Low complexity bit-parallel multiplier for F_2ⁿ defined by repeated polynomials

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 C1, C2 and C3, respectively.