--- Log opened Wed Feb 13 00:00:48 2019
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12:46 < JackH> do we know what BIP is being enforced on the network at the moment?
12:46 < JackH> if its even a BIP
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12:49 < sipa> JackH: no
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13:17 < JackH> maybe its yet another BIP to enforce another BIP like last time :D
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13:23 < booyah> a general question, if it's ok here - why are EC point operations (add, mul) defined this way, why they have this results?
13:24 < sipa> "because it works" (tm)
13:24 < booyah> someone just told me that it has practical meaning such that A+B=C the point C represents angle equal to sum of angles of A and B. but why is that? is it that way for all additions on 2d fields?
13:24 < sipa> the only thing that matters is the group structure
13:25 < sipa> someone noticed that if you pick that particular definition for "addition" on an elliptic curve, the resulting set satsify the definitions of a group
13:25 < booyah> sipa: so it could be any rule as long as long as the defined operators obey some laws like A+B = B+A,  A*O = something and so on?
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13:26 < sipa> yes, A+B must be equal to B+A, (A+B)+C must be equal to A+(B+C), there is a 0 such that A+0 and 0+A == A, and every element A has an inverse -A such that A + (-A) = 0
13:26 < booyah> (though some particullary bad rules might result in for example lessen security etc)
13:26 < sipa> oh this has nothing to do with security
13:26 < sipa> security comes from the fact that people have tried and failed to solve the discrete logarithm problem for EC groups
13:27 < sipa> but ECDSA, Schnorr, ring signatures, bulletproofs, ... all just need a abelian prime-ordered group in which the DL problem is hard
13:27 < sipa> it doesn't matter what that group actually is
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13:28 < sipa> (and the fact that DL is hard in some groups is an assumption, not something we can derive)
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13:30 < sipa> with a slightly stronger assumption (namely that if you're given (P,aP,bP) you can't compute abP), you can do DH key negotiation
13:31 < booyah> are there any evidences for DL being hard, besides that no one yet had any idea for it?
13:31 < sipa> it's not just nobody has any idea
13:31 < nsh> the absence of a break
13:32 < sipa> there are plenty of ideas, and in some cases, breaks that apply to DL
13:32 < sipa> but we pick the security parameter (size of the group) high enough that none of these are feasible
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13:33 < sipa> booyah: note that the definition of EC multiplication is just repeated application of the group operation (which for EC is called point addition)
13:34 < sipa> but for example you can also use multiplication of integers modulo certain big primes as group operation; the equivalent of EC multiplication then becomes exponentiation modulo that prime
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13:35 < booyah> sipa: you mean, as in normal DSA/RSA ?
13:35 < sipa> yes, DSA
13:36 < sipa> RSA is based on a completely different assumption
13:36 < sipa> (not discrete logarithm based)
13:36 < sipa> so there is no equivalent of RSA applied to EC groups, for example
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13:41 < waxwing> booyah, part of the reason EC curves are the way they are is that's the only way you can get a group operation out of an algebraic curve - choose two points on a cubic and there is a unique third cut through the line defined on them (except when there isn't any at all).
13:42 < waxwing> so if groups are defined by operations on pairs of points resulting in a third point in the group (that's kinda the idea of a group), it wouldn't work e.g. with a second order equation.
13:43 < waxwing> also on that last point, i've always wondered whether at some deeper level, assumptions like the hardness of factoring/RSA aren't somehow related to discrete log in a prime order group like that, but it's at least above my paygrade, maybe some mathematicians have theories about that?
13:44 < waxwing> heh "EC curves" .. i did one of those.
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13:44 < sipa> error correction curves? :p
13:45 < sipa> waxwing: the fact that number field sieves are the best known algorithm for solving both factoring and integer DL feels like they're related on an abstract level
13:46 < waxwing> yes i suppose. maybe that's just another way of saying "it's really goddamn random, no joke" :)
13:46 < waxwing> RH?
13:47 < sipa> RH?
13:47 < waxwing> riemann hypothesis
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13:48 < sipa> well as far as groups go, it feels like EC groups are the most erratic ones
13:48 < sipa> (where erratic means lack of structure, i guess)
13:49 < sipa> as the best solving algorithm for DL on them does not use any EC properties, just generic group operations
13:49 < sipa> (apart from some constant factors)
13:49 < waxwing> right, no factorization i guess is the reason?
13:50 < waxwing> anyway not having some nonexistence result (of some cheaty- fast algo) seems a bit suboptimal.
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14:09  * nsh smiles
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--- Log closed Thu Feb 14 00:00:49 2019