Hi all!

I've been thinking a lot about how to add the benefits that lightning provides in terms of privacy and speed to the smart contracts unchained setup. The high-level idea is to utilize the fact that a lightning channel already has on-chain funds locked up, and if parties cooperate, some of these funds can be moved into the 2/3 MultiSig output needed for the escrow scheme by cooperating off-chain (and then moved back to their channel balances off-chain as well). The following is an admittedly pretty rough outline of how this might be accomplished.

A - B : Smart Contracts in a Lightning Channel

1) Parties both commit to a 2/3 MultiSig output on their next commitment transaction
2) Parties then both revoke_and_ack
3) When the contract yields a result, the to_local and to_remote balances can be updated and the 2/3 MultiSig output can be removed
4) If either party is uncooperative, their counter-party can force close the channel and funds can be resolved on-chain using the escrow

If either party does not revoke_and_ack well before any potential for them to discover if they have an advantage in the contract (or after some small but reasonable time), their counter-party should go on chain with the commitment transaction containing the 2/3 MultiSig

A - B - C : Single Hop Smart Contracts (Useful if someone, B in this case, wants to provide a hub that matches users wanting to enter smart contracts)

1) A irrevocably commits to a 2/3 MultiSig output on their commitment transaction with B (which B also commits to but does not yet revoke their old state)
2) C irrevocably commits to the same 2/3 MultiSig output on their commitment transaction with B (which B also commits to)
3) B irrevocably commits to both outputs
4) When the contract yields a result, say A should win some money from C, then A can ask B to remove that output (and update balances) by revealing to B how to claim funds from C
5) B can then ask C to remove the output and add to B's balance

If B does not revoke_and_ack on either channel, then the affected counter-party should close the channel and go on chain with the 2/3 MultiSig transaction
If B refuses to remove the output, A can claim their funds on-chain where B can learn how to claim funds from C
If C refuses to remove the output, B can claim their funds on-chain using the information revealed by A

Problems: How do we ensure that only B can claim the 2/3 MultiSig from C, and not anyone who sees A's on-chain spend of their 2/3 MultiSig? I'm pretty sure this is possible to do but I don't know Script well enough

A - B - C - D : Fully Routed Smart Contracts

1) Given the n possible outcomes in which A gets money from the contract between A and D, a_1 < a_2 < ... < a_n, and the m possible outcomes in which D gets money, d_1 < d_2 < ... < d_m, D must send n HTLCs to A with the amounts a_1, a_2 - a_1, a_3 - a_2, ..., a_n - a_(n-1) and A must send m HTLCs to D with amounts d_1, d_2 - d_1, d_3 - d_2, ..., d_m - d_(m-1)
2) These HTLCs must be special and have two hashes, where either preimage unlocks the funds
3) In the payments from A to D, A knows one preimage and the smart contracting platform knows the other (and similarly for D to A)
4) Should a_i be the outcome of the contract, D should tell A what the preimages are to payments 1 through i
5) D should fail all m payments
6) A should fail all payments i+1 through n
(It is possible and in fact likely that there can be ways to use fewer transactions and thus less collateral than this, perhaps by using subtraction and not just addition as in a_i - d_j, what I've presented is simply a lower bound that works in all cases)

If D does not reveal their preimages, A can get the relevant preimages from the smart contracting platform

Problems: The smart contracting platform is given more information about the contract in the happy path in this scheme. Also, all routers need to support special double-hash HTLCs

An alternative way to possibly do multi-hop routing that would require less be told to the escrow service, is to have each routing node add an output on either side where it takes one position in one channel and the other position in the other channel (essentially allowing them to break event when the contract is completed). This has the same problems as the Single Hop case as well as the additional problem (that I couldn't imagine a solution for) of making the commitments to the 2/3 MultiSig output on commitment transactions atomic; in the single hop case incentives seem to work out but I don't know how "failed routing" would be detected or handled in the multi-hop case.

Feedback welcome!

Best,

Nadav