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06:26 < jimmysong> Question for the crew here, Schnorr Signatures, using the canonical form is checked with: R = s*G - H(R||z) * P
06:26 < jimmysong> If you do that, you can compute P just from the signature using
06:26 < jimmysong> H(R||z)^-1 * (s*G - R)
06:27 < jimmysong> The musig paper, however, uses another construction: https://eprint.iacr.org/2018/068.pdf
06:27 < jimmysong> specifically, you end up using H(P||R||z), which precludes the possibility of computing P from just the Signature
06:28 < jimmysong> Two questions:
06:29 < jimmysong> 1. What is the reason that for Segwit Version 0, that we didn't do something similar with pubkeys. After all, the pubkey can be derived using just the signature, so why is the pubkey in the witness program?
06:29 < jimmysong> Specifically, there are 4 possible pubkey values, we could have just specified which one in the witness program (2 bits) instead of the 33 bytes required for a compressed SEC pubkey
06:30 < jimmysong> 2. Why does the Schnorr construction use P in the hashing function?
06:30 < jimmysong> I'm sure I'm missing something, I would like to know what the reasoning is
06:30 < jimmysong> Obviously, removing the pubkey from the witness program would be a pretty big win from a space savings perspective
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06:31 < jimmysong> I'm missing the drawbacks or the vulnerabilities of doing something like that
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06:33 < jimmysong> *hattip to one of my students asking this
06:33 < kanzure> "pubkey can be derived using just the signature" ecdsa pubkey recovery?
06:34 < waxwing> yeah for 1, that's the same question. i remember there was a thread on btctalk years ago about that
06:34 < waxwing> i guess verification issues? but i was never clear on that.
06:38 < jimmysong> maybe sipa, luke-jr or gmaxwell can comment? Just trying to understand so I can explain this
06:39 < waxwing> for 2, if you don't hash the pubkey into the Schnorr sig, it's interesting to observe it's not a zkpok of the private key if the pubkey is not known in advance. a (s, R, m) tuple alone. how that fact plays in in the bitcoin context isn't completely clear though.
06:41 < harding> jimmysong: is this your student, or is it just a popular week for this question?  https://bitcoin.stackexchange.com/questions/75322/why-do-we-need-public-key-as-part-of-witness-in-p2wpkh-transactions
06:41 < waxwing> (sorry incomplete, i meant "a s, R, m tuple alone doesn't prove knowledge of the private key x if you use s = k + H(R||m)x)
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06:42 < jimmysong> I don't know. The student's name is not Jakob, though.
06:44 < kanzure> pubkey recovery is incompatible with schnorr and breaks batch invalidation
06:44 < kanzure> whoops i mean batch validation
06:44 < jimmysong> what's batch validation?
06:44 < kanzure> a whole bunch of exponentiation
06:45 < jimmysong> haha
06:45 < waxwing> https://cr.yp.to/badbatch/badbatch-20120919.pdf <- this doc explains the general idea (from DJB)
06:45 < jimmysong> so there's a tradeoff between the space savings and computational ease of validation, then
06:45 < kanzure> batch validation discussed here https://diyhpl.us/wiki/transcripts/bitcoin-core-dev-tech/2017-09-06-signature-aggregation/
06:46 < kanzure> ease? validation cost
06:46 < waxwing> basically because it's a linear thing, you can add up a bunch of sigs and validate them all together, but it's not secure without first randomizing the terms; then you're using the curious fact that doing a lot of elliptic curve scalar mults at once is much quicker than doing them all individually
06:47 < waxwing> oh yeah istr gmaxwell telling me once that that's the reason for (R, s) rather than (Hash, s) being the preferred schnorr sig form (for batch validation). maybe there's other reasons, not sure.
06:47 < jimmysong> ok, thanks. That explains 2. How about #1?
06:49 < kanzure> was my pubkey recovery answer unsatisfying?
06:53 < waxwing> kanzure, to be specific: "pubkey recovery is incompatible with schnorr": are you saying it's incompatible with schnorr aggregation?
06:54 < kanzure> i'm not actually sure, i haven't investigated the details
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06:55 < waxwing> right; i think as per jimmysong 's Q, it's straightforward if just a single key schnorr, unless i missed something obvious
06:56 < kanzure> actually i mean ecdsa pubkey recovery is incompatible, and i shouldn't be bullshiting around, apologies.
06:59 < waxwing> yeah this is very tricky stuff. but i think not hashing the pubkey into a schnorr sig construction is dodgy as per my earlier zkpok comment and i suspect, specifically, if you try to use schnorr's linearity (as you do when you aggregate keys or signatures) you end up with naughtiness :) and if you *do* hash the key (H(P||R||m), then of course recovery is not possible, you need the P before you start :)
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07:23 < jimmysong> i missed something. What do you mean ECDSA pubkey recovery is incompatible? With batch invalidation?
07:24 < kanzure> incompatible with schnorr was the message i received from andytoshi
07:24 < kanzure> https://github.com/bitcoin-core/secp256k1/blob/master/src/modules/recovery/main_impl.h
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07:27 < jimmysong> ok, will have to ask him next time unless he answers here
07:29 < sipa> jimmysong: schnorr with key prefixing (secure against key malleation) is incompaitble with pubkey recovery
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07:32 < sipa> jimmysong: without key prefixing, you can take a signature for a pubkey P and msssage m, and turn it into a valid signature for a key P+aG and message m, for any a
07:34 < sipa> jimmysong: MuSig also requires key prefixing for its security proof
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07:35 < sipa> jimmysong: and most importantly, batch validation is inherently incompatible with pubkey recovery (you can only recover at most one pubkey from the batch), and signature aggregation gives far bigger gains
07:36 < sipa> it's been known for a while too: https://bitcointalk.org/index.php?topic=6430.0
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07:40 < jimmysong> sipa: so the main reason is for batch validation? do we have batch validation for ECDSA? I wasn't aware
07:40 < jimmysong> I thought it was only for Schnorr
07:44 < sipa> jimmysong: it's how the signmessage/verifymessage functionality works!
07:44 < sipa> using ECDSA pubkey recovery
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07:46 < sipa> jimmysong: yes, the main reason not to do it is batch validation
07:47 < sipa> (and sort of being superseded by signature aggregation - you can again only recovery one pubkey at best from an aggregate)
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08:00 < kanzure> "Okamoto beats Schnorr: On the provable security of multi-signatures" https://eprint.iacr.org/2018/417.pdf
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08:13 < kanzure> sipa: is there a modern chaumian cash library better than credlib/lucre? maybe maintained, etc.
08:14 < sipa> kanzure: no idea
08:25 < kanzure> .tw https://twitter.com/adam3us/status/944360914584817664
08:25 < yoleaux> @nopara73 agree, NB you can use Brands' ecash protocol http://cypherspace.org/credlib/ which is ECDL compatible, also has blinding, can use Bitcoin curve, supports multiple denominations & should be CT compatible (similar to the CT construction) doing public audit seems hard & conflicts with scale (@adam3us, in reply to tw:944333907373318144)
08:30 < andytoshi> jimmysong: 1. segwit v0 did not change anything about the signature scheme except to restructure the sighash (but importantly no semantics were changed). this is because segwit had enough scope already.
08:31 < andytoshi> 1a. The reason not to use pubkey recovery is that it's incompatible with batch validation
08:31 < andytoshi> 2. (also 1b). Committing to P ensures that the signature is not only a strong signature, but also a proof of knowledge of the secret key. this prevents key malleability attacks and greatly simplifies the analysis of integrating with larger cryptosystems
08:33 < andytoshi> as waxwing said
08:34 < andytoshi> jimmysong: re batch validation with ECDSA, we do not have it, unfortunately the ECDSA signature malleability means that you can't batch validate ECDSA sigs unless you can somehow determine which complete R point corresponds to the r value in the sig
08:35 < andytoshi> and our choice of symmetry breaking in BIP66 does _not_ fix the R point, something (afaik) it did not occur to us was possible until over a year after bip66 was deployed
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09:29 < gmaxwell> jimmysong: beyond the security implications-- which could be addressed by putting the scriptPubkey or key hash in H(), certicom has a patent on key recovery that could potentially apply to that construction.
09:29 < gmaxwell> (and of course batch validation what whatnot)
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12:57 < jimmysong> thanks andytoshi, sipa and gmaxwell. i'll have to read more into batch validation.
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--- Log closed Sun Jun 03 00:00:35 2018