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.
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Keyword(in English) elliptic curve / discrete logarithm / Wieferich prime / rank
Paper # ISEC99-81
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Committee ISEC
Conference Date 2000/1/25(1days)
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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