Pre-computation in width-w tau-adic NAF implementations on Koblitz curves.

详细信息   

• 作者：Trost ; William R.
• 学历：Master
• 年：2014
• 毕业院校：The University of Wisconsin
• Department：Computer Science.
• ISBN：9781321010749
• CBH：1560014
• Country：USA
• 语种：English
• FileSize：1212974
• Pages：98

文摘

This paper examines scalar multiplication on Koblitz curves employing the Frobenius endomorphism. We examine simple binary scalar multiplication,binary Non Adjacent Formats or NAFs,followed by tau-NAF methods. We pay particular attention to width-w tau-NAF where we focus on pre-computation. We present alternative pre-computation arrangements for alpha u for width sizes of 5 and 6 which are better than any previously published results since they: involve a single power of tau are based on least norms； and have a maximum of 2w -- 2 -- 1 elliptic curve operations. We then study widths of 7 and 8 producing efficient arrangements. Arrangements for width sizes of 7 and 8 have never before appeared in the literature. Furthermore,we introduce a simplified rounding technique for reduction modulo taum -- 1)/tau -- 1) relaxing the requirement of least norms. Lastly,we discuss an On) technique for finding arbitrary powers of tau in software.