Hi Lloyd,thanks for taking a look.
> I think your view of the uselessness of single signer adaptors is too pessimistic. The claim you make is that they "don't provide a way to create enforcement that the publication of signature on a pre-defined message will reveal a secret'' and so are useless. I think this is wrong. If I hold a secret key for X and create a signature adaptor with some encryption key Y with message m and do not create any further signatures (adaptor or otherwise) on m, then any signature on m that is published necessarily reveals the secret on Y to me. This is very useful and has already been used for years by DLCs in production.
I'm struggling with this one - say I hold privkey x for pubkey X. And I publish adaptor for a point Y (DL y) for message m, like: s' = k - y + H(R|X|m)x with k the nonce and R the nonce point.
And to get the basics clear first, if I publish s = k + H(R|X|m)x then of course the secret y is revealed.
What do you mean in saying "any signature on m that is published reveals y"? Clearly you don't mean any signature on any key (i.e. not the key X). But I also can't parse it if you mean "any signature on m using key X", because if I go ahead and publish s = k_2 + H(R_2|X|m)x, it has no algebraic relationship to the adaptor s' as defined above, right?
Yes but suppose you do *not* create another signature adaptor or otherwise on m. Since you've only generated one adaptor signature on m and no other signatures on m there is no possibility that a signature on m that appears under your key would not reveal y to you. This is an useful property in theory and in practice.
I think the point of confusion is maybe about the DLC construct? I referenced that in Section 4.2, parenthetically, because it's analogous in one sense - in MuSig(2) you're fixing R via a negotiation, whereas in Dryja's construct you're fixing R "by definition". When I was talking about single key Schnorr, I was saying that's what's missing, and thereby making them useless.
I was not referencing the DLC oracle attestation protocol - I am pointing out that DLC client implementations have been using single signer adaptor signatures as signature encryption in practice for years for the transaction signatures. There are even channel implementations using them as well as atomic swaps doing this iirc. It's a pretty useful thing!
Cheers,
LL