We are designing an off-chain coin-swap protocol that will work with the statechain implementation we are developing (https://github.com/commerceblock/mercury). The general idea is that coins deposited with a statechain entity (statecoins) can be transacted peer-to-peer off-chain in a way that the statechain entity (SCE) is trusted, but the statecoins always remain in the custody of the owners. A statecoin swapping service would enable owners to mix their coins with other users, giving the same privacy benefits of on-chain CoinSwap protocols, but by being off-chain statecoin swaps would be much faster and cheaper.

The swapping service (conductor) would not have custody of the statecoins at any point. The aim is to have the conductor coordinate the swap amongst a group of statecoins (i.e. determine the which statecoin should be sent to which new random owner in the group) without being able to learn the link between owners and their provided addresses. To do this we will use a blind signature scheme in a similar way to the zerolink protocol.

Here is a high-level description of how this blinding can operate - with the aim that the conductor does learn how the ownership of individual coins has changed.
For example, imagine 4 individuals (A,B,C and D) who own equal value statecoins utxo1, utxo2, utxo3 and utxo4 respectively. They want to swap ownership privately, trusting the conductor/SCE to enforce atomicity. In other words, the conductor will randomly assign each statecoin to one of the owners (the mix), but will not be able to gain knowledge of that assignment.
1. A,B,C and D signal their participation by signing the swap_token (which has details of the swap) with the proof-key of their input coin. (A statecoin address is formed of a concatenation of the proof key and backup address).
2. Each of A,B,C and D then generate a new statecoin address (where they what to receive the swapped coin), which they blind (encrypt) and sign with the proof key of their input coin: add1, add2, add3 and add4 and send to the conductor.
3. The conductor authenticates each signature and then signs each payload (i.e. the blinded destination addresses) with a blinded signature scheme and returns these signatures to A,B,C and D.
4. Each of A,B,C and D then reconnects over TOR with a new identity.
5. Each of A,B,C and D then send their unblinded destination address with the conductor signature to the conductor (the conductor now knows that these 4 addresses belong to A,B,C and D, but not which ones map to each input.)
6. The conductor randomly assigns each address to one of utxo1, utxo2, utxo3 and utxo4 (e.g. utxo1:add3, utxo2:add1, utxo3:add4 and utxo4:add2) and requests each participant to initiate the transfer to the given address.
7. Each participant then finalises each transfer - if any transfer fails (due to a participant disappearing or acting maliciously) then all transfers are reverted - here atomicity is guaranteed by the SCE.

The interesting problem we have with this protocol is how to assign blame in the case that one or more participants in the swap causes it to fail, so that the corresponding statecoins can be penalized (prevented from participating in further swaps for some timeout) to make any DoS attack costly. In the case of an on-chain coinjoin, this is easy: whoever didn't sign their input is to blame. However, in our statechain system a statecoin transfer is a two stage process (to update the private key shares): the sender performs an operation with the SCE (transfer_sender) and then sends an encrypted value to the receiver, who then performs the second operation with the SCE (transfer_reciever) which updates the UTXO private key shares for the new owner (https://github.com/commerceblock/mercury/blob/master/doc/statechains.md for more details). If the second stage fails (i.e. the values used for the key update protocol are wrong) this could be due to either the sender sending a bad/manipulated value to the receiver, or the receiver using bad values in the second operation with the SCE. Essentially, either the sender or the receiver can cause the transfer to fail, and it is not possible to determine which one is malicious without revealing the encrypted value sent between the sender and receiver (which must be kept secret from the SCE).

All this means that if a multi-party coinswap fails, we will know which statecoin was involved in the failure, but we cannot determine whether the sender or receiver of that coin caused the failure. One potential solution to this is to have each sender generate a zero knowledge proof that the encrypted value sent to the receiver is correct/valid (see last section in https://github.com/commerceblock/mercury/blob/master/doc/swaps.md for more details) which can be used to assign blame in a failure. This proof could be generated and verified using a zkSNARK/zkSTARK framework, but this is not trivial to implement and would likely add significant computational burden to user wallets to generate proofs - so we would like to avoid this if possible, and we are trying to come up with a simpler solution.

Any comments on the above are welcome, and happy to provide more details if anyone is interested.

Cheers,

Tom