Modified Sequential Multipliers for Type-k Gaussian Normal Bases

Finite fields are widely applied to ECC and cryptographic area, so many of researchers interested in efficient finite field arithmetic. In particular, it is efficient to use the normal basis in hardware implementation. Using the fact that the finite field GF(2^m) is the subfield of GF(2^mk) when GF(2^mk) has the type-I optimal normal basis, in this paper, we propose a new multiplier. Comparing the complexity of the proposed multiplier with Reyhani-Masoleh´s multiplier proposed in 2006 which is faster, and has smaller number of XOR gates than the existing multipliers, the number of XOR gates of the multiplier is equal to that of ours for k=4,6 and 10, the XOR critical path delay, however, is more than that of the proposed one by 20% for k=10.