Bit-serial multipliers for exponentiation and division in GF(2(m)) using irreducible AOP

Abstract

Finite field GF(2(m)) is important to many practical application of modern communication. Exponentiation, division, and inversion are time-consuming operations that slow down the arithmetic over finite field GF(2(m)). They can be implemented by the iterative application of multiplication and squaring. However, it is efficient to use AB(2) operations rather than multiplication and squaring for computing exponentiation, division, and inversion. In ICCSA 2003 Lee et al. proposed a bit-serial AB(2) multiplier, which is more efficient than previous works. We propose new AB(2) multipliers using irreducible AOP (All One Polynomial) in this paper. Our multipliers require a smaller numbers of gates and have less latency than Lee et al.'s multiplier.