Computational Algorithm and Architecture for AB2 Multiplication in Finite Fields

Abstract

In this paper, we present an effective algorithm and a simple hardware structure for the implementation of AB 2 multiplication using irreducible all one polynomial (AOP) in finite field GF(2m). We argue with a problem that conventional algorithms using irreducible AOP are operated in extended basis, then we propose an effective algorithm and an architecture which are operated in the polynomial basis. The proposed algorithm is substantially considered relationships between operands based on inner-product computation. Based on the algorithm, we propose an architecture in which its results can be immediately used for other operations. Specially, the algorithm and architecture are useful conception for modular exponentiation since exponentiation is computed by repetition of AB 2 multiplication.KeywordsClock CycleFinite FieldSystolic ArrayPolynomial BasisHardware ComplexityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.