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Springer, Lecture Notes in Computer Science, p. 353-364, 2001

DOI: 10.1007/3-540-44586-2_26

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Compact Encoding of Non-Adjacent Forms with Applications to Elliptic Curve Cryptography

Journal article published in 2001 by Marc Joye, Christophe Tymen
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Techniques for fast exponentiation (multiplication) in vari- ous groups have been extensively studied for use in cryptographic prim- itives. Specically , the coding of the exponent (multiplier) plays an im- portant role in the performances of the algorithms used. The crucial optimization relies in general on minimizing the Hamming weight of the exponent (multiplier). This can be performed optimally with non- adjacent representations. This paper introduces a compact encoding of non-adjacent representations that allows to skip the exponent recoding step. Furthermore, a straightforward technique for picking random num- bers that already satisfy the non-adjacence property is proposed. Several examples of application are given, in particular in the context of scalar multiplication on elliptic curves.