Presentation | 2014-11-21 Elliptic Curves subjected to the GHS Attack over Prime Degree Extension Fields in Odd Characteristic Tsutomu IIJIMA, Jinhui CHAO, |
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Abstract(in Japanese) | (See Japanese page) |
Abstract(in English) | One of the most powerful attacks to elliptic curve and hyperelliptic based cryptosystems defined over an extension of a finite field is known as the GHS attack or cover attack. This attack maps the discrete logarithm problem (DLP) in the Jacobian of a curve C_0 defined over the d degree extension field k_d of k:=F_q to the DLP in the Jacobian of a covering curve C of C_0 over k. However, understanding including analysis of and defence against this attack has been a rather nontrivial task. Recently, a complete classification for elliptic curves C_0 over prime degree extension fields of odd characteristic which possess (2,...,2) covering C/k of P^1, or a complete list of all elliptic curves subjected to this attack was obtained in [26]. In this paper, we first explain implication and usage of this result of classification or the list. Next, based on this classification list, we discuss elliptic curves C_0/k_d subjected to the GHS attack and certain class of secure elliptic curves against the GHS attack. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | Elliptic/Hyperelliptic curves / Elliptic/Hyperelliptic curve cryptosystems / GHS attack / Coversing curve / Galois representation |
Paper # | ISEC2014-59,SITE2014-50,LOIS2014-29 |
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Committee | SITE |
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Conference Date | 2014/11/14(1days) |
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Registration To | Social Implications of Technology and Information Ethics (SITE) |
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Language | JPN |
Title (in Japanese) | (See Japanese page) |
Sub Title (in Japanese) | (See Japanese page) |
Title (in English) | Elliptic Curves subjected to the GHS Attack over Prime Degree Extension Fields in Odd Characteristic |
Sub Title (in English) | |
Keyword(1) | Elliptic/Hyperelliptic curves |
Keyword(2) | Elliptic/Hyperelliptic curve cryptosystems |
Keyword(3) | GHS attack |
Keyword(4) | Coversing curve |
Keyword(5) | Galois representation |
1st Author's Name | Tsutomu IIJIMA |
1st Author's Affiliation | Koden Electronics Co., Ltd() |
2nd Author's Name | Jinhui CHAO |
2nd Author's Affiliation | Chuo University |
Date | 2014-11-21 |
Paper # | ISEC2014-59,SITE2014-50,LOIS2014-29 |
Volume (vol) | vol.114 |
Number (no) | 320 |
Page | pp.pp.- |
#Pages | 8 |
Date of Issue |