Efficient Hybrid GF(2^m) Multiplier for All-one Polynomial Using Varied Karatsuba Algorithm

Abstract

The PCHS (Park-Chang-Hong-Seo) algorithm is a varied Karatsuba algorithm (KA) that utilizes a different splitting strategy with no overlap module. Such an algorithm has been applied to develop efficient hybrid GF(2^m) multipliers for irreducible trinomials and pentanomials. However, compared with KA-based hybrid multipliers, these multipliers usually match space complexity but require more gates delay. In this paper, we proposed a new design of hybrid multiplier using PCHS algorithm for irreducible all-one polynomial. The proposed scheme skillfully utilizes redundant representation to combine and simplify the subexpressions computation, which result in a significant speedup of the implementation. As a main contribution, the proposed multiplier has exactly the same space and time complexities compared with the KA-based scheme. It is the first time to show that different splitting strategy for KA also can develop the same efficient multiplier.