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A Montgomery's algorithm in GF(2m) based on the Hankel matrix-vector representation is proposed. The hardware architecture obtained from this algorithm indicates low-complexity bit-parallel systolic multipliers with irreducible trinomials. The results reveal that the proposed multiplier saves approximately 36% of space complexity as compared to an existing systolic Montgomery multiplier for trinomials. A scalable and systolic Montgomery multiplier is also developed by applying the block-Hankel matrix-vector representation. The proposed scalable systolic architecture is demonstrated to have significantly less time-area product complexity than existing digit-serial systolic architectures. Furthermore, the proposed architectures have regularity, modularity and local interconnectability, making the.m highly appropriate for VLSI implementation.