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sipa changed the topic of #bitcoin-wizards to: This channel is for discussing theoretical ideas with regard to cryptocurrencies, not about short-term Bitcoin development | http://bitcoin.ninja/ | This channel is logged. | For logs and more information, visit http://bitcoin.ninja

<gammastorm>
normally for encryption, you have a function computing an output from an input, where when you have the output only, you will never know the input

<gammastorm>
murch, but SAT solvers CAN compute the input from the outpu give the encryption algorithm as known

<gammastorm>
murch, but SAT solvers CAN compute the input from the output, given the encryption algorithm as known

<nsh>
we probably don't need to hear about it until you factor a 1024 bit modulus with your SAT solver, gammastorm :)

<murch>
gammastorm: I think you have a wrong understanding of the properties of the cryptographic function in use.

<murch>
A SAT solver is a program that checks whether a large number of predicates can be satisfied at the same time.

<murch>
I don't think I am well versed enough in elliptic curve cryptography to completely allay that but I'd expect that partial solutions don't give you any benefit whatsoever, so I'd be very surprised if you could use a SAT solver to extract the private key from a public key. – If I understand correctly that this is what you're trying to do.

<Chris_Stewart_5>
I don't know much about SAT solvers, but don't they essentially prove that a there exists a key k s.t. public key p was derived from k?

<nsh>
you can convert a[n ECC] discrete logarithm problem into conjunctive normal form and then solve it by constraint satisfaction

<nsh>
i would assume so, but i don't know how it would affect the complexity of the CNF representation

<nsh>
not much discussion of reductions of DLP to other problem varieties that i can find. would have expected more

<murch>
It does seem to depend on ciphers though, and I'm not versed enough to say whether it translates to extracting one key from the other or from a signature

<nsh>
also: http://courses.cs.washington.edu/courses/cse573/04au/Project/mini1/TheS&Ateam/SATeamFinalPaper.pdf

<murch>
I might be dense, but I don't get why phrasing the key relation as a set of predicate would reduce the workload to evaluate all the predicates.

<murch>
well, it's been shown that you can translate the 21 known NP hard problems into one another, so you'd probably be able to apply any of the algorithms to all the problems. I'm just not sure that it provides a significant complexity reduction in this case.

<nsh>
(there is a relation between integral points on elliptic curves and sphere packing, but it's unlikely to give such magical delights)

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