An efficient technique for synthesis and optimization of polynomials in GF(2m)

Abstract

This paper presents an efficient technique for synthesis and optimization of polynomials over GF(2m), where mis a non-zero positive integer. The technique is based on a graph-based decomposition and factorization of polynomials over GF(2m), followed by efficient network factorization and optimization. A technique for efficiently computing coefficients over GF(pm), where p is a prime number, is first presented. The coefficients are stored as polynomial graphs over GF(pm). The synthesis and optimization is initiated from this graph based representation. The technique has been applied to minimize multipliers over all the 51 fields in GF(2k), k = 2... 8 in 0.18 micron CMOS technology with the help of the Synopsysreg design compiler. It has also been applied to minimize combinational exponentiation circuits, and other multivariate bit- as well as word-level polynomials. The experimental results suggest that the proposed technique can reduce area, delay, and power by significant amount