hal-00835446, version 2

## A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic

Razvan Barbulescu (, ) 1, Pierrick Gaudry () 1, Antoine Joux 23, Emmanuel Thomé (, ) 1

Eurocrypt 2014 8441 (2014) 1-16

Résumé : In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main result gives a quasi-polynomial heuristic complexity for the discrete logarithm problem in finite field of small characteristic. By quasi-polynomial, we mean a complexity of type $n^{O(\log n)}$ where $n$ is the bit-size of the cardinality of the finite field. Such a complexity is smaller than any $L(\varepsilon)$ for $\epsilon>0$. It remains super-polynomial in the size of the input, but offers a major asymptotic improvement compared to $L(1/4+o(1))$.

• hal-00835446, version 2
• oai:hal.inria.fr:hal-00835446
• Contributeur :
• Soumis le : Lundi 25 Novembre 2013, 21:36:59
• Dernière modification le : Vendredi 16 Mai 2014, 02:06:08