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arXiv · 1901.11485

Efficient and secure modular operations using the Adapted Modular Number System

Laurent-Stéphane Didier·Fanga-Yssouf Dosso·Pascal Véron
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Abstract

The Adapted Modular Number System (AMNS) is a sytem of representation of integers to speed up arithmetic operations modulo a prime p. Such a system can be defined by a tuple (p, n, γ, ρ, E) where E is in Z[X]. In [13] conditions are given to build AMNS with E(X) = {X^n +1}. In this paper, we generalize their results and show how to generate multiple AMNS for a given prime p with E(X)={X^n-λ} and λ in Z. Moreover, we propose a complete set of algorithms without conditional branching to perform arithmetic and conversion operations in the AMNS, using a Montgomery-like method described in [15].

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Laurent-Stéphane Didier, Fanga-Yssouf Dosso, Pascal Véron. 2019-01-31. Efficient and secure modular operations using the Adapted Modular Number System. https://arxiv.org/abs/1901.11485

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