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

06/25/2019

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by   Thorsten Kleinjung, et al.

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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_2(n) + O(1).