Analysis of the Xedni calculus attack
type: Item
instance of: scholarly article
title: Analysis of the Xedni calculus attack
zbMATH Open document ID: 0948.11048
DOI: 10.1023/A:1008312401197
author: Neal Koblitz
author: Joseph H. Silverman
author: Edlyn Teske
author: Michael J. Jacobson jun.
author: Andreas Stein
published in: Designs, Codes and Cryptography
publication date: 2000-11-20T00:00:00Z
review text: Elliptic curves defined over finite fields provide secure cryptosystems that are currently included in several industrial products. A crucial question hence concerns the security of the elliptic curve discrete logarithm problem (ECDLP). The Xedni attack on ECDLP involves lifting points and the curve from the considered finite field to \({\mathbb Q}\). If the lifted points are linearly dependant, then the ECDLP is solved. This article describes in details the Xedni attack, and provides valuable background (Hasse-Weil \(L\)-function, Taniyama conjecture, conjecture of Birch and Swinnerton-Dyer, heights). It is shown that this attack is asymptotically unlikely succesful. Moreover, even for small base finite fields, this attack fails very often (how often is made precise in the article), so that the Xedni calculus is impractical for the fields used in elliptic curve cryptography.
Mathematics Subject Classification ID: 11Y16
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 1441591
zbMATH Keywords: elliptic curves
zbMATH Keywords: rank
zbMATH Keywords: Xedni calculus attack
zbMATH Keywords: discrete logarithm problem
reviewed by: Franck Leprévost
MaRDI profile type: Publication
Recommended article: Selected Areas in Cryptography
Recommended article: Information and Communications Security
Recommended article: On the Automatic Analysis of Recursive Security Protocols with XOR
Recommended article: Fault attacks on XEX mode with application to certain authenticated encryption modes
Recommended article: Analysis of Differential Attacks in ARX Constructions
Recommended article: Further Security Analysis of XTR
Recommended article: Differential Power Analysis of XMSS and SPHINCS
Recommended article: Improved Security Analysis of XEX and LRW Modes
Recommended article: Soft Analytical Side-Channel Attacks
description: scientific article; zbMATH DE number 1441591