Low Complexity Bit-Parallel Multipliers Based on a Class of Irreducible Pentanomials

In this paper, we consider the design of bit-parallel canonical basis multipliers over the finite fieldGF(2ᵐ)generated by a special type ofirreducible pentanomialthat is used as an irreducible polynomial in theAdvanced Encryption Standard(AES). Explicit formulas for the coordinates of the multiplier are given. The main advantage of our design is that some of the expressions obtained are common toanyirreducible polynomial, so our multiplier can be generalized to perform the multiplication overgeneral irreducible polynomials. Moreover, the obtained expressions can be easily converted to parameterizable code using hardware description languages. The theoretical complexity analysis also shows that our bit-parallel multipliers present a reduced number ofxorgates with respect to the best known results found in the literature.