A novel approach for bit-serial AB2 multiplication in finite fields GF(2m)

This paper presents a new inner product AB² multiplication algorithm and effective hardware architecture for exponentiation in finite fields GF(2^m). Exponentiation is more efficiently implemented by applying AB² multiplication repeatedly rather than AB multiplication. Thus, efficient AB² multiplication algorithms and simple architectures are the key to implementing exponentiation. Accordingly, this paper proposes an efficient inner product multiplication algorithm based on an irreducible all one polynomial (AOP) and simple architecture, which has the same hardware equipment as Fenn's AB multiplier. The proposed bit-serial multiplication algorithm and architecture are highly regular and simpler than those of previous works.