[Resource Topic] 2005/402: Some Analysis of Radix-r Representations

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Some Analysis of Radix-r Representations

Authors: Dong-Guk Han, Tsuyoshi Takagi


We deal with the radix-r representation used for the scalar
multiplication of pairing-based cryptosystems with characteristic
r. Our goal of this paper is to present some invariant
properties about the signed radix-r representation; (1)
approximation formulae for the average significant length and the
average hamming weight of gNAF and wrNAF representation, (2)
some classification formulae of equivalent classes called as
Cutting Lemma, Collision Lemma, and Search Space Theorem. We also
analyze the security of signed radix-r representations in the
sense of side channel attacks, and to this end we propose a secure

ePrint: https://eprint.iacr.org/2005/402

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