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From: moonsettler <moonsettler@protonmail.com>
To: "bitcoin-dev@lists.linuxfoundation.org"
	<bitcoin-dev@lists.linuxfoundation.org>
Subject: [bitcoin-dev]  Blinded 2-party Musig2
Date: Wed, 26 Jul 2023 09:44:50 +0000	[thread overview]
Message-ID: <O3LTbUbjNa3SLUfJzSKDNLBCIhED_6rdOcmgLpYB9byX6HBVg3BMu3hrvY37fH4SGL8th8oJaVV6_ogl_ZOA0qTXgENq8xqQNSRB-VsHem4=@protonmail.com> (raw)
In-Reply-To: <b770096c-e8c4-70f7-8cd7-d74c27181413@gmail.com>

Hi All,

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

Signing:

X = X1 + X2
K1 = k1G
K2 = k2G

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

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

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

Verification:

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

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

Been trying to get a review on this for a while, please let me know if I got 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.
> 
> 
> Actually, it seems like a blinding step is missing. Assume the server (party 1)
> received some c during the signature protocol. Can't the server scan the
> blockchain for signatures, compute corresponding hashes c' = H(R||X||m) as in
> signature verification and then check c == c'? If true, then the server has the
> preimage for the c received from the client, including m.
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev


  parent reply	other threads:[~2023-07-26  9:45 UTC|newest]

Thread overview: 34+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2023-07-24  7:46 [bitcoin-dev] Blinded 2-party Musig2 Tom Trevethan
2023-07-24 10:50 ` ZmnSCPxj
2023-07-24 14:25   ` Erik Aronesty
2023-07-24 16:08     ` Tom Trevethan
2023-07-24 15:57   ` Tom Trevethan
2023-07-24 14:12 ` Jonas Nick
2023-07-24 14:40   ` Erik Aronesty
2023-07-24 15:40     ` Jonas Nick
2023-07-24 16:51   ` AdamISZ
2023-07-25 14:12     ` Erik Aronesty
2023-07-25 16:05       ` Tom Trevethan
2023-07-26  4:09         ` Erik Aronesty
2023-07-26 17:40           ` Andrew Poelstra
2023-07-26 19:59           ` Jonas Nick
2023-07-26 20:35             ` Tom Trevethan
2023-07-26 22:06               ` Erik Aronesty
2023-07-27  2:54                 ` Lloyd Fournier
2023-07-27  8:07               ` Jonas Nick
     [not found]                 ` <CAJvkSsfa8rzbwXiatZBpwQ6d4d94yLQifK8gyq3k-rq_1SH4OQ@mail.gmail.com>
2023-07-27 13:25                   ` [bitcoin-dev] Fwd: " Tom Trevethan
2023-08-07  0:55                     ` [bitcoin-dev] " Tom Trevethan
2023-08-08 17:44                       ` moonsettler
2023-08-09 15:14                         ` Tom Trevethan
2023-08-10  3:30                           ` Lloyd Fournier
2023-08-10 11:59                             ` Tom Trevethan
2023-08-14  6:31                               ` Lloyd Fournier
2023-08-30 10:52                       ` Tom Trevethan
2023-07-24 15:39 ` Jonas Nick
2023-07-24 16:22   ` Tom Trevethan
2023-07-26  9:44   ` moonsettler [this message]
2023-07-26 14:59     ` Jonas Nick
2023-07-26 19:19     ` AdamISZ
2023-07-26 19:28       ` moonsettler
2023-07-27  5:51         ` AdamISZ
     [not found] <mailman.125690.1690381971.956.bitcoin-dev@lists.linuxfoundation.org>
2023-07-26 16:32 ` Tom Trevethan

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