Date: Tue, 19 Jul 2022 14:48:27 +0000
To: Ruben Somsen <rsomsen@gmail.com>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] How to do Proof of Micro-Burn?
Precedence: list


Good morning Ruben,

> Good evening ZmnSCPxj,
> Interesting attempt.
>
> >a * G + b * G + k * G
>
> Unfortunately I don't think this qualifies as a commitment, since one cou=
ld trivially open the "commitment" to some uncommitted value x (e.g. a is s=
et to x and b is set to a+b-x). Perhaps you were thinking of Pedersen commi=
tments (a * G + b * H + k * J)?

I believe this is only possible for somebody who knows `k`?
As mentioned, an opening here includes a signature using `b + k` as the pri=
vate key, so the signature can only be generated with knowledge of both `b`=
 and `k`.

I suppose that means that the knower of `k` is a trusted party; it is trust=
ed to only issue commitments and not generate fake ones.

> Even if we fixed the above with some clever cryptography, the crucial mer=
kle sum tree property is missing, so "double spending" a burn becomes possi=
ble.

I do not understand what this property is and how it is relevant, can you p=
lease explain this to a non-mathematician?

> You also still run into the same atomicity issue, except the risk is move=
d to the seller side, as the buyer could refuse to finalize the purchase af=
ter the on-chain commitment was made by the seller. Arguably this is worse,=
 since generally only the seller has a reputation to lose, not the buyer.

A buyer can indeed impose this cost on the seller, though the buyer then is=
 unable to get a valid opening of its commitment, as it does not know `k`.
Assuming the opening of the commitment is actually what has value (since th=
e lack of such an opening means the buyer cannot prove the commitment) then=
 the buyer has every incentive to actually pay for the opening.

Regards,
ZmnSCPxj