rich1.0npub19helcfnqgk2jrwzjex2aflq6jwfc8zd9uzzkwlgwhve7lykv23mq5zkvn4https://nostr.ae/npub19helcfnqgk2jrwzjex2aflq6jwfc8zd9uzzkwlgwhve7lykv23mq5zkvn4njumphttps://nostr.ae📅 Original date posted:2018-05-07 📝 Original message: Hi Pedro, Very cool stuff! When I originally discovered the Lindell's technique, my immediate thought was the we could phase this in as a way to _immediately_ (no additional Script upgrades required), replace the regular 2-of-2 mulit-sig with a single p2wkh. The immediate advantages of this would: be lower fees for opening/closing channels (as the public key script, and witness are smaller), openings and cooperative close transactions would blend in with the anonymity set of regular p2wkh transactions, and finally the htlc timeout+success transactions can be made smaller as we can remove the multi-sig. The second benefit is nerfed a bit if the channel are advertised, but non-advertised channels would be able to take advantage of this "stealth" feature. The upside of the original application I hand in mind is that it wouldn't require any end-to-end changes, as it would only be a link level change (diff output for the funding transaction). If we wanted to allow these styles of channels to be used outside of non-advertised channels, then we would need to update the way channels are verified in the gossip layer. Applying this to the realm of allowing us to use randomized payment identifiers across the route is obviously much, much doper. So then the question would be what the process of integrating the scheme into the existing protocol would look like. The primary thing we'd need to account for is the additional cryptographic overhead this scheme would add if integrated. Re-reviewing the paper, there's an initial setup and verification phase (which was omitted from y'alls note for brevity) where both parties need to complete before the actually signing process can take place. Ideally, we can piggy-back this setup on top of the existing accept_channel/open_channel dance both sides need to go through in order to advance the channel negotiation process today. Conner actually started to implement this when we first discovered the scheme, so we have a pretty good feel w.r.t the implementation of the initial set of proofs. The three proofs required for the set up phase are: 1. A proof that that the Paillier public key is well formed. In the paper they only execute this step for the party that wishes to _obtain_ the signature. In our case, since we'll need to sign for HTLCs in both directions, but parties will need to execute this step. 2. A dlog proof for the signing keys themselves. We already do this more or less, as if the remote party isn't able to sign with their target key, then we won't be able to update the channel, or even create a valid commitment in the first place. 3. A proof that value encrypted (the Paillier ciphertext) is actually the dlog of the public key to be used for signing. (as an aside this is the part of the protocol that made me do a double take when first reading it: using one cryptosystem to encrypt the private key of another cryptosystem in order to construct a 2pc to allow signing in the latter cryptosystem! soo clever!) First, we'll examine the initial proof. This only needs to be done once by both parties AFAICT. As a result, we may be able to piggyback this onto the initial channel funding steps. Reviewing the paper cited on the Lindell paper [1], it appears this would take 1 RTT, so this shouldn't result in any additional round trips during the funding process. We should be able to use a Paillier modulos of 2048 bits, so nothing too crazy. This would just result in a slightly bigger opening message. Skipping the second proofs as it's pretty standard. The third proof as described (Section 6 of the Lindell paper) is interactive. It also contains a ZK range proof as a sub-protocol which as described in Appendix A is also interactive. However, it was pointed out to us by Omer Shlomovits on the lnd slack, that we can actually replace their custom range proofs with Bulletproofs. This would make this section non-interactive, allowing the proof itself to take 1.5 RTT AFAICT. Additionally, this would only need to be done once at the start, as AFIACT, we can re-use the encryption of the secp256k1 private key of both parties. The current channel opening process requires 2 RTT, so it seems that we'd be able to easily piggy back all the opening proofs on top of the existing funding protocol. The main cost would be the increased size of these opening messages, and also the additional computational cost of operations within the Paillier modulus and the new range proof. The additional components that would need to be modified are the process of adding+settling an HTLC, and also the onion payload that drops off the point whose dlog is r_1*alpha. Within the current protocol, adding and settling an HTLC are more or less non-interactive, we have a single message for each, which is then staged to be committed in new commitments for both parties. With this new scheme (if I follow it correctly), adding an HTLC now requires N RTT: 1. Alice sends A = G*alpha to Bob. Here alpha is the payment secret. 2. Bob sends R_3 = (G*alpha)*r_2 (along w/ a proof of knowledge of r_2 and relation to A) 3. Alice sends R_3' = (G*alpha)*r_3 (along with a similar proof as above) 4. Bob then computes c3 (the encrypted partial sig which when completed will reveal a) to Alice. 5. Alice decrypts c3 to get the plaintext partial sig (s'), then finalizes the set up by sending s'' to Bob. This process takes 2.5 RTT, and would require re-working the state machine slightly to only actually commit an HTLC after step 5 has been completed. When Bob obtains a from the next party in the path, we Alice can then then over the signature, from which Alice can extract alpha. So adding HTLCs is now a bit more interactive, but settling them is the same a before. Finally, the onion payload would need to be re-interpreted in order to encode G*alpha which takes 33 bytes. We can shave this down to 32 by selecting the x coordinate (at the sender) to always be either even or odd. Currently, we have 12 unused bytes in the onion payload. The HMAC is currently 32 bytes. One path would be to allocate a portion of HMAC space to encoding this point. A 16-byte HMAC would probably have been enough in the beginning, so we can drop down to that. However, that still leaves 4 bytes somewhere that has to give...one could either obtain these extra bytes from the CLTV and Amount fields, or just have each hop consume an extra payload. The latter path would mean that the new upper hop limit is actually 10. However, given that we would need need a new global feature bit in order to roll this out, it may make sense to re-work the onion format all together which would mean that we wouldn't need to hack the old format a bit to accommodate this additional data. One aspect of introducing a new end-to-end contract type which I hadn't considered before is that each new type effectively partitions the network. This is due to the fact that these HTLCs will now only be able to be carried along paths that understand this new feature. As a result, plausible path diversity takes as we can no longer utilize all channels on the network for routing. This would suggest that introducing new end to end contract types (if one wishes to use them widely across arbitrary channels and not for specific contract protocols) may be a strong point of synchronization w.r.t updates across the network. As a result, we may need to be a bit more discerning w.r.t new candidates for e2e contracts given the coordination costs. So the takeaways are: * we can probably piggy back the extra proofs onto the channel opening process * one of the subproofs can use bulletproofs to make the proof shorter and also non-interactive * adding an HTLC would take 2.5 RTT's, but settling is just as quick as before * the onion payload would either need to be hacked, or extended to support packaging the point. * the utility of the scheme won't shine until all/most of the network uses it * we could start w/ just the introduction of the OG 2PC scheme as a multi-sig replacement [1]: https://eprint.iacr.org/2011/494.pdf (section 3.3) -- Laolu On Fri, Apr 27, 2018 at 11:42 AM Pedro Moreno Sanchez <pmorenos at purdue.edu> wrote: > Hello guys, > > as some of you already know, I am working on some cryptographic > constructions that might be of interest and useful for the Lightning > Network. > > Recently, I have come up with a scriptless version of the adaptor > signatures and the contract required in the Lighting Network using only > 2-party ECDSA signatures. The main advantage is that, instead of waiting > for Schnorr signatures to be deployed in Bitcoin so that Poelstra's > scriptless scripts can be used, I believe that this ECDSA-version of the > scriptless scripts can be directly applied today. > > Details are in the attached PDF. I am looking forward to hearing your > comments and suggestions. > > Cheers, > Pedro. > > _______________________________________________ > Lightning-dev mailing list > Lightning-dev at lists.linuxfoundation.org > https://lists.linuxfoundation.org/mailman/listinfo/lightning-dev > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.linuxfoundation.org/pipermail/lightning-dev/attachments/20180507/32b51086/attachment-0001.html>