International Association
for Cryptologic Research

For $q$ a prime power, the discrete logarithm problem (DLP) in $\\mathbb{F}_{q}^{\\times}$ consists in finding, for any $g \\in \\mathbb{F}_{q}^{\\times}$ and $h \\in \\langle g \\rangle$, an integer $x$ such that $g^x = h$. For each prime $p$ we exhibit infinitely many extension fields $\\mathbb{F}_{p^n}$ for which the DLP in $\\mathbb{F}_{p^n}^{\\times}$ can be solved in expected quasi-polynomial time.