 y Fl(\000)452 453 y Fw(q)p 429 494 92 4 v 429 577 a FI(2)p Fw(p)530 387 y Fg(\023)617 515 y FI(+)708 387 y Fg(\022)815 453 y FI(~)h Fw(q)p 785 494 V 785 577 a FI(2)p Fw(p)906 515 y Fl(\000)1007 453 y FI(1)p 1007 494 46 4 v 1007 577 a(2)1063 387 y Fg(\023)1155 515 y FI(=)1267 453 y(~)g Fw(q)23 b Fl(\000)d Fw(q)p 1261 494 199 4 v 1314 577 a FI(2)p Fw(p)1495 515 y FI(=)1607 453 y(2)p Fw(t)p 1601 494 92 4 v 1601 577 a FI(2)p Fw(p)1727 515 y Fl(\024)1833 449 y FI(2)1878 392 y Fl(p)p 1954 392 46 4 v 57 x Fw(p)p 1833 494 167 4 v 1894 577 a(p)2035 515 y Fl(\024)2179 453 y FI(2)p 2141 494 122 4 v 2141 521 a Fl(p)p 2217 521 46 4 v 56 x Fw(p)2298 515 y Fl(\024)2503 453 y FI(2)p 2404 494 245 4 v 2404 512 a Fl(p)p 2479 512 169 4 v 2479 594 a FI(2)2524 568 y Ft(`)p Fj(\000)p FH(1)2683 515 y Fl(\024)2789 453 y FI(2)2834 378 y Fl(p)p 2910 378 46 4 v 75 x FI(2)p 2789 494 167 4 v 2795 512 a Fl(p)p 2871 512 79 4 v 82 x FI(2)2916 568 y Ft(`)2966 515 y Fw(:)3897 758 y Fl(u)-61 b(t)-58 1020 y Fz(F.2)105 b(Pro)s(of)36 b(of)f(Lemma)f(14)-58 1200 y FI(No)m(w,)27 b(w)m(e)g(pro)m(v)m(e)g(that)g(the)f(statistical)j (distance)e(b)s(et)m(w)m(een)g(the)g(uniform)e(distribution)g(in)h(the) h(space)g Fu(F)3525 1214 y Ft(p)3589 1200 y Fl(\030)e Fu(Z)3746 1214 y Ft(p)3811 1200 y FI(and)-58 1313 y(the)i(uniform)f (distribution)g(in)h(the)g(space)h Fl(f)p FI(0)p Fw(;)15 b FI(1)p Fl(g)1641 1280 y Ft(`)1701 1313 y Fl(\030)25 b(f)p FI(0)p Fw(;)15 b(:)g(:)g(:)j(;)d FI(2)2135 1280 y Ft(`)2182 1313 y Fl(\000)e FI(1)p Fl(g)p FI(,)28 b(where)e(2)2713 1280 y Ft(`)2760 1313 y Fl(\000)13 b Fw(")26 b Fl(\024)f Fw(p)g(<)g FI(2)3220 1280 y Ft(`)3280 1313 y FI(and)h(0)g Fw(<)f(")h Fl(\024)f FI(2)3829 1280 y Ft(`=)p FH(2)3933 1313 y FI(,)-58 1426 y(is)31 b(less)f(than)g(1)p Fw(=)503 1344 y Fl(p)p 580 1344 V 580 1426 a FI(2)625 1399 y Ft(`)658 1426 y FI(.)51 1734 y Fw(\016)94 1697 y Fj(0)141 1734 y FI(=)308 1648 y Fg(X)235 1853 y Ft(x)p Fj(2f)p FH(0)p Ft(;)p FH(1)p Fj(g)482 1834 y Fn(`)528 1548 y Fg(\014)528 1603 y(\014)528 1657 y(\014)528 1712 y(\014)528 1766 y(\014)528 1821 y(\014)630 1734 y FI(Pr)558 1830 y Ft(X)633 1792 y Fn(R)621 1830 y Fj( U)736 1856 y FG(2)766 1842 y Fn(`)800 1734 y FI([)p Fw(X)j FI(=)25 b Fw(x)p FI(])c Fl(\000)78 b FI(Pr)1218 1830 y Ft(X)1293 1792 y Fn(R)1281 1830 y Fj( )o(U)1395 1838 y Fn(p)1431 1734 y FI([)p Fw(X)33 b FI(=)25 b Fw(x)p FI(])1737 1548 y Fg(\014)1737 1603 y(\014)1737 1657 y(\014)1737 1712 y(\014)1737 1766 y(\014)1737 1821 y(\014)141 2098 y FI(=)304 2012 y Fg(X)245 2212 y Fn(x)p Fa(2f)p FG(0)p Fn(;)p FG(1)p Fa(g)465 2198 y Fn(`)312 2269 y(x