Fast Bit-Parallel Polynomial Basis Multiplier for GF(2(m)) 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.
polynomial basis pentanomials weakly dual basis finite field arithmetic bit-parallel multiplier