Mastrovito multiplier for all trinomials

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 m²-1 XOR and m² AND gales. 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+xⁿ+1, where m≠2n, also requires m²-1 XOR and m² AND gates, However, m²-x^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 x⁷+x⁴+1 and x⁶+x³+1