Roberto Maria Avanzi, Clemens Heuberger, Helmut Prodinger  Home/Search
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Abstract: In order to e#ciently perform scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the #-adic NAF, introduced by Solinas. Some properties of this expansion, such as the average weight, are well known, but in the literature there is no proof of its optimality, i.e. that it always has minimal weight. In this paper we provide the first proof of this fact. (Update)
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BibTeX entry: (Update)
@misc{ koblitz-minimality,
author = "Roberto Maria Avanzi and Clemens Heuberger and Helmut Prodinger",
title = "Minimality of the Hamming Weight of the $\tau$-Naf For Koblitz Curves and Improved Combination with Point Halving",
url = "citeseer.ist.psu.edu/avanzi05minimality.html" }
Citations (may not include all citations):257 Elliptic curve cryptosystems (context) - Koblitz - 1987
228 Use of elliptic curves in cryptography (context) - Miller - 1986
143 Digital Signature Standard (context) - of, Technology - 2000
108 An Introduction to the Analysis of Algorithms (context) - Sedgewick, Flajolet - 1996
55 An improved algorithm for arithmetic on a family of elliptic.. (context) - Solinas - 1997
53 IEEE Standard Specifications for Public-Key Cryptography (context) - Std - 2000
49 CM-curves with good cryptographic properties (context) - Koblitz - 1991
45 Binary arithmetic (context) - Reitwiesner - 1960
12 cient Arithmetic on Koblitz Curves (context) - Solinas - 2000
10 Low complexity normal bases (context) - Ash, Blake et al. - 1989
8 Elliptic Scalar Multiplication Using Point Halving (context) - Knudsen - 1999
3 Elliptic curve point ambiguity resolution apparatus and meth.. (context) - Schroeppel - 2000
2 Faster Scalar Multiplication on Koblitz Curves combining Poi.. (context) - Avanzi, Ciet et al. - 2004
1 Software Implementatin of Elliptic Curve Cryprography over B.. (context) - Hankerson, Lopez-Hernandez et al. - 2001
1 University of Illinois at Urbana-Champaign; and (context) - Schroeppel, wins et al. - 2001
http://www.cs.siu.edu/~kfong/research/ECCpaper.ps
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