Date: Mon, 22 Apr 2019 19:22:52 +0000
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: Ryan Perkins <riperk@protonmail.com>
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Subject: [bitcoin-dev] CoinJoin Jigsaw
Precedence: list

Earlier today ZmnSCPxj posted to the mailing list with an interesting post =
about payjoin. In it he mentioned:

> Any non-equal-value coinjoin is easily solvable via [value sudoku](https:=
//www.coinjoinsudoku.com/advisory/).

Which doesn't seem right to me.

I came up with something I call a "CoinJoin Jigsaw". A "CoinJoin Jigsaw" is=
 send-to-self coinjoin transaction in which every input is ambiguously asso=
ciated with an output (i.e. every transaction input must belong to at least=
 one subset of every output amount).


For simplicity I've used minizinc to model this. To make it clean, I decide=
d to model as two users (affectionately called 'A' and 'B') who trust a com=
mon party to orchestrate the CoinJoin Jigsaw for them. A and B don't trust =
each other, so they want to get all their money atomically in this one tran=
saction. We also want the "CoinJoin Jigsaw" to have exactly 2 outputs. One =
for A, and one for B. That way at first approximation it looks like a prett=
y standard bitcoin payment. (Of course the problem is substantially easier =
to solve if we allow A and B to have N outputs, but that creates an ugly tr=
ansaction).

We also need to make sure that both A and B are paying a fee proportional t=
o the amount of inputs they added, and the total transaction fee is satisfa=
ctory.

So I've modelled it as A and B provide their utxo to the orchestrater. The =
orchestrater will pick the largest subset of A's and B's utxo and such that=
 satisfies our CoinJoin Jigsaw properties. I ended up copy-and-pasting a lo=
t more than I'd like:

https://gist.github.com/riperk/7be6698f291e865ad5c930d0edb0cd5a

I'm not sure it has much practical utility, but it's kind of cool. Maybe.