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A heuristic quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic
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 $L(1/4+o(1))$.
Cited literature [19 references]
https://hal.inria.fr/hal-00835446
Contributor : Emmanuel Thomé Connect in order to contact the contributor
Submitted on : Monday, November 25, 2013 - 9:36:59 PM
Last modification on : Friday, January 21, 2022 - 4:13:21 AM
Long-term archiving on: : Wednesday, February 26, 2014 - 8:35:09 AM
Contributor : Emmanuel Thomé Connect in order to contact the contributor
Submitted on : Monday, November 25, 2013 - 9:36:59 PM
Last modification on : Friday, January 21, 2022 - 4:13:21 AM
Long-term archiving on: : Wednesday, February 26, 2014 - 8:35:09 AM
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