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People tend to equate asymmetric crypto with the likes of RSA; systems where the efficient factoring of large numbers is a death sentence. But there's a whole slew of other asymmetric cryptosystems without such properties, e.g. elliptic-curve cryptography.

Shors algorithm also breaks elliptic-curve cryptography.

Oh, wow, I've never seen the variant that breaks ECC; that's really quite awesome. Time to read some papers!

Nielsen, Michael A.; Chuang, Isaac L. Quantum Computation and Quantum Information. p. 202 is what you want ;)

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