Parallel Multiplication in F2n Using Condensed Matrix Representation

Abstract: In this paper we explore a matrix representation of binary fields F2n defined by an irreducible trinomial P = X + X + 1. We obtain a multiplier with time complexity of TA + (⌈log2(n)⌉)TX and space complexity of (2n − 1)n AND and (2n − 1)(n − 1) XOR . This multiplier reaches the lower bound on time complexity. Until now this was possible only for binary field defined by AOP (Silverman, 1999), which are quite few. The interest of this multiplier remains theoretical since the size of the architecture is roughly two times bigger than usual polynomial basis multiplier (Mastrovito, 1991; Koc and Sunar, 1999).