Polynomial Residue Number System GF(2m) multiplier using trinomials

This paper introduces a new approach for implementing GF(2 m ) multiplication using Polynomial Residue Number Systems (PRNS). Irreducible trinomials are selected as the generating polynomials for the PRNS channels to enable conversion to-and-from PRNS to be implemented using simple XOR networks. A novel approach for modular reduction over GF(2 m ) is also presented for the PRNS architecture to achieve better performance.