The lifting problem for the ECDLP and the Selmer rank
type: Item
instance of: scholarly article
zbMATH Open document ID: 1275.11099
author: Masaya Yasuda
publication date: 2012-03-28T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 6018733
zbMATH Keywords: elliptic curve discrete logarithm problem
zbMATH Keywords: ECDLP
MaRDI profile type: Publication
title: The lifting problem for the ECDLP and the Selmer rank
published in: International Journal of Pure and Applied Mathematics
review text: Let \(K=\mathbb{F}_p\) be a finite prime field, \(E/K\) an elliptic curve, \(S\) and \(T\) points on \(E(K)\). The discrete logarithm problem is the problem to determine a \(d\) such that \(T=dS\), provided such a \(d\) exists. This problem can be solved efficiently if there is an elliptic curve \(\tilde{E}\) over \(\mathbb{Q}\) such that \(\tilde{E}(\mathbb{Q})\) has rank one and \(T\) and \(S\) are reductions modulo \(p\) of points on \(\tilde{E}(\mathbb{Q})\). This is the so-called rank one attack. However, constructing such a curve \(\tilde{E}\) is non-trivial. The authors argue that the current strategies to construct an \(\tilde{E}\) of rank one for given \((E,S,T)\) are not sufficiently good for the rank one attack to be efficient.
reviewed by: Remke Kloosterman
description: scientific article; zbMATH DE number 6018733