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

Razvan Barbulescu 1 Pierrick Gaudry 1 Antoine Joux 2 Emmanuel Thomé 1
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 $L(1/4+o(1))$.
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https://hal.inria.fr/hal-00835446
Contributor : Emmanuel Thomé <>
Submitted on : Tuesday, June 18, 2013 - 4:28:43 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:25 PM
Long-term archiving on : Thursday, September 19, 2013 - 4:13:24 AM

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

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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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