GF(2m) multiplier using Polynomial Residue Number System

This paper studies the polynomial residue representation of Galois field (2^m) elements and polynomial residue arithmetic (PRA), according to which a novel approach of performing GF(2^m) multiplication using polynomial residue number system (PRNS) is introduced. A channel-serial and a channel-parallel architecture of the PRNS multiplier over GF(2^m) are presented. Conclusion is drawn by comparing the synthesis results of these two architectures.