Paper 2013/660 Original: eprint.iacr.org/2013/660 ↗
Discrete Logarithms and Mordell-Weil Groups
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.
- History
- 2013-10-24: last updated
- 2013-10-24: published
- Short URL
- https://ia.cr/2013/660
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}