GF(P(M)) MULTIPLICATION USING POLYNOMIAL RESIDUE NUMBER-SYSTEMS

GF(p(m)) multiplication is computed in two stages. First, the polynomi al product is computed modulus: a highly factorizable degree S polynom ial, M(x), with S greater than or equal to 2 . m - 1. This enables the product to be computed using a polynomial residue number system (PRNS ). Second, the result is reduced by the irreducible polynomial, I(x), over which GF(p(m)) is defined. Suitable choices for S. M(x) and I(x) are discussed and an iterative method for the factorization of x(T) - k polynomials, k is an element of GF(p), is presented. Finally, multid imensional PRNS is proposed to solve the upper limit constraint on m, which is dependent on p.