Date: Wed, 26 Jul 2023 09:44:50 +0000
To: "bitcoin-dev@lists.linuxfoundation.org"
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From: moonsettler <moonsettler@protonmail.com>
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Subject: [bitcoin-dev]  Blinded 2-party Musig2
Precedence: list

Hi All,

I believe it's fairly simple to solve the blinding (sorry for the bastard n=
otation!):

Signing:

X =3D X1 + X2
K1 =3D k1G
K2 =3D k2G

R =3D K1 + K2 + bX
e =3D hash(R||X||m)

e' =3D e + b
s =3D (k1 + e'*x1) + (k2 + e'*x2)
s =3D (k1 + k2 + b(x1 + x2)) + e(x1 + x2)

sG =3D (K1 + K2 + bX) + eX
sG =3D R + eX

Verification:

Rv =3D sG - eX
ev =3D hash(R||X||m)
e ?=3D ev

https://gist.github.com/moonsettler/05f5948291ba8dba63a3985b786233bb

Been trying to get a review on this for a while, please let me know if I go=
t it wrong!

BR,
moonsettler


------- Original Message -------
On Monday, July 24th, 2023 at 5:39 PM, Jonas Nick via bitcoin-dev <bitcoin-=
dev@lists.linuxfoundation.org> wrote:


> > Party 1 never learns the final value of (R,s1+s2) or m.
>=20
>=20
> Actually, it seems like a blinding step is missing. Assume the server (pa=
rty 1)
> received some c during the signature protocol. Can't the server scan the
> blockchain for signatures, compute corresponding hashes c' =3D H(R||X||m)=
 as in
> signature verification and then check c =3D=3D c'? If true, then the serv=
er has the
> preimage for the c received from the client, including m.
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