Subquadratic Binary Field Multiplier in Double Polynomial System

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

1 LP2A - Laboratoire de Physique Appliquée et d'Automatique
2 Centre for Computer and Information Security Research

We propose a new space efficient operator to multiply elements lying in a binary field GF(2^k). Our approach is based on a novel system of representation called "Double Polynomial System" which set elements as a bivariate polynomials over GF(2). Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a space complexity of O(k^1.31) improving previous best known method.

Domains: Cryptography and Security [cs.CR]; Computer Arithmetic; Symbolic Computation [cs.SC]

Pascal Giorgi, Christophe Negre, Thomas Plantard. Subquadratic Binary Field Multiplier in Double Polynomial System. SECRYPT'2007: International Conference on Security and Cryptography,, Jul 2007, Barcelona, Spain. pp.229--236. ⟨hal-00140082⟩