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Article Dans Une Revue Journal of Cryptographic Engineering Année : 2020

Efficient modular operations using the adapted modular number system

Résumé

The Adapted Modular Number System (AMNS) is an integer number system which aims to speed up arithmetic operations modulo a prime p. Such a system is defined by a tuple (p, n, γ, ρ, E), where p, n, γ and ρ are integers and E ∈ Z[X]. In [12] conditions required to build AMNS with E(X) = X n + 1 are provided. In this paper, we generalise their approach and provide a method to generate multiple AMNS for a given prime p with E(X) = X n − λ and λ ∈ Z \ {0}. Moreover, we propose a complete set of algorithms without conditional branching to perform arithmetic and conversion operations in the AMNS, using a Mont-gomery-like method described in [26]. We show that our implementation outperforms GNU MP and OpenSSL libraries. Finally, we highlight some properties of the AMNS which state that it could lead to a helpful countermeasure against some side channel attacks.
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Dates et versions

hal-02486345 , version 1 (20-02-2020)

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Laurent-Stéphane Didier, Fangan-Yssouf Dosso, Pascal Véron. Efficient modular operations using the adapted modular number system. Journal of Cryptographic Engineering, 2020, ⟨10.1007/s13389-019-00221-7⟩. ⟨hal-02486345⟩

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