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
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<waxwing> sipa: seems to have stopped updating? http://bitcoin.sipa.be/ver9-2k.png
<sipa> oops, yes indeed
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<stevenroose> yeah I noticed that too, was refreshing it with the BU exploit
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<fluffypony> waxwing: yeah Koinster's paper generator
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<yoleaux> A ransomware attack on MimbleWimble with Schnorr signatures : Mailing list archive : mimblewimble team in Launchpad
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<sipa> kanzure: apoelstra tells me it's wrong, but he can't respond right now :)
<tromp_> sipa: I hope it's wrong, since I like Schnorr signatures:)
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* gmaxwell guesses without looking: using malleability of outputs to change a valid payment to X into a payment to X+P?
<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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<andytoshi-web> basically ya, blocked because our ringsigs commit to the the pedersen commits
<andytoshi-web> like our schorr sigs commit to the keys. to prevent exactly this sorta related key attack
<andytoshi-web> this makes is a pok which is necessary for security, cf my mimblewimble paper
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<tromp_> oh, i see. ok, then i can reply to my own post...
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<oleganza> Hello. andytoshi et al: Have read your CA paper this morning - pretty impressive trick to shave off 25% from the rangeproof. Congrats!
<kanzure> link?
<AdrianG> would be nice
<AdrianG> thx
<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.
<oleganza> I started with a ring signature as presented here: https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf (Boneh, Gentry, Lynn, Shacham)
<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]
<oleganza> where {S_i} are _points_ similar to s-scalars in Schnorr ringsig.
<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.
<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
<oleganza> so for N commitemnts {C_k} the merged range proof would work like this:
<oleganza> Product[e(Hash(C_k), G), k=1..N] == e(Sum[Hash(C_k), k=1..N], G)
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<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)
<oleganza> as follows:
<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]
<oleganza> The bandwidth, unfortunately, is not saved: you need N*M points {S_i_k}
<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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<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).
<oleganza> err, 256*5 point additions, i mean.
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<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.
<oleganza> s/equality of the individual ringsigs/validity.../
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