Given $g^a$ in $Z_p$, it is hard to get the solution $a$. Everyone says yes, I wonder why it is hard. Could anyone give a specific mathematical way to show it is indeed hard?
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It's hard not because it's proven so, it's because all known algorithms that can be run on feasible computers (thus precluding quantum computers) are at least super-polynomial in time or space. – DannyNiu Mar 13 '20 at 05:19
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For information, the best known algorithm achieved to solve a 795-bit discrete logarithm last december. – Mar 13 '20 at 07:39
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It is depending on the group. Some have easy solutions some have not. and also Summarize the mathematical problem at the heart of breaking a Curve25519 public key – kelalaka Mar 13 '20 at 08:36