Date: Mon, 28 Jan 2019 04:14:41 +0000
To: "rhavar@protonmail.com" <rhavar@protonmail.com>,
	Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
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Subject: Re: [bitcoin-dev] bustapay BIP :: a practical sender/receiver
	coinjoin protocol
Precedence: list

Good morning Ryan and Adam,

> [UIH2 snipped]

Perhaps I am being naive, but I seem, the B2EP and similar do not need to w=
orry about UIH2.

From the github discussion:

> "UIH2": one input is larger than any output.
.
I.e. there exists an input, for all outputs, input > output
To avoid this, we should ensure that, for all inputs, there exists an outpu=
t, input < output.

From the proposal BIP:

> The receiver then adds one of his own inputs (known as the "contributed i=
nput") and increase the output that pays himself by the contributed input a=
mount.

Suppose the original transaction avoids the UIH2 (i.e. for all inputs, ther=
e exists an output, input < output).
The single added input will also avoid the UIH2, since the contributed outp=
ut value is added to the receiver output, thereby ensuring that contributed=
 input < output.

Suppose the original transaction does not avoid the UIH2.
The receiver adding their own contributed input would then have a chance th=
at the addition on the output will now cause the final transaction to avoid=
 the UIH2, since the sum of the receiver amount and the contributed input m=
ay now exceed the largest sender input.
But since there are more transactions that avoid the UIH2 than not avoid UI=
H2, the increased probability of now avoiding the UIH2 will lead to a great=
er anonymity set (especially for the sender, whose coin selection algorithm=
 might have a consistent bias that makes it create transactions that trigge=
r UIH2).

So it seems to me that the simple solution, i.e. sender uses standard coin =
selection algorithms already in use today, and receiver does not do any UIH=
2 checks at all, would be an improvement in both privacy and implementation=
 simplicity.

Regards,
ZmnSCPxj