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06:27 < RubenSomsen> andytoshi: I was going through blind schnorr sigs again today, and there's one part that seemed broken to me. I am probably just misunderstanding something... Using the example from Jonas' slides ( https://nickler.ninja/slides/2018-bob.pdf ) can't the blind signer check every signature on the blockchain, calculate c - c' = alpha and s'- s = beta and check if R' == R + alpha*G + beta*P? If true, the blind signature
06:27 < RubenSomsen> is now linked to the unblinded signature;;
06:28 < RubenSomsen> nickler: I guess I should tag you too :)
06:38 < andytoshi> RubenSomsen: because every single signature ever will satisfy that equation
06:41 < RubenSomsen> andytoshi: but only signer P knows k*G = R
06:43 < andytoshi> RubenSomsen: implement this in sage and see what happens when you try to distinguish sigs with it
06:44 < andytoshi> that is, i can give you a random c', you choose R and s', then go pick whatever sig you want to extract alpha/beta
06:45 < RubenSomsen> andytoshi: Really? Haha OK, I'll look into it. Thanks for pointing me in the right direction.
06:46 < andytoshi> (alternately, you can do this algebraically; start from the fact that your blind sig (s', R') was valid and the fact that the blockchain sig (s, R) was valid, using the same key; and you'll see that R must satisfy the equation you describe when you define alpha to be the difference of s's and beta to be the difference of c's)
06:48 < RubenSomsen> andytoshi: I'll chew on that for a while, thanks :)
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09:14 < RubenSomsen> andytoshi: I have confirmed the math adds up, thanks again :)
09:15 < nsh> <Crimer> darnit!
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09:22 < andytoshi> if it helps, i have an old email i sent to matt green with exactly this 'attack', and he literally replied by forwarding his response to the last person who'd sent it in
09:22 < andytoshi> along with "i didn't read your message that closely, please follow up if this isn't what you're talking about"
09:22 < andytoshi> but it was :}
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09:24 < nsh> heh
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13:44 < gmaxwell> andytoshi: Are you aware of a signature scheme which preserves addition of messages?  E.g.  say you have Pub1, Msg1, Sig1  and Pub2, Msg2, Sig2,   does a scheme exists where you can take those and compute Sig3 which is valid for Pub1 + Pub2, Msg1 xor Msg2 (or other addition operator)?
13:44 < gmaxwell> If so, it could be used to eliminate quadratic bandwidth blowup in a dicemix like protocol in the common case.
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14:16 < nsh> maybe with Pintsov-Vanstone sigs [due to confidential partial message recovery] with some message redundancy allowing composition by parity
14:17 < nsh> (i have no idea what i'm talking about obviously)
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14:24 < nsh> (also there's additive homomorphic exponential elgamal over EC for small message spaces: https://crypto.stackexchange.com/questions/3626/can-elgamal-be-made-additively-homomorphic-and-how-could-it-be-used-for-e-voting/3630 )
14:25 < nsh> nominally relevant use-case performance analysis: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.66.7766&rep=rep1&type=pdf
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16:23 < WAhVdGsK1> gmaxwell: I think BLS where messages, signatures, and pub keys are multiplied works for that, no signer coordination. But of course, pairings... I think the problem with ElGamal, or any of the other homomorphic schemes, is coordination on the r values. Maybe it's possible with one of them, but I don't see how, at least for ElGamal.
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16:29 < gmaxwell> I was thinking of pairing, though I think this means that m1 then needs to be in the curve's field, which is a bit annoying.
16:30 < gmaxwell> and if the message is larger than one, you probably need a different pubkey for each digit to prevent permuting them.
16:33 < sipa> gmaxwell: it works for pairing
16:34 < sipa> but it breaks the assumption that the message is hashed onto the curve
16:34 < sipa> if you're doing arithmetic on it after the hashing
16:34 < sipa> by "works" i guess i mean that the result will verify correctly; i'm doubtful that it's secure
16:37 < sipa> specifically, BLS is normally: hash the message onto the curve, and then multiply the resulting point with the private key
16:37 < gmaxwell> Right and the 'hash' is the identity function in that case, which I agree seems suspect!
16:39 < sipa> well... you could define the hash function onto the curve for messages as "chop the message into 32-byte groups, hash each onto the curve, and sum the resulting points"
16:39 < sipa> now you have a scheme that lets you produce signatures for concatenation of messages by summing the signatures
16:39 < sipa> (again, very doubtful this is secure)
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16:41 < gmaxwell> Right, but what I was going for was elimiating the n^2 communication in the inner step of a dicemix like protocol.  You compute your share of the polynomial, sign it, send it to the next guy, who adds his, and then adds his signature. :P
16:41 < sipa> ah, yes.
16:42 < sipa> my hobby: forgetting the end goal
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16:43 < gmaxwell> In particular, for moderate N like... all the bandwidth is in that N^2.  So, for example, if you replace the polynomial with IBLT, you end up with something massively scalable except for the n^2 broadcast.  (the n^2 key agreement is one time setup that can be amortized across any number of messages).
16:43 < WAhVdGsK1> lol
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16:55 < WAhVdGsK1> Are there any public key schemes where the "message" isn't assumed to be a hash of a longer message? Ie. one that operates on arbitrary length bitstreams or "public key block ciphers" that can be combined under some mode?
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23:13 < maaku> .tell WAhVdGsK1 any public key scheme can be used to do that, but they aren't because it's hideously slow. both hash functions and symmetric ciphers are much, much faster. so if you're signing a message, hash it and sign the digest. if you're encrypting, AES encrypt the data and ECIES encrypt the symmetric key
23:13 < yoleaux> maaku: I'll pass your message to WAhVdGsK1.
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--- Log closed Wed Aug 22 00:00:47 2018