1. A method, comprising generating a binary representation of a first polynomial over a GF(2) field, in an arithmetic circuit of a processor, generating a plurality of right shifted binary representations of the first polynomial, in the arithmetic circuit, generating a binary representation of a reciprocal of the first polynomial based upon a bitwise exclusive-OR of the binary representation of the first polynomial and one or more right shifted binary representations selected from the plurality of right shifted binary representations, in the arithmetic circuit, and storing the binary representation of the first polynomial reciprocal to a storage location.