Fast Bit-Parallel Polynomial Basis Multiplier for GF(2m) Defined by Pentanomials Using Weakly Dual Basis

In this paper, we derive a fast polynomial basis multiplier for GF(2(m)) defined by pentanomials x(m) + x(k3) + x(k2) + x(k1) + 1 with 1 <= k(1) < k(2) < k(3) <= m/2 using the presented method by Park and Chang. The proposed multiplier has the time delay T-A (2 + left perpendicularlog(2)(m - 1)right perpendicular)T-X or T-A + (3 + left perpendicularlog(2)(m - 1)right perpendicular)T-X which is the lowest one compared with known multipliers for pentanomials except for special types, where T-A and T-X denote the delays of one AND gate and one XOR gate, respectively. On the other hand, its space complexity is very slightly greater than the best known results.