GF(p/sup m/) multiplication using polynomial residue number systems
Michael Parker, Mohammed Benaissa · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · 1995
GF(p/sup m/) multiplication is computed in two stages. First, the polynomial product is computed modulus: a highly factorizable degree S polynomial, M(x), with S/spl ges/2/spl middot/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/sup m/) is defined. Suitable choices for S, M(x) and I(x) are discussed and an iterative method for the factorization of x/sup T/-k polynomials, k /spl epsiv/ GF(p), is presented. Finally, multidimensional PRNS is proposed to solve the upper limit constraint on m, which is dependent on p.>