A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic - Archive ouverte HAL Access content directly
Conference Papers Year : 2014

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

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Razvan Barbulescu
• Function : Author
• PersonId : 899831
Pierrick Gaudry
Antoine Joux
Emmanuel Thomé

#### 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 $L(1/4+o(1))$.

### Dates and versions

hal-00835446 , version 1 (18-06-2013)
hal-00835446 , version 2 (25-11-2013)

### Identifiers

• HAL Id : hal-00835446 , version 2
• ARXIV :
• DOI :

### Cite

Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé. A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. Advances in Cryptology -- EUROCRYPT 2014, May 2014, Copenhagen, Denmark. pp.1-16, ⟨10.1007/978-3-642-55220-5_1⟩. ⟨hal-00835446v2⟩

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