Good morning Yuval,

> Additionally (though is a broader criticism of CoinJoin based privacy and not 
> specific to unequal amounts, and in particular refers to ZmnSCPxj's assertion 
> of 0 linkability) I am very worried that perspectives that focus on 
> linkability information revealed by a single coinjoin transaction in 
> isolation. This problem was alluded in the document, to but I don't see that 
> it was addressed. Naively the post/pre mix transaction graph would seem to 
> present a computationally much harder problem when looking at the 
> combinatorics through the same lens, but reality it can also be used to place 
> many constraints on valid partitions/sub-transaction assignments for a single 
> transaction with equal amounts. The trivial example is post mix linking of 
> outputs, but there are many other ways to draw inferences or eliminate 
> possible interpretations of a single transaction based on its wider context, 
> which in turn may be used to attack other transactions.

Indeed, this is a problem still of equal-valued CoinJoin.
In theory the ZeroLink protocol fixes this by strongly constraining user 
behavior, but ZeroLink is not "purely" implemented in e.g. Wasabi: Wasabi still 
allows spending pre- and post-mix coins in the same tx (ZeroLink disallows 
this) and any mix change should be considered as still linked to the inputs 
(though could be unlinked from the equal-valued output), i.e. returned to 
pre-mix wallet.

> Finally, the proof as well as its applicability seems suspect to me, since 
> seems to involve trusting the server:
> "Since the distinct list [...] [is] kept on the server and not shared with 
> the players"
> "The server knows the linkages of the commitments but does not participate as 
> a verifier "
> "If there is a problem [...] each component is assigned to another player at 
> random for verification"
> these 3 statements together seems to suggest the server is trusted to not use 
> sybils in order the compromise privacy by participating in the verification 
> process?

Equal-valued CoinJoins fix this by using a Chaumian bank, which constrains 
value transfers to specific fixed amounts.
Since an equal-valued CoinJoin uses a single fixed amount anyway, it is not an 
additional restriction.
CashFusion cannot use the same technique without dropping into something very 
much like an equal-valued CoinJoin.

Regards,
ZmnSCPxj
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