A multiplication algorithm in Fpm such that p > m with a special class of Gauss period normal bases

Hidehiro Kato; Yasuyuki Nogami; Tomoki Yoshida; Yoshitaka Morikawa

doi:10.1587/transfun.E92.A.173

A multiplication algorithm in F_p^m such that p > m with a special class of Gauss period normal bases

Hidehiro Kato, Yasuyuki Nogami, Tomoki Yoshida, Yoshitaka Morikawa

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

6 Citations (Scopus)

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
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	https://doi.org/10.1587/transfun.E92.A.173
Publication status	Published - Jan 2009

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

Access to Document

10.1587/transfun.E92.A.173

Cite this

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