Abstract

An efficient algorithm for the multiplication in GF(2 m) was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x m +x+1 was given as m 2 − 1 XOR and m 2 AND gates. In this paper, we describe an architecture based on a new formulation of the multiplication matrix, and show that the Mastrovito multiplier for the generating trinomial x m + x n +1, where m � = 2n, also requires m 2 − 1 XOR and m 2 AND gates. However, m 2 − m/2 XOR gates are sufficient when the generating trinomial is of the form x m + x m/2 +1 for an even m. We also calculate the time complexity of the proposed Mastrovito multiplier, and give design examples for the irreducible trinomials x 7 + x 4 +1 and x 6 + x 3 +1.

Citations