Elliptic curve lifting problem and its applications
type: Item
instance of: scholarly article
title: Elliptic curve lifting problem and its applications
zbMATH Open document ID: 0948.11050
author: Hwan Joon Kim
author: Jung Hee Cheon
author: Sang Geun Hahn
published in: Proceedings of the Japan Academy. Series A
publication date: 2000-11-20T00:00:00Z
review text: This paper considers a possible way of solving the elliptic curve discrete logarithm problem, a problem upon which a number of cryptographic systems are based. The basic idea of the paper is to lift an elliptic curve over a finite field, together with some points on it, to the rationals. Then, by finding a linear combination between the lifted points, assuming the lifted points are independent in the Mordell-Weil group, one can hopefully solve the original discrete logarithm problem. This idea was independently discovered by \textit{J. H. Silverman} [Des. Codes Cryptography 20, 5-40 (2000; Zbl 0948.11051)]. Silverman's paper contains a number of refinements on the method of the current paper. However in a later paper \textit{M. J. Jacobson} et. al., Des. Codes Cryptography 20, 41-64 (2000; Zbl 0948.11049)] the method is shown not to be a threat to elliptic curve cryptosystems. However, the method (dubbed the Xedni calculus by Silverman) does contain some interesting mathematical ideas.
Mathematics Subject Classification ID: 11Y16
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 1443391
zbMATH Keywords: elliptic curves
zbMATH Keywords: discrete logarithm
zbMATH Keywords: cryptography
MaRDI profile type: Publication
full work available at URL: pjaa.75.166
OpenAlex ID: W2029114583
cites work: Reducing elliptic curve logarithms to logarithms in a finite field
cites work: Q4217446
cites work: Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝
cites work: The discrete logarithm problem on elliptic curves of trace one
cites work: Computing canonical heights with little (or no) factorization
cites work: The Xedni calculus and the elliptic curve discrete logarithm problem
cites work: Analysis of the Xedni calculus attack
cites work: Q4249259
cites work: Q4317891
cites work: Q4023805
DOI: 10.3792/PJAA.75.166
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description: scientific article; zbMATH DE number 1443391