Low complexity LFSR based bit-serial montgomery multiplier in GF(2m)

Montgomery multiplication in GF(2^m) is defined as ABr^-1 mod f(α), where f(x) is the irreducible polynomial defining the field and r is a fixed field element. In this paper, a low complexity Montgomery multiplier in GF(2^m) is proposed with r=α^m-1 or α^m. Linear feedback shift register (LFSR) is adopted as the main module for the presented architecture. It is shown that the proposed multiplier has lower space complexity than any of the existing similar works we found in the literature. The time complexity of the proposed multiplier is slightly higher than the best result among the existing works.