On 200704201113, Robert J. Hansen wrote: > > Yeah, again. I completely agree on the practical aspect of it, but > > would nevertheless like to see proofs of complexity that weren't > > dependent on the current models of computations. > > I don't mean to sound flip, but as soon as you invent a hypercomputer > I would love to revisit this issue with you.
I realise(d). See below. > For now, all our computational theoretic proofs will be limited by > the the lambda calculus. I don't mean to sound blunt there, but our > current model of computation is extraordinarily robust, and there are > very strong arguments that hypercomputation is both physically and > mathematically impossible. (If any problem in UNDECIDABLE can be > solved by an oracle, then math goes from incomplete and inconsistent > straight into pervasively self-contradictory and broken. That's the > rationale for hypercomputation being physically and mathematically > impossible.) A pretty good one, too. In any case, if I want a model-of-computation-unbound proof of difficulty, you'll simply invent a new model-of-computation that handles my problem efficiently. The point that you're telling me and I'm telling you is that such proofs can't exist and aren't feasible to pursue. > So yeah, I'm not sure why you want flawless perfect proofs of > security when reality shows that provably secure systems never are. ``never'' is in this case based on one case of provable secure scheme (that was notably difficult in implementation)? > > Though it sounds sweet, it's beyond the scope of cryptography to > > ensure such protection (to some extent, though, security should > > limit room for personnel ``breakage''). > > It's beyond the realm of mathematical cryptography, but not the field > as a whole. > > My day job involves security analysis of electronic voting machines > for the National Science Foundation [*]. We spend far, far more time > scrutinizing the human side of the cryptography than the mathematical > side. Probably an order of magnitude. I could easily imagine. Also, I assume that your systems limit room of human control. Regards, skrewz.
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