New Bit-Level Serial GF (2^m) Multiplication Using Polynomial Basis

Abstract

The Polynomial basis (PB) representation offers efficient hardware realizations of GF(2 ^m ) multipliers. Bit-level serial multiplication over GF(2 ^m ) trades-off the computational latency for lower silicon area, and hence, is favored in resource constrained applications. In such area critical applications, extra clock cycles might take place to read the inputs of the multiplication if the data-path has limited capacity. In this paper, we present a new bit-level serial PB multiplication scheme which generates its output bits in parallel after m clock cycles without requiring any preloading of the inputs, for the first time in the open literature. The proposed architecture, referred to as fully-serial-in-parallel-out (FSIPO), is useful for achieving higher throughput in resource constrained environments if the data-path for entering inputs has limited capacity, especially, for large dimensions of the field GF (2 ^m ).