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.