Good morning Tom,

> 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.

Okay, I suppose this is much too high-level a view, and I have no idea what you 
mean by "statecoin" exactly.

Let me try to fill in the details and correct me if I am wrong okay?

I imagine that the `add1` etc. are implemented as 2-of-2 between the purported 
owner and the tr\*sted signing module.
The owner of that address can easily create this knowing only the pubkey of the 
tr\*sted signing module.

The initial `utxo1`... are also in similar 2-of-2s.

(they cannot be unilateral control, since then a participant can broadcast a 
replacement transaction, even without RBF, almost directly to miners.)

So when the coordinator talks to Alice, who owns `utxo1` and destination 
`addr1`, it provides partially-signed transactions of `utxo#:addr#`.
Alice then checks that its `addr1` is on one of those transactions, with the 
correct amount, then provides a signature for the `utxo1:addr#` transaction.

However, then the coordinator, who happens to be in cahoots with Bob, Charlie, 
and Dave, simply broadcasts that transaction without soliciting the 
`utxo#:addr1` transaction.

So it seems to me that this requires tr\*st that the coordinator is not going 
to collude with other participants.
This is strictly worse than say Wasabi, where the coordinator colluding with 
other participants only allows the coordinator to break privacy, not outright 
steal funds.

It seems to me that the trust-minimized CoinSwap plan by belcher_ is superior 
to this, with reduced scope for theft.
The plan by belcher_ is potentially compatible with using watchtowers that can 
be used for both CoinSwap and Lightning as well (if we design it well) with the 
watchtower potentially not even learning whether it is watching a CoinSwap or a 
Lightning channel.

Though of course I could be misunderstanding the scheme itself.
Is my understanding correct?

Regards,
ZmnSCPxj
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