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Journal Articles Journal of the American Mathematical Society Year : 2022

Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

Abstract

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log_2(n) + O(1)}$.
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Dates and versions

hal-03347994 , version 1 (17-09-2021)

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Thorsten Kleinjung, Benjamin Wesolowski. Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic. Journal of the American Mathematical Society, 2022, 35, pp.581-624. ⟨10.1090/jams/985⟩. ⟨hal-03347994⟩
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