### Abstract

In this paper, a multiplication algorithm in extension field F _{p}^{m} is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p > m, 4p does not divide m(p - 1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.

Original language | English |
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Pages (from-to) | 173-181 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E92-A |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2009 |

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### Keywords

- Extension field
- Fast implementation
- Gauss period normal bases
- Optimal normal basis
- Public-key cryptography

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

_{p}

^{m}such that p > m with a special class of Gauss period normal bases.

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E92-A*(1), 173-181. https://doi.org/10.1587/transfun.E92.A.173