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

Abstract

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 ≤ k₁ < k₂ < k₃ ≤ m/2 using the presented method by Park and Chang. The proposed multiplier has the time delay T_A+(2+⌈log₂(m-1)⌉)T_X or T_A+(3+⌈log₂(m-1)⌉)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.