Discrete Logarithms and Mordell-Weil Groups

Mohammad Sadek

Paper 2013/660

Discrete Logarithms and Mordell-Weil Groups

Mohammad Sadek

Abstract

Let $E_{p}$ be an elliptic curve over a prime finite field $\Fp$ , $p \geq 5$ , and $P_{p}, Q_{p} \in E_{p} (\Fp)$ . The elliptic curve discrete logarithm problem, ECDLP, on $E_{p}$ is to find $m_{p} \in F_{p}^{\times}$ such that $Q_{p} = m_{p} P_{p}$ if $Q_{p} \in ⟨ P_{p} ⟩$ . We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear dependence in Mordell-Weil groups of elliptic curves via a finite number of reductions.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Elliptic Curves Discrete Logarithm Problem
Contact author(s): mmsadek @ aucegypt edu
History: 2013-10-24: received
Short URL: https://ia.cr/2013/660
License: CC BY

BibTeX

@misc{cryptoeprint:2013/660,
      author = {Mohammad Sadek},
      title = {Discrete Logarithms and Mordell-Weil Groups},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/660},
      year = {2013},
      url = {https://eprint.iacr.org/2013/660}
}