Presentation | 2000/1/25 Elliptic Curve Discrete Logarithms and Wieferich Primes Jung Hee Cheon, Dong Hoon Lee, Sang Geun Hahn, Seongtaek Chee, |
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Abstract(in English) | Recently, a new method, called by Xedni calculus, to solve ECDLP was proposed by Silverman and Kim et.al. [11, 5]. The Xedni addresses a novel idea, but has two difficulties. One is to find good liftings and the other is to compute the dependence relation among lifted rational points. In this paper, we propose a fast algorithm to compute the dependence relation modulo the order, n_ , of P^^~ for given two dependent rational points of elliptic curve ober Q. Using this, if we could find liftings P, Q and E with rank 1 of P^^~, Q^^~, E^^~, then we can solve the ECDLP very fast. Moreover, by this algorithm, we can easily check whether two lifted points are linearly independent or not. Also we investigate the possibility to get such liftings for elliptic curves with a non-trivial 2-torsion, and generate lots of liftings of rank ≤ 2. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | elliptic curve / discrete logarithm / Wieferich prime / rank |
Paper # | ISEC99-81 |
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Committee | ISEC |
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Conference Date | 2000/1/25(1days) |
Place (in Japanese) | (See Japanese page) |
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Registration To | Information Security (ISEC) |
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Language | ENG |
Title (in Japanese) | (See Japanese page) |
Sub Title (in Japanese) | (See Japanese page) |
Title (in English) | Elliptic Curve Discrete Logarithms and Wieferich Primes |
Sub Title (in English) | |
Keyword(1) | elliptic curve |
Keyword(2) | discrete logarithm |
Keyword(3) | Wieferich prime |
Keyword(4) | rank |
1st Author's Name | Jung Hee Cheon |
1st Author's Affiliation | Electronics and Telecommunications Research Institute(ETRI)() |
2nd Author's Name | Dong Hoon Lee |
2nd Author's Affiliation | Electronics and Telecommunications Research Institute(ETRI) |
3rd Author's Name | Sang Geun Hahn |
3rd Author's Affiliation | Electronics and Telecommunications Research Institute(ETRI) |
4th Author's Name | Seongtaek Chee |
4th Author's Affiliation | Electronics and Telecommunications Research Institute(ETRI) |
Date | 2000/1/25 |
Paper # | ISEC99-81 |
Volume (vol) | vol.99 |
Number (no) | 584 |
Page | pp.pp.- |
#Pages | 8 |
Date of Issue |