Mastrovito Multiplier for All Trinomials

An efficient algorithm for the multiplication in GF (2) was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x +x+1 was given as m − 1 XOR and m 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 + x + 1, where m = 2n, also requires m − 1 XOR and m AND gates. However, m − m/2 XOR gates are sufficient when the generating trinomial is of the form x + x + 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 + x + 1 and x + x + 1.