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

Hidehiro Kato; Yasuyuki Nogami; Tomoki Yoshida; Yoshitaka Morikawa

doi:10.4218/etrij.07.0107.0040

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

Hidehiro Kato, Yasuyuki Nogami, Tomoki Yoshida, Yoshitaka Morikawa

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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
DOIs	https://doi.org/10.4218/etrij.07.0107.0040
Publication status	Published - Dec 2007

Keywords

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

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Computer Science(all)
Electrical and Electronic Engineering

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10.4218/etrij.07.0107.0040

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abstract = "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.",

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AU - Kato, Hidehiro

AU - Nogami, Yasuyuki

AU - Yoshida, Tomoki

AU - Morikawa, Yoshitaka

PY - 2007/12

Y1 - 2007/12

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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

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

Abstract

Keywords

ASJC Scopus subject areas

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