Unified Digit Serial Systolic Montgomery Multiplication Architecture for Special Classes of Polynomials over GF(2m)

Abstract

This paper presents an unified digit-serial systolic multiplication architecture for all-one polynomials (AOP) and trinomial over GF (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) for efficient implementation of Montgomery Multiplication (MM) algorithm suitable for cryptosystem. This is the first reported unified digit serial systolic digit level pipelined MM architecture for AOP and trinomials over GF (2). Analysis shows that the latency and circuit complexity of the proposed architecture are significantly less compared to earlier design for same class of polynomials. The proposed multiplier has clock cycle latency of (2N) where N=⌈m/L⌉, m is the word size and L is the digit size.