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

Chiou-Yng LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.6   pp.1470-1477
Publication Date: 2008/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.6.1470
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Circuit Theory
bit-parallel systolic multiplier,  Toeplitz matrix-vector,  elliptic curve digital signature algorithm,  trinomial,  pentanomial,  

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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.