Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation

Authors:
Christophe Negre;Thomas Plantard
Affiliations:
Team DALI, University of Perpignan, France;Centre for Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia
Venue:
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Year:
2008

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Abstract

In 2004, Bajard, Imbert and Plantard introduced a new system of representation to perform arithmetic modulo a prime integer p, the Adapted Modular Number System (AMNS). In this system, the elements are seen as polynomial of degree n驴 1 with the coefficients of size p1/n. The best method for multiplication in AMNS works only for some specific moduli p. In this paper, we propose a novel algorithm to perform the modular multiplication in the AMNS. This method works for any AMNS, and does not use a special form of the modulo p. We also present a version of this algorithm in Lagrange Representationwhich performs the polynomial multiplication part of the first algorithm efficiently using Fast Fourier Transform.