[Lightning-dev] Scriptless Scripts with ECDSA

Olaoluwa Osuntokun laolu32 at gmail.com
Mon May 7 23:57:39 UTC 2018

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_
additional Script upgrades required), replace the regular 2-of-2 mulit-sig
a single p2wkh. The immediate advantages of this would: be lower fees for
opening/closing channels (as the public key script, and witness are
openings and cooperative close transactions would blend in with the
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
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
update the way channels are verified in the gossip layer.

Applying this to the realm of allowing us to use randomized payment
across the route is obviously much, much doper. So then the question would
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
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
on top of the existing accept_channel/open_channel dance both sides need to
through in order to advance the channel negotiation process today.

Conner actually started to implement this when we first discovered the
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
  less, as if the remote party isn't able to sign with their target key,
  we won't be able to update the channel, or even create a valid commitment
  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
  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
  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
parties AFAICT. As a result, we may be able to piggyback this onto the
channel funding steps. Reviewing the paper cited on the Lindell paper [1],
appears this would take 1 RTT, so this shouldn't result in any additional
trips during the funding process. We should be able to use a Paillier
of 2048 bits, so nothing too crazy. This would just result in a slightly
opening message.

Skipping the second proofs as it's pretty standard.

The third proof as described (Section 6 of the Lindell paper) is
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
need to be done once at the start, as AFIACT, we can re-use the encryption
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
protocol. The main cost would be the increased size of these opening
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,
is then staged to be committed in new commitments for both parties. With
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)
  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.
Bob obtains a from the next party in the path, we Alice can then then over
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
G*alpha which takes 33 bytes. We can shave this down to 32 by selecting the
coordinate (at the sender) to always be either even or odd. Currently, we
12 unused bytes in the onion payload. The HMAC is currently 32 bytes. One
would be to allocate a portion of HMAC space to encoding this point. A
HMAC would probably have been enough in the beginning, so we can drop down
that. However, that still leaves 4 bytes somewhere that has to give...one
either obtain these extra bytes from the CLTV and Amount fields, or just
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
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
which I hadn't considered before is that each new type effectively
the network. This is due to the fact that these HTLCs will now only be able
be carried along paths that understand this new feature. As a result,
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
(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

So the takeaways are:
  * we can probably piggy back the extra proofs onto the channel opening
      * one of the subproofs can use bulletproofs to make the proof shorter
        also non-interactive
  * adding an HTLC would take 2.5 RTT's, but settling is just as quick as
  * 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

[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>

> 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
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