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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.


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.


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


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