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Discrete Log over subgroups of finite fields of fixed characteristic (meaning $\mathbb{F}_{p^n}$ as $n\to\infty$) is known to be in quasi-polynomial time, see Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic by Thorsten Kleinjung and Benjamin Wesolowski. The hardness of (classical) DL-based cryptography is based on the ...


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