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Title:
A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic
Authors: Razvan Barbulescu, 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)).
ePrint: https://eprint.iacr.org/2013/400
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