Prime Field Multiplication in Adapated Modular Number System using Lagrange Representation

Christophe Negre (1, 2) , Thomas Plantard (2)

1 LP2A - Laboratoire de Physique Appliquée et d'Automatique
2 DALI - Digits, Architectures et Logiciels Informatiques

In SAC'04 Bajard~\textit{et al.} introduced a new system of representation for integer arithmetic modulo a prime integer $P$, the Adapted Modular Number System. The multiplication in the AMNS consists of a multiplication of two polynomials and a AMNS-Carrying process. In this paper, we propose to use a \emph{Lagrange Representation} to perform the polynomial multiplication in the AMNS system. This method provides a multiplier which decreases by 2 the complexity of previous best known methods.

Mots clés: Prime; integer modular multiplication; ECC

Domaines: Cryptographie et sécurité [cs.CR]

Christophe Negre, Thomas Plantard. Prime Field Multiplication in Adapated Modular Number System using Lagrange Representation. 2007. ⟨hal-00079454v4⟩