## 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 C1, C2 and C3, respectively.

Original language | English |
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Pages (from-to) | 2-12 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 241 |

DOIs | |

Publication status | Published - 2018 May 31 |

## Keywords

- Finite field
- Irreducible polynomial
- Multiplication
- Polynomial basis

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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