Digit-Serial Gaussian Normal Basis Multiplier over GF(2m) Using Toeplitz Matrix-Approach

This paper presents a novel algorithm for type-t Gaussian normal basis (GNB) binary finite field multiplication using Toeplitz matrix-vector representation. It is shown that the GNB multiplication can be realized through block Toeplitz matrix-vector-products. A digit-serial systolic GNB multiplier is proposed where each processing element is comprised of a Toeplitz multiplier and three registers. Analytical results indicate that our proposed architecture has significantly lower area complexity than existing digit-serial multipliers.