### Abstract

This paper proposes a multiplication algorithm for F_{pm}, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p-1). It uses a special class of type-(k, m) Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.

Original language | English |
---|---|

Pages (from-to) | 769-777 |

Number of pages | 9 |

Journal | ETRI Journal |

Volume | 29 |

Issue number | 6 |

Publication status | Published - Dec 2007 |

### Fingerprint

### Keywords

- Extension field
- Fast implementation
- Optimal extension field
- Optimal normal basis
- Public-key cryptosystem

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Networks and Communications

### Cite this

*ETRI Journal*,

*29*(6), 769-777.

**Cyclic vector multiplication algorithm based on a special class of gauss period normal basis.** / Kato, Hidehiro; Nogami, Yasuyuki; Yoshida, Tomoki; Morikawa, Yoshitaka.

Research output: Contribution to journal › Article

*ETRI Journal*, vol. 29, no. 6, pp. 769-777.

}

TY - JOUR

T1 - Cyclic vector multiplication algorithm based on a special class of gauss period normal basis

AU - Kato, Hidehiro

AU - Nogami, Yasuyuki

AU - Yoshida, Tomoki

AU - Morikawa, Yoshitaka

PY - 2007/12

Y1 - 2007/12

N2 - This paper proposes a multiplication algorithm for Fpm, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p-1). It uses a special class of type-(k, m) Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.

AB - This paper proposes a multiplication algorithm for Fpm, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p-1). It uses a special class of type-(k, m) Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.

KW - Extension field

KW - Fast implementation

KW - Optimal extension field

KW - Optimal normal basis

KW - Public-key cryptosystem

UR - http://www.scopus.com/inward/record.url?scp=37249027228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37249027228&partnerID=8YFLogxK

M3 - Article

VL - 29

SP - 769

EP - 777

JO - ETRI Journal

JF - ETRI Journal

SN - 1225-6463

IS - 6

ER -