Computational algorithm and architecture for AB2 multiplication in finite fields

Authors:
Jun-Cheol Jeon;Kee-Young Yoo
Affiliations:
Department of Computer Engineeing, Kyungpook National University, Daegu, Korea;Department of Computer Engineeing, Kyungpook National University, Daegu, Korea
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Year:
2003

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Abstract

In this paper, we present an effective algorithm and a simple hardware structure for the implementation of AB2 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 AB2 multiplication.