Presentation	2005-07-21 On Security of Superelliptic Curves and C_ Curves Based Cryptosystems against GHS Weil Descent Attack Tsutomu IIJIMA, Mahoro SHIMURA, Jinhui CHAO, Shigeo TSUJII,
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Abstract(in English)	The GHS Weil descent attack by Gaudry, Hess and Smart was originally proposed to elliptic curves over finite fields of characteristic two. In this paper, we consider GHS Weil descent attacks to algebraic curves whose function fields are Galois extensions of the rational function field. Lower bounds of genera of the function fields of their Weil restrictions are obtained when the function fields of the curves are tame Galois extensions. This class of curves can be divided into cyclic Galois extensions which contain superelliptic curves as a special case and non-cyclic Galois extensions which contain C_ curves. If we restrict ourselves to genus four or three cases, there are only two such C_ curves : C_<92>, C_<43>. Therefore, a detailed analysis on security against such attacks is shown for cryptosystems based on superelliptic curves and on C_<92>, C_<43>, Such analysis is based on the above theoretical results and computational complexity comparisons between Pollard's rho algorithm, Gaudry's variant of the ADH algorithm and Gaudry-Enge version of the ADH algorithm.
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Keyword(in English)	GHS Weil descent attack / superelliptic curves / C_ curves / function fields / Pollard's rho algorithm / Gaudry's algorithm / Adleman-DeMarrais-Huang algorithm
Paper #	ISEC2005-16,SITE2005-14
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Committee	SITE
Conference Date	2005/7/14(1days)
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Registration To	Social Implications of Technology and Information Ethics (SITE)
Language	ENG
Title (in Japanese)	(See Japanese page)
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Title (in English)	On Security of Superelliptic Curves and C_ Curves Based Cryptosystems against GHS Weil Descent Attack
Sub Title (in English)
Keyword(1)	GHS Weil descent attack
Keyword(2)	superelliptic curves
Keyword(3)	C_ curves
Keyword(4)	function fields
Keyword(5)	Pollard's rho algorithm
Keyword(6)	Gaudry's algorithm
Keyword(7)	Adleman-DeMarrais-Huang algorithm
1st Author's Name	Tsutomu IIJIMA
1st Author's Affiliation	Chuo University()
2nd Author's Name	Mahoro SHIMURA
2nd Author's Affiliation	Chuo University
3rd Author's Name	Jinhui CHAO
3rd Author's Affiliation	Chuo University
4th Author's Name	Shigeo TSUJII
4th Author's Affiliation	Institute of Information Security
Date	2005-07-21
Paper #	ISEC2005-16,SITE2005-14
Volume (vol)	vol.105
Number (no)	192
Page	pp.pp.-
#Pages	8
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