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which makes our bruteforcing polynomial rather than exponential

I think that's wrong. Grover's algorithm let's us speed up any algorithm, but not exponentially. You just take the sqrt of the run time.

https://en.wikipedia.org/wiki/Grovers_algorithm

Shor's algorithm lets us factor numbers in polynomial time. This would break RSA, but not every algorithm in general. I think, but I'm not 100% sure, that elliptic curve methods have no known polynomial time quantum algorithms, for example.

https://en.wikipedia.org/wiki/Shors_algorithm




A version of Shor's algorithm applies to elliptic curve crypto:

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.38...




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