--- Log opened Thu Jan 13 00:00:17 2022
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15:13 < jeremyrubin> sipa: yep i should have been more explicit about the negligible function. unless you meant something else?
15:14 < sipa> really the point i want to make is that there is a huge difference between (close to) uniform distribution, and distribution computationally indistinguishable from random
15:15 < sipa> e.g. the distribution you get from SHA256(32 uniform bytes) is very much nonuniform.
15:15 < sipa> Some outputs can't be reached at all!
15:17 < sipa> But without an oracle that can invert SHA256, or one that can tell you the number of preimages under SHA256(32 bytes), it's computationally infeasible to distinguish SHA256(32 uniform bytes) from (32 uniform bytes).
15:19 < sipa> So I disagree with your statement that secure encryption (assuming you mean semantic security) implies the distribution of ciphertext must be close to uniform.
15:21 < jeremyrubin> maybe there's something I'm missing, but my recollection was that semantic security can be equivalently stated as ciphertext indistinguishability?
15:23 < jeremyrubin> and I thought it was the case that it's an equivalence, not A ==> B and B =/=> A
15:24 < jeremyrubin> but maybe CI does not imply uniformity (up to negl)?
15:43 < sipa> that's exactly my point
15:43 < sipa> indistinguishabilty is a computational property
15:44 < sipa> uniformity is an informational theoretical one
15:47 < sipa> things do not need to be uniform in order to be indistinguishable
15:47 < sipa> (and not even close to it)
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--- Log closed Fri Jan 14 00:00:29 2022