On Wed, Mar 21, 2018 at 03:53:59AM -0400, ZmnSCPxj wrote: > Good morning aj,
Good evening Zeeman! [pulled from the bottom of your mail] > This way, rather than gathering signatures, we gather public keys for > aggregate signature checking. Sorry, I probably didn't explain it well (or at all): during the script, you're collecting public keys and messages (ie, BIP 143 style digests) which then go into the signing/verification algorithm to produce/check the signature. You do need to gather signatures from each private key holder when producing the aggregate signature, but that happens at the wallet/p2p level, rather than the consensus level. > I am probably wrong, but could solution 2 be simplified by using the below > opcodes for aggregated signatures? > > OP_ADD_AGG_PUBKEY - Adds a public key for verification of an aggregated > signature. > OP_CHECK_AGG_SIG[VERIFY] - Check that the gathered public keys matches the > aggregated signature. Checking the gathered public keys match the aggregated signature is something that only happens for the entire transaction as a whole, so you don't need an opcode for it in the scripts, since they're per-input. Otherwise, I think that's pretty similar to what I was already saying; having: SIGHASH_ALL|BUCKET_1 pubkey OP_CHECKSIG would be adding "pubkey" and a message hash calculated via the SIGHASH_ALL hashing rules to the list of things that the signature for bucket 1 verifies. FWIW, the Bellare-Neven verification algorithm looks something like: s*G = R + K (s,R is the signature) K = sum( H(R, L, i, m) * X_i ) for i corresponding to each pubkey X_i L = the concatenation of all the pubkeys, X_0..X_n m = the concatenation of all the message hashes, m_0..m_n So the way I look at it is each input puts a public key and a message hash (X_i, m_i) into the bucket via a CHECKSIG operation (or similar), and once you're done, you look into the bucket and there's just a single signature (s,R) left to verify. You can't start verifying any of it until you've looked through all the scripts because you need to know L and m before you can do anything, and both of those require info from every part of the aggregation. [0] [1] > The effect is that in the OP_CHECKCOVENANT case, pre-softfork nodes will not > actually do any checking. Pre-softfork nodes not doing any checking doesn't work with cross-input signature aggregation as far as I can see. If it did, all you would have to do to steal people's funds is mine a non-standard transaction: inputs: my-millions: pay-to-pubkey pubkey1 witness=SIGHASH_ALL|BUCKET_1 your-two-cents: pay-to-script-hash script=[1 OP_RETURN_TRUE pubkey2 CHECKSIG] witness=SIGHASH_ALL|BUCKET_1 bucket1: 64-random-bytes output: all-the-money: you Because there's no actual soft-fork at this point every node is an "old" node, so they all see the OP_RETURN_TRUE and stop validating signatures, accepting the transaction as valid, and giving you all my money, despite you being unable to actually produce my signature. Make sense? Cheers, aj [0] For completeness: constructing the signature for Bellare-Neven requires two communication phases amongst the signers, and looks roughly like: 1. each party generates a random variable r_i, and sharing the corresponding curve point R_i=r_i*G and their sighash choice (ie, m_i) with the other signers. 2. this allows each party to calculate R=sum(R_i) and m, and hence H(R,L,i,m), at which point each party calculates a partial signature using their respective private key, x_i: s_i = r_i + H(R,L,i,m)*x_i all these s_i values are then communicated to each signer. 3. these combine to give the final signature (s,R), with s=sum(s_i), allowing each signer to verify that the signing protocol completed successfully, and any signer can broadcast the transaction to the blockchain [1] muSig differs in the details, but is basically the same. _______________________________________________ bitcoin-dev mailing list bitcoin-dev@lists.linuxfoundation.org https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev