### 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 . 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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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | Accepted/In press - 2015 Aug 28 |

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### Keywords

- Finite field
- Irreducible polynomial
- Multiplication
- Polynomial basis

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*. https://doi.org/10.1016/j.dam.2016.07.014