| 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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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2014/11/14(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Information Security (ISEC) |
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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) | 319 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |