Low-Complexity Parallel Systolic Montgomery Multipliers over GF (2^m) Using Toeplitz Matrix-Vector Representation

Abstract

In this paper, a generalized Montgomery multiplication algorithm in GF (2^m) using the Toeplitz matrix-vector representation is presented. The hardware architectures derived from this algorithm provide low-complexity bit-parallel systolic multipliers with trinomials and pentanomials. The results reveal that our proposed multipliers reduce the space complexity of approximately 15% compared with an existing systolic Montgomery multiplier for trinomials. Moreover, the proposed architectures have the features of regularity, modularity, and local interconnection. Accordingly, they are well suited to VLSI implementation.