[bitcoin-dev] Question about PayJoin effectiveness

[Chris Belcher]

On 10/06/2020 05:01, Mr. Lee Chiffre via bitcoin-dev wrote:
> I am trying to learn about payjoin. I have a couple concerns on its
> effectiveness. Are my concerns valid or am I missing something?
> 
> concern 1
> If it is known to be a payjoin transaction anyone could determine the
> sender the recipient and amount right?
> 
> Lets assume that everyone has a single utxo because payjoin becomes common
> use and payjoin consolidates utxos through "snowballing". If Alice has a
> UTXO of 0.05 btc and Bob has a UTXO of 1.15 btc. Bob can be assumed to
> have more balance because he is a merchant and his customers payjoin him
> payments alot.
> 
> If Alice and Bob do a payjoin with Alice paying 0.01 btc to Bob, it would
> probably look like this right?
> 
>  0.05---> |____---->1.16
>  1.15---> |    ---->0.04
> 
> It is very obvious here the amount sent and the sender.  Even if Alice did
> combine another input it would still be very obvious. In this case Alice
> has another utxo with 0.4 BTC
> 
>  0.40---> |
>  0.05---> |____---->1.16
>  1.15---> |    ---->0.44
> 
> This is still obvious that Alice paid Bob 0.01 BTC isn't it?
> 
> 
> 
> concern 2
> If there is just one consolidated utxo after each payjoin, would it  be
> easy to break the privacy of transaction chains?
> 
> Alice---payjoin--->Bob
> Clark---payjoin--->Bob
> 
> or
> 
> Alice---payjoin--->Bob---payjoin--->Clark
> 
> For exmaple, lets say that Alice payjoins to Bob. Then later on Clark
> payjoins with Bob. Based on the payjoin between Clark and Bob, Clark now
> knows what UTXO was actually Bob's. And can then know which one was
> actually Alices. By transacting a payjoin with someone, they could decloak
> the payjoins before them right? If so, how far back the chain can they go?
> 
> The issue is not that someone knows the utxos of themselves and the entity
> they payjoined with. The issue is that someone can figure out the payjoins
> of others before them with the same entity.
> 
> 
> I surely must be missing something here. What am I not understanding?
> 

Adding to what other people have written, it's an important point that
PayJoin breaks the common-input-ownership heuristic. I.E. if PayJoins
become even moderately popular then it will no longer be a safe
assumption that all the inputs to a transaction are owned by the same
entity (taking away all the obvious breaks like equal-output-coinjoins).

This assumption is a huge reason why blockchain surveillance is so
effective. A good paper on that is here:
https://arxiv.org/abs/1605.06369 (The Unreasonable Effectiveness of
Address Clustering Harrigan, Martin & Fretter, Christoph. (2016))

The assumption is mentioned by Satoshi in the whitepaper where he
laments that the privacy loss is unavoidable. (One of the few outright
errors in the paper, perhaps the only error). The fact that we have
technology to break this assumption is a massive deal, and that's a big
value-add of PayJoin.