Low complexity bit-parallel multiplier for F-2n defined by repeated polynomials

Abstract

Wu recently proposed three types of irreducible polynomials for low-complexity bit-parallel multipliers over F-2n. In this paper, we consider new classes of irreducible polynomials for low-complexity bit-parallel multipliers over F-2n, namely, repeated polynomial (RP). The complexity of the proposed multipliers is lower than those based on irreducible pentanomials. A repeated polynomial can be classified by the complexity of bit-parallel multiplier based on RPs, namely, C1, C2 and C3. If we consider finite fields that have neither a ESP nor a trinomial as an irreducible polynomial when n <= 1000, then, in Wu's result, only 11 finite fields exist for three types of irreducible polynomials when n <= 1000. However, in our result, there are 181, 232(52.4%), and 443(100%) finite fields of class Cl, C2 and C3, respectively. (C) 2016 Elsevier B.V. All rights reserved.