Efficient Square-based Montgomery Multiplier for All Type C.1 Pentanomials

In this paper, we present a low complexity bit-parallel Montgomery multiplier for GF(2m) generated with a special class of irreducible pentanomials xm + xm−1 + xk + x + 1. Based on a combination of generalized polynomial basis (GPB) squarer and a newly proposed square-based divide and conquer approach, we can partition field multiplications into a composition of sub-polynomial multiplications and Montgomery/GPB squarings, which have simpler architecture and thus can be implemented efficiently. Consequently, the proposed multiplier roughly saves 1/4 logic gates compared with the fastest multipliers, while the time complexity matches previous multipliers using divide and conquer algorithms.