--- Log opened Fri Mar 17 00:00:00 2017
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00:12 < waxwing> sipa: seems to have stopped updating? http://bitcoin.sipa.be/ver9-2k.png
00:12 < sipa> oops, yes indeed
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01:16 < stevenroose> yeah I noticed that too, was refreshing it with the BU exploit
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09:28 < fluffypony> waxwing: yeah Koinster's paper generator
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13:38 < kanzure> https://www.reddit.com/r/Bitcoin/comments/5zz127/unfortunately_no_one_can_be_told_what_the_matrix/
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14:18 < kanzure> .title https://lists.launchpad.net/mimblewimble/msg00082.html
14:18 < yoleaux> A ransomware attack on MimbleWimble with Schnorr signatures : Mailing list archive : mimblewimble team in Launchpad
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14:25 < sipa> kanzure: apoelstra tells me it's wrong, but he can't respond right now :)
14:26 < tromp_> sipa: I hope it's wrong, since I like Schnorr signatures:)
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14:33  * gmaxwell guesses without looking: using malleability of outputs to change a valid payment to X into a payment to X+P?
14:34 < gmaxwell> I believe this is blocked by the inability of the malliator to provide a new signature with the nonce value, which binds the set.
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14:36 < andytoshi-web> basically ya, blocked because our ringsigs commit to the the pedersen commits
14:37 < andytoshi-web> like our schorr sigs commit to the keys. to prevent exactly this sorta related key attack
14:37 < andytoshi-web> this makes is a pok which is necessary for security, cf my mimblewimble paper
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14:41 < tromp_> oh, i see. ok, then i can reply to my own post...
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15:11 < oleganza> Hello. andytoshi et al: Have read your CA paper this morning - pretty impressive trick to shave off 25% from the rangeproof. Congrats!
15:12 < kanzure> link?
15:12 < oleganza> http://fc17.ifca.ai/bitcoin/schedule.html
15:12 < AdrianG> would be  nice
15:12 < oleganza> http://fc17.ifca.ai/bitcoin/papers/bitcoin17-final41.pdf
15:13 < AdrianG> thx
15:14 < oleganza> I've recently been thinking on aggregatable rangeproofs and thought of one idea that involves bilinear pairings that might be interesting. So while Schnorr rangeproofs require verifying N*M basic signature checks (N commitments with base M), pairing-based rangeproof can be merged by third party to have O(N*M) point additions and O(N+M) pairing operations.
15:15 < oleganza> I started with a ring signature as presented here: https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf (Boneh, Gentry, Lynn, Shacham)
15:16 < oleganza> say, commitment C=v*H+f*G is proved to be in range 0..m-1 by the following formula: e(Hash(C), G) == Product[e(S_i, C - i*H), i=0..m-1]
15:16 < oleganza> where {S_i} are _points_ similar to s-scalars in Schnorr ringsig.
15:17 < oleganza> Then, if you have N commitments {C_k} - where they do not necessary belong to one value, but could be commitments from all the output values in a block.
15:18 < oleganza> if we multiply the checks and re-arrange elements using pairing rule e(A,C)*e(B,C) == e(A+B,C), we can eliminate a bunch of pairing operations replacing them with simple point additions
15:19 < oleganza> so for N commitemnts {C_k} the merged range proof would work like this:
15:19 < oleganza> Product[e(Hash(C_k), G), k=1..N] == e(Sum[Hash(C_k), k=1..N], G)
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15:20 < oleganza> and Product[Product[e(S_i, C_k - i*H), i=0..m-1, k=1..N] is rearranged around C_k (shared by M pairings) and -i*H (shared by N pairings)
15:20 < oleganza> as follows:
15:21 < oleganza> Product[e(Sum[S_i_k, i=0..m-1], C_k), k=1..N] * Product[e(Sum[S_i_k, k=1..N], -i*H), i=0..m-1]
15:22 < oleganza> The bandwidth, unfortunately, is not saved: you need N*M points {S_i_k}
15:24 < oleganza> but my rough estimation is: if pairing operation is 5x slower than a Schnorr sig (two scalar mults), then N+M trumps N*M for properly chosen M for a given large N.
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15:28 < oleganza> E.g. 256 outputs with 38-bit numbers would optimally use 5 commitments per number using base 195, having roughly 50x CPU improvement (omitting cost of 256*8 point additions, though).
15:28 < oleganza> err, 256*5 point additions, i mean.
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15:31 < oleganza> I'm not sure if multiplying and arranging the sides of the equation like that is actually safe: meaning, that such equality implies equality of the individual ring signatures.
15:31 < oleganza> s/equality of the individual ringsigs/validity.../
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