%PDF-1.4 % 4 0 obj << /S /GoTo /D (section.1) >> endobj 7 0 obj (1. Introduction) endobj 8 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 11 0 obj (1.1. Context) endobj 12 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 15 0 obj (1.2. Contributions) endobj 16 0 obj << /S /GoTo /D (subsection.1.3) >> endobj 19 0 obj (1.3. Consequences and limitations) endobj 20 0 obj << /S /GoTo /D (subsection.1.4) >> endobj 23 0 obj (1.4. Related work) endobj 24 0 obj << /S /GoTo /D (subsection.1.5) >> endobj 27 0 obj (1.5. Organization of the paper) endobj 28 0 obj << /S /GoTo /D (section.2) >> endobj 31 0 obj (2. Point decomposition problem) endobj 32 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 35 0 obj (2.1. General method for solving the PDP) endobj 36 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 39 0 obj (2.2. Solving the PDP using summation polynomials) endobj 40 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 43 0 obj (2.3. Curve representations adding symmetries in the PDP) endobj 44 0 obj << /S /GoTo /D (section.3) >> endobj 47 0 obj (3. Solving polynomial systems and symmetries) endobj 48 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 51 0 obj (3.1. Gr\366bner basis) endobj 52 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 55 0 obj (3.2. Invariant ring and reflection groups) endobj 56 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 59 0 obj (3.3. Solving pointwise invariant system) endobj 60 0 obj << /S /GoTo /D (section.4) >> endobj 63 0 obj (4. Use of symmetries to improve the ECDLP solving) endobj 64 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 67 0 obj (4.1. Group action on the point decomposition problem) endobj 68 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 71 0 obj (4.2. Can the 4-torsion points be used in the same way?) endobj 72 0 obj << /S /GoTo /D (section.5) >> endobj 75 0 obj (5. Experimental results and security estimates) endobj 76 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 79 0 obj (5.1. Experiments with n=4) endobj 80 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 83 0 obj (5.2. Experiments for n=5 and n=6) endobj 84 0 obj << /S /GoTo /D (subsection.5.3) >> endobj 87 0 obj (5.3. Security level estimates) endobj 88 0 obj << /S /GoTo /D (section.6) >> endobj 91 0 obj (6. Perspectives) endobj 92 0 obj << /S /GoTo /D (section*.9) >> endobj 95 0 obj (References) endobj 96 0 obj << /S /GoTo /D [97 0 R /Fit ] >> endobj 102 0 obj << /Length 3317 /Filter /FlateDecode >> stream xڥZY۸~#Ue!8xf+U+X^&
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