Low complexity bit-parallel multiplier for F2n defined by repeated polynomials

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Abstract

Wu recently proposed three types of irreducible polynomials for low-complexity bit-parallel multipliers over F2n. In this paper, we consider new classes of irreducible polynomials for low-complexity bit-parallel multipliers over F2n, 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 n1000, then, in Wu’s result, only 11 finite fields exist for three types of irreducible polynomials when n1000. However, in our result, there are 181, 232(52.4%), and 443(100%) finite fields of class C1, C2 and C3, respectively.

Keywords

Finite field
Irreducible polynomial
Polynomial basis
Multiplication

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This research was supported by Next-Generation Information Computing Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. NRF-2014M3C4A7030649).