Good morning Billy,

  The two participants in the channel can sign a plaintext containing their node pubkeys and how much each owns

Sure, but even if both participants in the channel sign a correct statement of truth, one of the participants can send funds out in the next second, invalidating that truth. While proof of ownership of on-chain UTXOs can be seen publicly in real time if they are spent, LN transactions aren't public like that. So any balance attestation is at best only valid the instant its taken, and can't be used as verification the money is still owned by the same channel partner in the next second. 

The same problem really also exists onchain --- a thief (or "thief") who has gotten a copy of the key can sign a transaction that spends it, one second after the proof-of-reserves is made.

Really, though, the issue is that ownership of funds is conditional on *knowledge* of keys.
And *knowledge* is easily copyable.

Thus, it is possible that the funds that are "proven" to be the reserve of a custodian is actually *also* owned by someone else who has gotten to the privkeys (e.g. somebody threw a copy of it from a boating accident and a fearless scuba diver rescued it), and thus can also move the funds outside of the control of the custodian.
This condition can remain for many months or years, as well, without knowledge of the custodian clients, *or* of the custodian itself.

There is no way to prove that there is no alternate copy of the privkeys, hence "if only one could prove that he won't get into a boating accident".

On the other hand, one could argue that at least the onchain proof requires more conditions to occur, so we might plausibly live with "we cannot prove we will never get into a boating accident but we can show evidence that we live in a landlocked city far from any lakes, seas, or rivers".

Regards,
ZmnSCPxj

  a custodian Lightning node is unable to "freeze" a snapshot of its current state and make an atomic proof-of-reserves of *all* channels

That would be a neat trick. But yeah, I don't know how that would be possible. 

  I believe it is one reason why custodian proof-of-reserves is not that popular ... it does not prove that the key will not get lost

True, but at least if funds do get lost, it would be come clear far quicker. Today, an insolvent company could go many months without the public finding out. 

On Mon, Jul 5, 2021 at 5:09 PM ZmnSCPxj <ZmnSCPxj@protonmail.com> wrote:

Good morning e,

If only one could prove that he won’t get into a boating accident.

At least in the context of Lightning channels, if one party in the channel loses its key in a boating accident, the other party (assuming it is a true separate person and not a sockpuppet) has every incentive to unilaterally close the channel, which reveals the exact amounts (though not necessarily who owns which).

If the other party then uses its funds in a new proof-of-reserves, then obviously the other output of the unilateral close was the one lost in the boating accident.

On the other hand, yes, custodians losing custodied funds in boating accidents is much too common.

I believe it is one reason why custodian proof-of-reserves is not that popular --- it only proves that the funds were owned under a particular key at some snapshot of the past, it does not prove that the key will not get lost (or "lost and then salvaged by a scuba diver") later.

Regards,

ZmnSCPxj

e

On Jul 5, 2021, at 16:26, ZmnSCPxj via bitcoin-dev bitcoin-dev@lists.linuxfoundation.org wrote:

Good morning Billy,

I wonder if there would be some way to include the ability to prove balances held on the lightning network, but I suspect that isn't generally possible.

Thinking about this in terms of economic logic:

Every channel is anchored onchain, and that anchor (the funding txout) is proof of the existence, and size, of the channel.

The two participants in the channel can sign a plaintext containing their node pubkeys and how much each owns.

One of the participants should provably be the custodian.

-   If the counterparty is a true third party, it has no incentive to lie about its money.

-   Especially if the counterparty is another custodian who wants proof-of-reserves, it has every incentive to overreport, but then the first party will refuse to sign.

     It has a disincentive to underreport, and would itself refuse to sign a dishonest report that assigns more funds to the first party.

     The only case that would be acceptable to both custodians would be to honestly report their holdings in the Lightning channel.

-   If the counterparty is a sockpuppet of the custodian, then the entire channel is owned by the custodian and it would be fairly dumb of he custodian to claim to have less funds than the entire channel.

Perhaps a more practical problem is that Lightning channel states change fairly quickly, and there are possible race conditions, due to network latency (remember, both nodes need to sign, meaning both of them need to communicate with each other, thus hit by network latency and other race conditions) where a custodian Lightning node is unable to "freeze" a snapshot of its current state and make an atomic proof-of-reserves of all channels.

Regards,

ZmnSCPxj

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