An Efficient CRT-based Bit-parallel Multiplier for Special Pentanomials

Abstract

The Chinese remainder theorem (CRT)-based multiplier is a new type of hybrid bit-parallel multiplier, which can achieve nearly the same time complexity compared with the fastest multiplier known to date with reduced space complexity. However, the current CRT-based multipliers are only applicable to trinomials. In this paper, we propose an efficient CRT-based bit-parallel multiplier for a special type of pentanomial $x^m+x^{m-k}+x^{m-2k}+x^{m-3k}+1, 5k<m\leq 7k$. Through transforming the non-constant part $x^m+x^{m-k}+x^{m-2k}+x^{m-3k}$ into a binomial, we can obtain relatively simpler quotient and remainder computations, which lead to faster implementation with reduced space complexity compared with classic quadratic multipliers. Moreover, for some $m$, our proposal can achieve the same time delay as the fastest multipliers for irreducible Type II and Type C.1 pentanomials of the same degree, but the space complexities are reduced