Scalable and systolic Montgomery multiplier over GF(2m) generated by trinomials

A Montgomery’s algorithm in GF(2) 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 them highly appropriate for VLSI implementation.