# A heuristic 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
2 Chaire de cryptologie
UPMC - Université Pierre et Marie Curie - Paris 6
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 $L(1/4+o(1))$.
Document type :
Conference papers
Phong Q. Nguyen and Elisabeth Oswald. Eurocrypt 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.1-16, 2014, Advances in Cryptology - EUROCRYPT 2014; Lecture Notes in Computer Science. <10.1007/978-3-642-55220-5_1>
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https://hal.inria.fr/hal-00835446
Contributor : Emmanuel Thomé <>
Submitted on : Monday, November 25, 2013 - 9:36:59 PM
Last modification on : Wednesday, December 16, 2015 - 1:09:51 AM
Document(s) archivé(s) le : Wednesday, February 26, 2014 - 8:35:09 AM

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### Citation

Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé. A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. Phong Q. Nguyen and Elisabeth Oswald. Eurocrypt 2014, May 2014, Copenhagen, Denmark. Springer, 8441, pp.1-16, 2014, Advances in Cryptology - EUROCRYPT 2014; Lecture Notes in Computer Science. <10.1007/978-3-642-55220-5_1>. <hal-00835446v2>

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