Olaoluwa Osuntokun [ARCHIVE] on Nostr: 📅 Original date posted:2018-05-07 📝 Original message: Actually, just thought ...

📅 Original date posted:2018-05-07
📝 Original message:
Actually, just thought about this a bit more and I think it's possible to
deploy this in unison with (or after) any sort of SS based on schnorr
becomes
possible in Bitcoin. My observation is that since both techniques are based
on
the same underlying technique (revealing a secret value in a signature) and
they center around leveraging the onion payload to drop off a payment point
(G*a, or G*a_1*a_2*a_3, etc), then the disclosure within the _links_ can be
heterogeneous, as the same secret is still revealed in an end-to-end matter.

As an illustration, consider: A <-> B <-> C. The A <-> B link could use the
2pc
pailier technique, while the B <-> C link could use the OG SS technique
based
on schnorr. If i'm correct, then this would mean that we can deploy both
techniques, without worrying about fragmenting the network due to the
existence
of two similar but incompatible e2e payment routing schemes!

-- Laolu


On Mon, May 7, 2018 at 4:57 PM Olaoluwa Osuntokun <laolu32 at gmail.com> wrote:

> 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
>>
>
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