[bitcoin-dev] Statechain coinswap: assigning blame for failure in a two-stage transfer protocol.

[Tom Trevethan <tom@commerceblock.com>]

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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

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