Method and apparatus for efficiently performing galois field multiplication

Abstract

A method and apparatus for performing Galois field multiplication with reduced redundancy. Generally, multiplication by a Galois field multiplier involves the multiplication of two polynomials modulo another polynomial. The Galois field multiplier has two Galois Field elements in a field of GF(2) that correspond to the binary polynomials A[X] and B[X]:,,where n corresponds to a number of terms in a Galois extension field of the Galois multiplier, and n-1 is an order of the polynomial A[X]. Premultiplier logic translates the binary polynomial A[X] into a binary vector c, where r is the number of terms of the vector. The premultiplier logic is configured to modulo-2 add together various coefficients of the athrough a, coefficients to produce various terms cthrough cof the cbinary vector. Binary multiplication and addition logic then operates on the cthrough ccoefficients and the bthrough bcoefficients to produce dthrough dcoefficients of a binary polynomial D[X]. The coefficients dthrough dare the output of the Galois field multiplier. Utilization of the premultiplier logic component reduces the amount of binary multiplication and addition logic needed to produce the coefficients dthrough dof the binary polynomial D[X].