A fast RNS Galois field multiplier

An approach to the design of a fast residue-number-system (RNS)-based multiplier over a Galois field GF(p), where p is a prime number, is presented. This design uses an isomorphic mapping from the additive index group, modulo (p-1,), of GF(p) onto a set of submodular additive groups. The submoduli are selected for minimizing the hardware and increasing the speed. This is accomplished by fully exploiting the properties of a Galois field. This multiplier is faster and uses less silicon area than previously published designs.<>