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    <title>2007 Reports</title>
    <link>http://eprint.iacr.org/forum/list.php?7</link>
    <description><![CDATA[Discussion forum for Cryptology ePrint Archive reports posted in 2007.
Please put the report number in the subject.

]]></description>
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    <pubDate>Fri, 23 Nov 2007 12:08:17 -0700</pubDate>
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      <title>Report 2007/414, Optimizing double-base elliptic-curve single-scalar multiplication</title>
      <link>http://eprint.iacr.org/forum/read.php?7,37,37#msg-37</link>
      <author>jamuir</author>
      <description><![CDATA[Report 2007/414 is &quot;Optimizing double-base elliptic-curve single-scalar multiplication&quot; by Bernstein, Birkner, Lange and Peters.  I think it is a very nice paper, but I wondered if someone might be able to help me track down the origins of one of the ideas mentioned in it.

In the discussion in the section &quot;Computing a chain&quot;, which starts at the bottom of page 8, the first two paragraphs mention what I call closest-choice decompositions of the integer 314159.  It is mentioned that these decompositions correspond to an addition chain method by Thurber.  Specifically, &quot;Thurber's base-2 sliding window chain&quot; is mentioned.  I assume that this a reference to Thurber's DMJ paper (cited as [22]).

When I look through [22] I don't find any discussion there about closest-choice decompositions.  Moreover, Thurber treats only addition chains rather than addition-subtraction chains.  Does anyone know if there is some other work by Thurber where this can be found?

In [22], Thurber does, however, present an example (page 912) where he uses the binary representation of n to identify what he calls critical numbers.  His strategy seems to differ from the close-choice strategy because he selects the first critical number to be larger than the others.

Can anyone help me track down the origins of closest choice representations?

-James]]></description>
      <category>2007 Reports</category>
      <guid isPermaLink="true">http://eprint.iacr.org/forum/read.php?7,37,37#msg-37</guid>
      <pubDate>Fri, 23 Nov 2007 12:08:17 -0700</pubDate>
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