If 'x' is public, that makes it identifiable and privacy-losing across inputs.

To avoid "re-use" I suppose you'd want to sign some message like `HMAC("ownership proof", H(A || x) )` instead. Otherwise any signature you make using `A` ends up being used as a proof you don't know the input(this seems like just details but to be more clear)...

To reiterate:

Sign `HMAC("ownership proof", H(A || x) )` using `A`. Public verifiers see `HMAC("ownership proof", some_random_hash_connected_to_A )` and the HWW that owns that input can recreate `some_random_hash_connected_to_A` by `H(A || x) )`

On Mon, Aug 21, 2017 at 2:36 PM, Jochen Hoenicke <hoenicke@gmail.com> wrote:

On 21.08.2017 20:12, Greg Sanders via bitcoin-dev wrote:
> To fix this I consulted with andytoshi and got something we think works
> for both cases:
>
> 1) When a signing device receives a partially signed transaction, all
> inputs must come with a ownership proof:
> - For the input at address A, a signature over H(A || x) using the key
> for A. 'x' is some private fixed key that only the signing device
> knows(most likely some privkey along some unique bip32 path).
> - For each input ownership proof, the HW wallet validates each signature
> over the hashed message, then attempts to "decode" the hash by applying
> its own 'x'. If the hash doesn't match, it cannot be its own input.
> - Sign for every input that is yours

Interesting, basically a proof of non-ownership :), a proof that the
hardware wallet doesn't own the address.

But shouldn't x be public, so that the device can verify the signature?
Can you expand on this, what is exactly signed with which key and how is
it checked?

One also has to make sure that it's not possible to reuse signatures as
ownership proof that were made for a different purpose.

Jochen