**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.

**Category / Keywords: **foundations / Elliptic Curves Discrete Logarithm Problem

**Date: **received 7 Oct 2013

**Contact author: **mmsadek at aucegypt edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20131024:074934 (All versions of this report)

**Short URL: **ia.cr/2013/660

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