Presentation	2009-12-16 A Construction Method of Basis Conversion Matrix by Using Small Multiplicative Group for Cryptographic Applications Hidehiro KATO, Yasuyuki NOGAMI, Satoshi UEHARA, Yoshitaka MORIKAWA,
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Abstract(in English)	Several methods for finding a basis conversion matrix between two different bases in extension field F_ have been proposed. Among them, the one based on Gauss period normal basis (GNB-based method) is averagely the most efficient. However, since it needs to construct a certain tower field F_<(p^m)^n, some inefficient cases in which the towering degree becomes relatively large have been reported. It is caused from the condition of GNB. In order to overcome the inefficiency, this paper proposes a method that does not need any GNBs in the target extension field F_ but uses a certain polynomial basis in F_ derived by a certain small cyclic group in F_<(p^m)^n. Then, the condition for the towering degree is relaxed, some experimental results show that the proposed method substantially accelerates the average computation time for finding a basis conversion matrix.
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Keyword(in English)	extension field / Gauss period normal basis / basis conversion
Paper #	ISEC2009-77
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Committee	ISEC
Conference Date	2009/12/9(1days)
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Paper Information
Registration To	Information Security (ISEC)
Language	ENG
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	A Construction Method of Basis Conversion Matrix by Using Small Multiplicative Group for Cryptographic Applications
Sub Title (in English)
Keyword(1)	extension field
Keyword(2)	Gauss period normal basis
Keyword(3)	basis conversion
1st Author's Name	Hidehiro KATO
1st Author's Affiliation	Graduate school of Natural Science and Technology, Okayama University()
2nd Author's Name	Yasuyuki NOGAMI
2nd Author's Affiliation	Graduate school of Natural Science and Technology, Okayama University
3rd Author's Name	Satoshi UEHARA
3rd Author's Affiliation	Faulty of Environmental Engineering, The University of Kitakyushu
4th Author's Name	Yoshitaka MORIKAWA
4th Author's Affiliation	Graduate school of Natural Science and Technology, Okayama University
Date	2009-12-16
Paper #	ISEC2009-77
Volume (vol)	vol.109
Number (no)	337
Page	pp.pp.-
#Pages	8
Date of Issue