Pipeline Design of Bit-Parallel Gaussian Normal Basis Multiplier over GF(2m)

The finite field multiplication over GF(2m) is the most important arithmetic operation for performing the elliptic curve cryptosystem which is very attractive in portable devices due to small key size. Design of finite field multiplier with low space complexity for elliptic curve cryptosystem is needed. The proposed bit-parallel GNB multiplier using pipeline XOR tree rather than XOR tree in traditional bit-parallel GNB multipliers. The proposed one can save about 99% number of both AND and XOR gates while comparing with existing bit-parallel GNB multipliers.