Low Complexity Bit-Parallel Multiplier for GF(2^m) Defined by All-One Polynomials Using Redundant Representation

This paper presents a new bit-parallel multiplier for the finite field GF(2/sup m/) defined by an irreducible all-one polynomial. In order to reduce the complexity of the multiplier, we introduce a redundant representation and use the well-known multiplication method proposed by Karatsuba. The main idea is to combine the redundant representation and the Karatsuba method to design an efficient bit-parallel multiplier. As a result, the proposed multiplier requires about 25 percent fewer AND/XOR gates than the previously proposed multipliers using an all-one polynomial, while it has almost the same time delay as the previously proposed ones.