--- Log opened Sun Dec 22 00:00:46 2019
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02:25 < sipa> waxwing: in https://joinmarket.me/blog/blog/avoiding-wagnerian-tragedies/ you mention using XOR as a way to combine the results of hash functions... if yiu actually use xor you can do much better than wagner's algorithm by treating the system as a set of linear equations over GF(2)
02:25 < sipa> so it's just a matrix inversion with O(n) hashes
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03:19 < gmaxwell> waxwing: aside, I don't get math formating in your blog posts unless I permit connecting to cloudflare. :(
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03:40 < waxwing> gmaxwell, oh. well that's not good, sorry.
03:45 < waxwing> sipa, sounds interesting, though i didn't entirely get it. got a link i could read?
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03:51 < sipa> waxwing: i think i learned this from the elliptic curve multiset hash paper
03:52 < sipa> https://arxiv.org/pdf/1601.06502.pdf
03:53 < sipa> waxwing: basically if you want to solve the generalized birthday problem, and the operation you use to combime hashes is bitwise xor
03:53 < sipa> you can just generate a random 256 bit hashes
03:53 < sipa> make them the rows of a GF(2) 256*256 matrix
03:54 < waxwing> "MuHash" .. get your lawyers on them :)
03:54 < sipa> invert that matrix, and multiply it with your desired hash sum vector
03:54 < sipa> this gives you a bit vector that identifes the subset of hashes to combine
03:55 < sipa> you can use wagner's algorithm too of course, but in this case there is a much more efficient algorithm for solving the problem
03:55 < waxwing> this paper is interesting, i like these points about homomorphic hashes
03:56 < waxwing> so thanks. i'll have a read and ask you if i still don't get it (though it sounds intuitively like it makes sense).
03:57 < sipa> so wagner's algorithm is really only optimal when your hash combination function defines a group that doesn't split into many tiny subgroups
03:57 < sipa> which is the case when you're working over GF(p)
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04:01 < sipa> waxwing: there is a lot of interesting stuff in that paper
04:02 < sipa> i hope i'm not misremembering that it's there that i read about xhash (xor of set hashes) being so trivial to break
04:04 < waxwing> it doesn't kind of violate the thread of my blog post, i was mainly trying to reach an understanding of the inapplicability of this attack to discrete-log-hard groups, it seemed like a really interesting thing to investigate.
04:04 < waxwing> that there's a substantially better way to do it in certain cases is definitely interesting though.
04:05 < sipa> yeah, agree - it's not wrong, just not a perfect example
04:05 < gmaxwell> it's a reason though perhaps to just avoid using xor as your leading example. :P
04:05 < gmaxwell> if you were to do a revision
04:06 < waxwing> gmaxwell, sure. but i was literally following the paper.
04:07 < sipa> random vaguely related fact: did you know that the probability that a GF(2) n*n matrix is invertible comverges rapidly to a constant 0.288788... as n grows?
04:07 < waxwing> thanks for the comments though, it's great to get some input on it.
04:08 < gmaxwell> sipa: I seem to recall discussing with you the more general case of other fields before.
04:10 < gmaxwell> prod(1-0.5^n,1,inf) might be more informative than the constant. :P
04:10 < waxwing> lol yeah i just found the proof. it's irritatingly simple.
04:10 < waxwing> found as in found on web, not worked it out :)
04:11 < sipa> yeah
04:12 < sipa> but this means that to solve generalized birthday for xhash you literally just need 3.5 ish iterations, independently of how large the hash is
04:12 < gmaxwell> it's not as simple to figure out how many additional you need to draw before you can find a subset thats invertable.
04:12 < sipa> yeah, just replace all of them
04:12 < gmaxwell> lame upper bound. :P
04:13 < sipa> you can do it row by row
04:13 < gmaxwell> usually you'll only fail by a single linear dependance, and can fix just that one.
04:13 < sipa> every new hash you add has to be linearly independent of the ones you have before
04:13 < sipa> if it isn't, replace just the last one
04:14 < sipa> and then continue
04:20 < gmaxwell> the same inversion trick should work for arbritary fields so long as you can include an entry an arbritary (potentially very large) number of times.
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04:46 < sipa> gmaxwell: invertibility for matrices over fields larger than gf(2) is harder as you need to account for linear combinations over all vectors
04:54 < gmaxwell> Yes, but they are invertable even more often than GF(2).
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04:59 < sipa> oh, it's still simple: https://math.stackexchange.com/a/2788900/614483
04:59 < gmaxwell> kanzure: https://diyhpl.us/wiki/transcripts/sf-bitcoin-meetup/2019-12-16-bip-taproot-bip-tapscript/ "You can add or remove it, as long as your transaction has signatures." should be can't.
04:59 < gmaxwell> (there were one or two other backwards things earlier but I didn't think they were worth mentioning)
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05:11 < sipa> ^ indeed
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05:19 < gmaxwell> sipa: your comments made me think you don't think the weight-modifying annex will ever be done?
05:24 < gmaxwell> one of the other edits was "Other witness versions remain encumbered,"  should be unencumbered.
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06:05 < sipa> gmaxwell: i don't know if we'll ever have a need for it
06:05 < sipa> as it depends on having some opcode with a high expected cpu cost to witness size
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09:04 < kanzure> fixed those errors
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--- Log opened Sun Dec 22 09:34:29 2019
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--- Log opened Sun Dec 22 09:44:03 2019
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--- Log closed Mon Dec 23 00:00:46 2019