From: ZmnSCPxj <ZmnSCPxj@protonmail•com>
To: "David A. Harding" <dave@dtrt•org>,
Bitcoin Protocol Discussion
<bitcoin-dev@lists•linuxfoundation.org>
Cc: lightning-dev <lightning-dev@lists•linuxfoundation.org>
Subject: Re: [bitcoin-dev] [Lightning-dev] RBF Pinning with Counterparties and Competing Interest
Date: Sat, 20 Jun 2020 16:01:16 +0000 [thread overview]
Message-ID: <wRX9uiX_fFrjZvlmgx3Sj64VA3DdXakJZJq2_7DHJWIS7QBlphgpaBDdm4SjdY4aij5pESsumww8iJw8QZe5mO8bPgpYFyp6eImF2xbaXR4=@protonmail.com> (raw)
In-Reply-To: <20200620103647.g62srlcxbjqpaqj6@ganymede>
Good morning Dave,
> ZmnSCPxj noted that pay-to-preimage doesn't work with PTLCs.[2] I was
> hoping one of Bitcoin's several inventive cryptographers would come
> along and describe how someone with an adaptor signature could use that
> information to create a pubkey that could be put into a transaction with
> a second output that OP_RETURN included the serialized adaptor
> signature. The pubkey would be designed to be spendable by anyone with
> the final signature in a way that revealed the hidden value to the
> pubkey's creator, allowing them to resolve the PTLC. But if that's
> fundamentally not possible, I think we could advocate for making
> pay-to-revealed-adaptor-signature possible using something like
> OP_CHECKSIGFROMSTACK.[3]
Not a cryptographer, I just play one on the Internet, but maybe the pay-for-signature construction could work...?
Assuming a PTLC has a pointlocked branch, which involves signing with MuSig(A, B).
A offers to B the amount if B reveals the secret `t` behind `T = t * G`; A knows `T` but not `t`.
This is done by B handing over `R[B]` and `s'[B]`:
R = R[A] + R[B] + T
s'[B] = r[B] + h(MuSig(A, B) | R | m) * b
Then A provides its partial signature to B.
s[A] = r[A] + h(MuSig(A, B) | R | m) * a
B has to complete the signature by:
s = s[A] + s'[B] + t
Since A knows both `s[A]` and `s'[B]`, once it knows `s`, it can compute `t`.
Now, we can massage the equation for `s`:
s = r[A] + h(MuSig(A, B) | R | m) * a + r[B] + h(MuSig(A, B) | R | m) * b + t
; multiply both sides by G
s * G = r[A] * G + h(MuSig(A, B) | R | m) * a * G + r[B] * G + h(MuSig(A, B) | R | m) * b * G + t * G
; replace with public points
s * G = R[A] + h(MuSig(A, B) | R | m) * A + R[B] + h(MuSig(A, B) | R | m) * B + T
Note that A can compute `s * G` above, because it generated `R[A]`, was given `R[B]` and `T`, and knows who `A` and `B` are.
So what A needs to do is to offer a fund that can only be claimed by leaking knowledge of `s` behind `s * G`.
A can do this by creating a new keypair `A[p4s] = a[p4s] * G` and putting a fund into it.
Then A generates an `R[A][p4s] = r[A][p4s] * G`, and computes:
R[p4s] = R[A][p4s] + s * G
s'[A][p4s] = r[A][p4s] + h(A | R[p4s] | m) * a[p4s]
The signed message could be a signature to `SIGHASH_NONE`, finally an actual use for that flag.
A reveals publicly (in an `OP_RETURN` as you suggest):
* `R[A][p4s]`
* `s * G`
* `s'[A][p4s]`
* `A[p4s]` - Already the Schnorr output pubkey.
In order to complete the above signature, a third party C has to learn `s` from B.
The third party has to scan every onchain 1-of-1 signature for an `s` that matches `s * G`, so there is greater processing (point multiplies are more expensive than hashes, also there are more 1-of-1s).
But once learned, the third party can complete the signature and claim the funds.
And A then learns `s`, from which it can derive `t`.
The third party learns about which channel (i.e. the UTXO that was spent to create the PTLC in the first place), but never learns `t` or `T`, which is a small but nice privacy bonus.
Regards,
ZmnSCPxj
next prev parent reply other threads:[~2020-06-20 16:01 UTC|newest]
Thread overview: 37+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-04-21 2:43 [bitcoin-dev] " Matt Corallo
2020-04-22 4:12 ` [bitcoin-dev] [Lightning-dev] " ZmnSCPxj
2020-04-22 4:18 ` Olaoluwa Osuntokun
2020-04-22 6:08 ` ZmnSCPxj
2020-04-22 8:01 ` Antoine Riard
2020-04-22 8:55 ` Bastien TEINTURIER
2020-04-22 23:05 ` Olaoluwa Osuntokun
2020-04-22 23:11 ` Olaoluwa Osuntokun
2020-04-22 16:56 ` Matt Corallo
2020-04-22 4:13 ` [bitcoin-dev] " Olaoluwa Osuntokun
2020-04-22 11:51 ` David A. Harding
2020-04-27 21:26 ` Rusty Russell
2020-04-22 16:50 ` Matt Corallo
2020-04-22 23:13 ` Olaoluwa Osuntokun
2020-04-22 23:20 ` Matt Corallo
2020-04-22 23:27 ` Olaoluwa Osuntokun
2020-04-23 1:10 ` Matt Corallo
2020-04-23 4:50 ` [bitcoin-dev] [Lightning-dev] " ZmnSCPxj
2020-04-23 6:21 ` Matt Corallo
2020-04-23 12:46 ` ZmnSCPxj
2020-04-23 22:47 ` Matt Corallo
2020-06-19 7:44 ` Bastien TEINTURIER
2020-06-19 19:58 ` David A. Harding
2020-06-19 20:52 ` David A. Harding
2020-06-20 8:54 ` Bastien TEINTURIER
2020-06-20 10:36 ` David A. Harding
2020-06-20 16:01 ` ZmnSCPxj [this message]
2020-06-21 2:10 ` ZmnSCPxj
2020-06-22 7:35 ` Bastien TEINTURIER
2020-06-22 8:15 ` ZmnSCPxj
2020-06-22 8:25 ` Bastien TEINTURIER
2020-06-24 8:32 ` Matt Corallo
2020-04-23 1:18 ` [bitcoin-dev] " Jeremy
2020-04-22 18:24 ` David A. Harding
2020-04-22 19:03 ` Antoine Riard
2020-04-22 20:28 ` David A. Harding
2020-04-22 22:53 Matt Corallo
2020-04-23 9:59 ` David A. Harding
2020-04-23 12:52 ` [bitcoin-dev] [Lightning-dev] " ZmnSCPxj
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