The least complex parallel Massey-Omura multiplier and its LCA and VLSI designs

It is known that for m>or=4 there is more than one irreducible polynomial which generates a GF(2^m) represented in normal basis. Therefore, a parallel Massey-Omura multiplier in GF(2^m) has more than one structure for m>or=4. The number of these structures is equal to the number of irreducible polynomials which can generate that specific Galois field in a normal-basis representation. In this paper, as an illustrative example, the structure of GF(2⁵) multipliers for different generator polynomials are compared. Based on this comparison, the least complex structure for this multiplier is introduced. The implementation of this structure using LCA (logic cell array) and VLSI (very large scale integration) technologies is given. Their complexities and propagation delays are compared.