Scalable and Systolic Montgomery Multipliers over GF(2m)

Abstract

This work presents a novel scalable and systolic Montgomery's algorithm in GF(2m). The proposed algorithm is based on the Toeplitz matrix-vector representation, which obtains the scalable and systolic Montgomery multiplier in a flexible manner, and can adapt to the required precision. Analytical results indicate that the proposed multiplier over the generic field of GF(2m) has a latency of d + n(2n + 1), where n = ⌈m/d⌉, and d denotes the selected digital size. The latency is reduced to d + n(n + 1) clock cycles when the field is constructed from generalized equally-spaced polynomials. Since the selected digital size is d ≥ 5 bits, the proposed architectures have lower time-space complexity than traditional digit-serial multipliers. Moreover, the proposed architectures have regularity, modularity and local interconnect ability, making them very suitable for VLSI implementation.