International Association
for Cryptologic Research

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.