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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<sipa> hi
<tloriato> hello!
<sipa> we're pretty close to writing up a proposal
<sipa> for aggregated signatures
<tloriato> i feel like everytime i have a doubt about bitcoin development you are here to help me, thanks buddy, for real
<tloriato> that's incredible
<sipa> there are two somewhat independent problems to solve here
<tloriato> i'm in first year of cs college myself, so i'm still trying to catch up on things, but schnorr signatures might be one of the most important updates for bitcoin ( even more than LN, for me)
<tloriato> alright, go ahead please, sorry
<sipa> one is the question of how to reduce the number of signatures per input to 1
<waxwing> sipa, you mean like a BIP for aggregated sigs? wouldn't it need a Schnorr BIP first or something?
<waxwing> sorry ignore me, i interrupted
<sipa> waxwing: yes, we'll probably write up two BIPs (one about the signature scheme itself), another about how to integrate it into opcodes etc
<sipa> and the other problem is how to reduce the number of signatures across multiple inputs to one
<sipa> for the first there are many solutions (if you accept complicated negotiations and proof protocols between the participants in a single input)
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<andytoshi> waxwing: to be clear: "aggregated sigs" and "schnorr" are the same thing. "schnorr signature" is not a super well-defined concept. aggregate signatures are a specific thing (that could be termed a 'schnorr signature', or rather a generalization of 'schnorr signature' to multiple signers) which has all the algebraic properties that our hearts desire from schnorr
<sipa> right, aggregated signature just means "a construction that allows multiple signers to jointly produce a single signature"
<waxwing> andytoshi, i'm surprised you put it like that .. the schnorr signature was patented after all :)
<sipa> schnorr signatures do permit this, but some serious caveats that actually make it (when used naively) insecure for the across-inputs case
<tloriato> waxwing: it expired in 2008
<andytoshi> waxwing: right, sure, there is a specific thing called a "schnorr signature" which was patented (tho it still did not specify e.g. what groups or hash function to use) and that thing was crappy
<sipa> however, it turns out there is a generalization of Schnorr signature for multiple parties that remains secure under very wide assumptions, called Bellare-Neven from 2006
<andytoshi> later there was a generalization by bellare-neven (which is what we're calling "aggregated signatures") which is also a specific thing
<sipa> in particular, the issue is that it remains secure even when all but one participant can choose their public keys in function of other participants
<andytoshi> but when we say "schnorr signature" in casual conversation this might refer to schnorr's scheme, schnorr's scheme + a pubkey commitment, bellare-neven, etc., sometmise i even use that term to refer to rangeproofs or ring signatures
<waxwing> tloriato, sure i know :) andytoshi i'm curious now, given that details like hash function and group weren't defined, in what sense was it crappy? i'm guessing you mean it doesn't consider pubkey commitment then.
<andytoshi> as a result we're trying to avoid using the term in anything we propose, to avoid confusion
<waxwing> hmm yes i can see how you'd end up in that situation now, thanks.
<andytoshi> waxwing: yes. and it looks tantalizingly like it'd give easy multisigs but actually it doesn't
<sipa> it gives easy multisigs under the assumption that all public keys are certified
<andytoshi> (i have also used "schorr signatures" to refer to many different multisignature schemes, some of which are broken)
<andytoshi> right
<sipa> as in: there is some magic involved that makes you believe that all participants actually have the keys they claim to have
<sipa> and in a blockchain setting, that assumption can't exist
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<sipa> the verifiers (=every full node) can't know who has which public key - that's exactly the problem it's trying to solve
<waxwing> well i can only earnestly wish you guys luck in shifting the language here :)
<sipa> anyway, Bellare-Neven is a trivial extension of Schnorr
<waxwing> this is the part where i say a schnorr sig is just a zkpok of the private key and then run away before gmaxwell finds me :)
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<andytoshi> heh, that is usually but not always what i mean by the term
<waxwing> (just jk about how it isn't if the pubkey isn't fixed in advance, i.e. the stuff you were already mentioning)
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<waxwing> hmm although it's in the weeds, it is kinda interesting since if a learner goes to wikipedia to read about Schnorr signatures they aren't going to see mention of this issue iirc
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<sipa> well the problem is really one of setting assumptions
<sipa> this idea that with schnorr you can "just" add up multiple signatures and you get a valid signature for the sum of the public key is true, but the normal schnorr security proof in no extends to that
<sipa> *in no way
<sipa> this is the paper that describes the Bellare-Neven scheme: https://cseweb.ucsd.edu/~mihir/papers/multisignatures-ccs.pdf
<sipa> (they call their own scheme MS-BN in the paper)
<waxwing> thanks.
<sipa> where Schnorr's validation equation is s*G = R + H(R,m)*X (with (R,s) the sig, m the message, X the pubkey)
<sipa> Bellare-Neven's equation is s*G = R + H(R,m,P1,P2,...,Pn,1)*P1 + H(R,m,P1,P2,...,Pn,2)*P2 + ... + H(R,m,P1,P2,...,Pn,n)*Pn
<sipa> with P1...Pn the pubkeys
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<waxwing> hmm that looks simpler than the construction you guys came up with?
<sipa> it is
<sipa> however, it doesn't permit key aggregation - the verifier needs to know all the public keys
<waxwing> so the wagner thing doesn't apply?
<sipa> no, wagner is not a concern here
<sipa> our construction uses s*G = H(R,m,Q)*H(P1,P2,...,Pn,1)*P1 + H(R,m,Q)*H(P1,P2,...,Pn,2)*P2 + ... + H(R,m,Q)*H(P1,P2,...,Pn,n)*Pn, where Q = H(P1,P2,...,Pn,1)*P1 + ... + H(P1,P2,...,Pn,n)*Pn
<sipa> which can be rewritten as s*G = R + H(R,m,Q)*Q, which is just the normal Schnorr verification equation
<sipa> oops, missing "R +" two lines up ^
<waxwing> ah so only one thing is hashed there
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<kanzure> "Updates on Confidential Transactions efficiency" https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-November/015283.html
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<waxwing> yeah just saw that, great, succinct and to the point
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<waxwing> (that was *not* an attempt at a joke ("succinct"))
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<eck> most people in this channel may have already read this, but for the lurkers (like me!), this is pretty cool: https://eprint.iacr.org/2017/1066
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<hdevalence> Hi, I'd like to benchmark group operations using secp256k1, but I'm not sure which of the existing benchmarks are the ones I'm looking for.
<hdevalence> Is there a benchmark for variable-base scalar mult, for instance?
<sipa> there is bench_internal
<sipa> variable-base scalar mult is pretty much just an ECDSA verification
<hdevalence> does secp have a multiscalar mult implementation?
<andytoshi> #secp256k1 might be better for this ... but we're working on it, there is an open PR for it
<sipa> not yet
<sipa> but a PR was just opened today for that
<sipa> also, #secp256k1
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