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

1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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 $L(1/4+o(1))$.
Type de document :
Pré-publication, Document de travail
2013
Domaine :

https://hal.inria.fr/hal-00835446
Contributeur : Emmanuel Thomé <>
Soumis le : mardi 18 juin 2013 - 16:28:43
Dernière modification le : vendredi 6 février 2015 - 13:31:41
Document(s) archivé(s) le : jeudi 19 septembre 2013 - 04:13:24

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quasi.pdf
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### Identifiants

• HAL Id : hal-00835446, version 1
• ARXIV : 1306.4244

### Citation

Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé. A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. 2013. <hal-00835446v1>

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