Thanks for the replies. As I understand it, the v=2 nonces signing protocol of musig2 prevents the Wagner attack. Also, that the challenge value c must be blinded from the server to prevent the server from being able to determine the signature from the on-chain state.
In addition, in order to update the server (party 1) keyshare when a statecoin is transferred between users, the key aggregation coefficient must be set to 1 for each key. The purpose of this coefficient in the Musig2 protocol is to prevent 'rogue key attacks' where one party can choose a public key derived from both their own secret key and the inverse of the other party's public key giving them the ability to unilaterally produce a valid signature over the aggregate key. However this can be prevented by the party producing a proof of knowledge of the private key corresponding to their supplied public key. This can be a signature, which is produced in any case by signing the statechain state in the mercury protocol. This signature must be verified by the receiver of a coin (who must also verify the server pubkey combines with the sender pubkey to get the coin address) which proves that the server is required to co-sign to generate any signature for this address.
Here is a modified protocol:
Keygen:
Server generates private key x1 and public key X1 = x1.G and sends X1 to user (party 2)
User generates private key x2 and public key X2 = x2.G and (random) blinding nonce z and computes the aggregate public key X = z.(X1 + X2) (server never learns of X, X2 or z).
Signing:
Server generates nonces r11 and r12 and R11 = r11.G and R12 = r12.G and sends R11 and R12 to the user.
User generates nonces r21 and r22 and R21 = r21.G and R22 = r22.G
User computes R1 = R11 + R21 and R2 = R12 + R22 and b = H(X,(R1,R2),m) and R = R1 + b.R2 and c = (X,R,m)
User sends the values y = cz and b to the server.
Server computes s1 = yx1 + r11 + br12 and sends it to the user.
User computes s2 = yx2 + r21 + br22 and s = s1 + s2 and signature (s,R)
Transfer:
In a statecoin transfer, when receiving a statecoin, in order to verify that the coin address (i.e. aggregate public key) is shared correctly between the previous owner and the server, the client must verify the following:
Retrieve the CURRENT public key from the server for this coin X1.
Retrieve the public key X2 and the blinding nonce z from the sender.
Verify that z.X1 + X2 = P the address of the statecoin.
Verify that the sender has the private key used to generate X2: this is done by verifying the statechain signature over the receiver public key X3 from X2.
This proves that the address P was generated (aggregated) with the server and can only be signed with cooperation with the server, i.e. no previous owner can hold the full key.
In order to update the key shares on transfer, the following protocol can be used:
Server (party 1) generates a random blinding nonce e and sends it to user.
User adds their private key to the nonce: t1 = e + x2
Client sends t1 and z to the reciever as part of transfer_msg (encrypted with the receiver public key X3 = x3.G).
Receiver client decrypts t1 and then subtracts their private key x3: t2 = e + x2 - x3.
Receiver client sends t2 to the server as part of transfer_receiver.
Server the updates the private key share x1_2 = x1 + t2 - e = x1 + e + x2 - x3 - e = x1 + x2 - x3
So now, x1_2 + x3 (the aggregation of the new server key share with the new client key share) is equal to x1 + x2 (the aggregation of the old server key share with the old client key share).
The server deletes x1.
On Tue, Jul 25, 2023 at 3:12 PM Erik Aronesty <
erik@q32.com> wrote:
posk is "proof of secret key". so you cannot use wagner to select R
@ZmnSCPxj:
yes, Wagner is the attack you were thinking of.
And yeah, to avoid it, you should have the 3rd round of MuSig1, i.e. the R commitments.
@Tom:
As per above it seems you were more considering MuSig1 here, not MuSig2. At least in this version. So you need the initial commitments to R.
Jonas' reply clearly has covered a lot of what matters here, but I wanted to mention (using your notation):
in s1 = c * a1 * x1 + r1, you expressed the idea that the challenge c could be given to the server, to construct s1, but since a1 = H(L, X1) and L is the serialization of all (in this case, 2) keys, that wouldn't work for blinding the final key, right?
But, is it possible that this addresses the other problem?
If the server is given c1*a1 instead as the challenge for signing (with their "pure" key x1), then perhaps it avoids the issue? Given what's on the blockchain ends up allowing calculation of 'c' and the aggregate key a1X1 + a2X2, is it the case that you cannot find a1 and therefore you cannot correlate the transaction with just the quantity 'c1*a1' which the server sees?
But I agree with Jonas that this is just the start, i.e. the fundamental requirement of a blind signing scheme is there has to be some guarantee of no 'one more forgery' possibility, so presumably there has to be some proof that the signing request is 'well formed' (Jonas expresses it below as a ZKP of a SHA2 preimage .. it does not seem pretty but I agree that on the face of it, that is what's needed).
@Jonas, Erik:
'posk' is probably meant as 'proof of secret key' which may(?) be a mixup with what is sometimes referred to in the literature as "KOSK" (iirc they used it in FROST for example). It isn't clear to me yet how that factors into this scenario, although ofc it is for sure a potential building block of these constructions.
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------- Original Message -------
On Monday, July 24th, 2023 at 08:12, Jonas Nick via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
> Hi Tom,
>
> I'm not convinced that this works. As far as I know blind musig is still an open
> research problem. What the scheme you propose appears to try to prevent is that
> the server signs K times, but the client ends up with K+1 Schnorr signatures for
> the aggregate of the server's and the clients key. I think it's possible to
> apply a variant of the attack that makes MuSig1 insecure if the nonce commitment
> round was skipped or if the message isn't determined before sending the nonce.
> Here's how a malicious client would do that:
>
> - Obtain K R-values R1[0], ..., R1[K-1] from the server
> - Let
> R[i] := R1[i] + R2[i] for all i <= K-1
> R[K] := R1[0] + ... + R1[K-1]
> c[i] := H(X, R[i], m[i]) for all i <= K.
> Using Wagner's algorithm, choose R2[0], ..., R2[K-1] such that
> c[0] + ... + c[K-1] = c[K].
> - Send c[0], ..., c[K-1] to the server to obtain s[0], ..., s[K-1].
> - Let
> s[K] = s[0] + ... + s[K-1].
> Then (s[K], R[K]) is a valid signature from the server, since
> s[K]G = R[K] + c[K]a1X1,
> which the client can complete to a signature for public key X.
>
> What may work in your case is the following scheme:
> - Client sends commitment to the public key X2, nonce R2 and message m to the
> server.
> - Server replies with nonce R1 = k1G
> - Client sends c to the server and proves in zero knowledge that c =
> SHA256(X1 + X2, R1 + R2, m).
> - Server replies with s1 = k1 + c*x1
>
> However, this is just some quick intuition and I'm not sure if this actually
> works, but maybe worth exploring.
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