| Presentation | 2015-03-02 Analysis on isomorphism classes of elliptic curves subjected to GHS attack over prime degree extensions of finite fields with odd characteristic Takayuki HOSOGAYA, Tsutomu IIJIMA, Mahoro SHIMURA, Jinhui CHAO, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The GHS attack is known to map the discrete logarithm problem (DLP) in the Jacobian of a curve C_0 defined over the d degree extension k_d of a finite field k to the DLP in the Jacobian of a new curve C over k which is a covering curve of C_0. Recently, classification of all elliptic curves possessing (2,...,2) covering C therefore subjected to the GHS attack is obtained in [27]. However, a such curve C_0 could be mapped by an k_d-isomorphism to another curve which also possesses a covering curve but with a different genus. In this paper, we present a detailed analysis on k_d-isomorphic classes of these curves. In particular, we show orbit-decomposition of them under action of PGL(2, k_d) in case of d = 2. Security against GHS attack of a curve C_0 is evaluated according to all possible genera g(C) among the curves belong to the PGL-orbit |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Elliptic Curve Cryptography / GHS attack |
| Paper # | IT2014-76,ISEC2014-89,WBS2014-68 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2015/2/23(1days) |
| Place (in Japanese) | (See Japanese page) |
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| 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) | Analysis on isomorphism classes of elliptic curves subjected to GHS attack over prime degree extensions of finite fields with odd characteristic |
| Sub Title (in English) | |
| Keyword(1) | Elliptic Curve Cryptography |
| Keyword(2) | GHS attack |
| 1st Author's Name | Takayuki HOSOGAYA |
| 1st Author's Affiliation | Information and System Engineering Course, Graduate School of Science and Engineering Chuo University() |
| 2nd Author's Name | Tsutomu IIJIMA |
| 2nd Author's Affiliation | Koden Electronics Co., Ltd |
| 3rd Author's Name | Mahoro SHIMURA |
| 3rd Author's Affiliation | Department of Mathematical Sciences Tokai University |
| 4th Author's Name | Jinhui CHAO |
| 4th Author's Affiliation | Department of Information and System Engineering, Faculty of Science and Engineering Chuo University |
| Date | 2015-03-02 |
| Paper # | IT2014-76,ISEC2014-89,WBS2014-68 |
| Volume (vol) | vol.114 |
| Number (no) | 471 |
| Page | pp.pp.- |
| #Pages | 7 |
| Date of Issue | |