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 $\Fp$, $p\ge5$, and $P_p,Q_p\in E_p(\Fp)$. The elliptic curve discrete logarithm problem, ECDLP, on $E_p$ is to find $m_p\in\mathbb{F}_p^{\times}$ such that $Q_p=m_p P_p$ if $Q_p\in\langle P_p\rangle$. 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}
}