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This paper presents a new bit-parallel multiplier for the finite field GF(2^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.
Index Terms- Bit-parallel multiplier, redundant representation, finite field arithmetic, AOP, Karatsuba method.
Ku-Young Chang, Dowon Hong, Hyun-Sook Cho, "Low Complexity Bit-Parallel Multiplier for GF(2^m) Defined by All-One Polynomials Using Redundant Representation", IEEE Transactions on Computers, vol. 54, no. , pp. 1628-1630, December 2005, doi:10.1109/TC.2005.199
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