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

In this paper, a generalized Montgomery multiplication algorithm in GF(2m) 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. key words: bit-parallel systolic multiplier, Toeplitz matrix-vector, elliptic curve digital signature algorithm, trinomial, pentanomial