Efficient Cellular Automata Based Montgomery AB2 Multipliers over GF(2m)

This paper presents two efficient cellular automata based Montgomery AB(2) multipliers for exponentiation in finite fields GF(2(m)) using a polynomial representation. The proposed type I multiplier produces the results in m + 1 cycles with a critical path delay of two 2-input AND gates, two 2-input XOR gates, and one flip-flop using O(m(2)) area-time complexity. The proposed type II multiplier produces the results in m + 1 cycles with a critical path delay of one 2-input AND gate, two 2-input XOR gates, and one flip-flop using O(m(2)) area-time complexity. The proposed architectures are highly modular, and consist of regular blocks of AND and XOR logic gates. Exponentiation is more efficiently implemented by applying AB(2) multiplication repeatedly rather than AB multiplication. Compared with related works, the proposed multipliers have lower area-time complexity, and computational and include the features of regularity, modularity, and cascadability.