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- W1758781646 abstract "The difficulty of computing discrete logarithms in fields (mathbb{F}_{q^k}) depends on the relative sizes of k and q. Until recently all the cases had a sub-exponential complexity of type L(1/3), similar to the factorization problem. In 2013, Joux designed a new algorithm with a complexity of L(1/4 + ε) in small characteristic. In the same spirit, we propose in this article another heuristic algorithm that provides a quasi-polynomial complexity when q is of size at most comparable with k. By quasi-polynomial, we mean a runtime of n O(logn) where n is the bit-size of the input. For larger values of q that stay below the limit (L_{q^k}(1/3)), our algorithm loses its quasi-polynomial nature, but still surpasses the Function Field Sieve. Complexity results in this article rely on heuristics which have been checked experimentally." @default.
- W1758781646 created "2016-06-24" @default.
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- W1758781646 date "2014-01-01" @default.
- W1758781646 modified "2023-10-09" @default.
- W1758781646 title "A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic" @default.
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- W1758781646 doi "https://doi.org/10.1007/978-3-642-55220-5_1" @default.
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