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JoshuaZ comments on Cryptographic Boxes for Unfriendly AI - Less Wrong
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I think most people strongly suspect that there exist cryptographic schemes which can't be broken, because they are actually hard. RSA is probably such a scheme against classical adversaries (as our AI would be). Its true that they could break it without factoring numbers, but they can't break it without defeating the RSA assumption.
We know that there exist such schemes. One times pads are an example. What we don't know is whether there exist secure crypto schemes without a shared source of randomness.
Note however that the existence of such systems implies that P != NP, so this is a fairly strong statement. The existence of secure homomorphic encryption implies that P != NP. So whatever your confidence is that P != NP your confidence in this should be lower.
I think we've had this very discussion before :)
Well, we had it about P ?= NP. So how much does your confidence go down for the stronger claim?
Significantly. Its very hard to put probabilities on this sort of thing, but I'd take a bet if the odds were... 100:1? I don't know if I would take significantly worse odds. My brain doesn't handle either small probabilities or epistemic uncertainty very well.
Hmm, that's very interesting. I'm surprised that the estimates aren't closer together. My own estimate for the existence of provably secure homomorphic encryption given that P != NP is very high, around, .75. So it seems that you much more strongly believe that P !=NP but are much less comfortable given that P !=NP assigning a high probability to the existence of homomorphic encryption.
Best to be careful with the term "provably secure" - since "provable security" is a technical term with a rather counter-intuitive meaning.