[Resource Topic] 2019/751: Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

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

Authors: Thorsten Kleinjung, Benjamin Wesolowski

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)}.

ePrint: https://eprint.iacr.org/2019/751

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