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NPC algorithms are roughly equivalent, so a P solution to one is a P solution to all. So, assuming the proof would be somewhat constructive, that would give you a P solution.

But, RSA (and probably other) cryptosystems aren't even thought to be NPC to solve... so they're probably unaffected. So, I guess it depends on the implementation details of the cryptosystem. Probably it wouldn't render them wide open, but it might make previously good keys far weaker, and mean that much longer must be spent on encryption for it to be safe (rather than now where a safe key can be decoded almost instantly on an embedded platform).




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