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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
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votes
Is there any theory why (for Bitcoin) the discrete logarithm problem is so hard to solve?
Yes. I'll talk about why elliptic curve discrete log is harder than ordinary discrete log.
Suppose we have $g, h$ and want to find $n$ such that $g^n = h$.
The usual methods for solving the discrete …