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

Razvan Barbulescu; Pierrick Gaudry; Antoine Joux; Emmanuel Thomé

doi:10.1007/978-3-642-55220-5_1

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

Razvan Barbulescu ¹ Pierrick Gaudry ¹ Antoine Joux ^{2, 3} Emmanuel Thomé ¹

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

3 CryptoExperts

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>

Domain :

Computer Science [cs] / Cryptography and Security [cs.CR]

Mathematics [math] / Number Theory [math.NT]

https://hal.inria.fr/hal-00835446
Contributor : Emmanuel Thomé <>
Submitted on : Monday, November 25, 2013 - 9:36:59 PM
Last modification on : Thursday, September 22, 2016 - 2:31:10 PM
Document(s) archivé(s) le : Wednesday, February 26, 2014 - 8:35:09 AM

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

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