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From: Erik Aronesty <erik@q32.com>
Date: Tue, 25 Jul 2023 10:12:31 -0400
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To: AdamISZ <AdamISZ@protonmail.com>, 
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Cc: Tom Trevethan <tom@commerceblock.com>
Subject: Re: [bitcoin-dev] Blinded 2-party Musig2
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posk is "proof of secret key".   so you cannot use wagner to select R

On Mon, Jul 24, 2023 at 1:59=E2=80=AFPM AdamISZ via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> @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 =3D c * a1 * x1 + r1, you expressed the idea that the challenge c
> could be given to the server, to construct s1, but since a1 =3D 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 t=
he
> 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 o=
f
> no 'one more forgery' possibility, so presumably there has to be some pro=
of
> 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 bloc=
k
> of these constructions.
>
> Sent with Proton Mail secure email.
>
> ------- 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 stil=
l
> 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 possibl=
e
> 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] :=3D R1[i] + R2[i] for all i <=3D K-1
> > R[K] :=3D R1[0] + ... + R1[K-1]
> > c[i] :=3D H(X, R[i], m[i]) for all i <=3D K.
> > Using Wagner's algorithm, choose R2[0], ..., R2[K-1] such that
> > c[0] + ... + c[K-1] =3D c[K].
> > - Send c[0], ..., c[K-1] to the server to obtain s[0], ..., s[K-1].
> > - Let
> > s[K] =3D s[0] + ... + s[K-1].
> > Then (s[K], R[K]) is a valid signature from the server, since
> > s[K]G =3D 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 =3D k1G
> > - Client sends c to the server and proves in zero knowledge that c =3D
> > SHA256(X1 + X2, R1 + R2, m).
> > - Server replies with s1 =3D k1 + c*x1
> >
> > However, this is just some quick intuition and I'm not sure if this
> actually
> > works, but maybe worth exploring.
> > _______________________________________________
> > bitcoin-dev mailing list
> > bitcoin-dev@lists.linuxfoundation.org
> > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

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<div dir=3D"ltr">posk is &quot;proof of secret key&quot;.=C2=A0 =C2=A0so yo=
u cannot use wagner to select R</div><br><div class=3D"gmail_quote"><div di=
r=3D"ltr" class=3D"gmail_attr">On Mon, Jul 24, 2023 at 1:59=E2=80=AFPM Adam=
ISZ via bitcoin-dev &lt;<a href=3D"mailto:bitcoin-dev@lists.linuxfoundation=
.org">bitcoin-dev@lists.linuxfoundation.org</a>&gt; wrote:<br></div><blockq=
uote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1p=
x solid rgb(204,204,204);padding-left:1ex">@ZmnSCPxj:<br>
<br>
yes, Wagner is the attack you were thinking of.<br>
<br>
And yeah, to avoid it, you should have the 3rd round of MuSig1, i.e. the R =
commitments.<br>
<br>
@Tom:<br>
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.<br>
<br>
Jonas&#39; reply clearly has covered a lot of what matters here, but I want=
ed to mention (using your notation):<br>
<br>
in s1 =3D c * a1 * x1 + r1, you expressed the idea that the challenge c cou=
ld be given to the server, to construct s1, but since a1 =3D H(L, X1) and L=
 is the serialization of all (in this case, 2) keys, that wouldn&#39;t work=
 for blinding the final key, right?<br>
But, is it possible that this addresses the other problem?<br>
If the server is given c1*a1 instead as the challenge for signing (with the=
ir &quot;pure&quot; key x1), then perhaps it avoids the issue? Given what&#=
39;s on the blockchain ends up allowing calculation of &#39;c&#39; and the =
aggregate key a1X1 + a2X2, is it the case that you cannot find a1 and there=
fore you cannot correlate the transaction with just the quantity &#39;c1*a1=
&#39; which the server sees?<br>
<br>
But I agree with Jonas that this is just the start, i.e. the fundamental re=
quirement of a blind signing scheme is there has to be some guarantee of no=
 &#39;one more forgery&#39; possibility, so presumably there has to be some=
 proof that the signing request is &#39;well formed&#39; (Jonas expresses i=
t 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&#39;s needed).<br>
<br>
@Jonas, Erik:<br>
&#39;posk&#39; is probably meant as &#39;proof of secret key&#39; which may=
(?) be a mixup with what is sometimes referred to in the literature as &quo=
t;KOSK&quot; (iirc they used it in FROST for example). It isn&#39;t clear t=
o me yet how that factors into this scenario, although ofc it is for sure a=
 potential building block of these constructions.<br>
<br>
Sent with Proton Mail secure email.<br>
<br>
------- Original Message -------<br>
On Monday, July 24th, 2023 at 08:12, Jonas Nick via bitcoin-dev &lt;<a href=
=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_blank">bitcoin=
-dev@lists.linuxfoundation.org</a>&gt; wrote:<br>
<br>
<br>
&gt; Hi Tom,<br>
&gt; <br>
&gt; I&#39;m not convinced that this works. As far as I know blind musig is=
 still an open<br>
&gt; research problem. What the scheme you propose appears to try to preven=
t is that<br>
&gt; the server signs K times, but the client ends up with K+1 Schnorr sign=
atures for<br>
&gt; the aggregate of the server&#39;s and the clients key. I think it&#39;=
s possible to<br>
&gt; apply a variant of the attack that makes MuSig1 insecure if the nonce =
commitment<br>
&gt; round was skipped or if the message isn&#39;t determined before sendin=
g the nonce.<br>
&gt; Here&#39;s how a malicious client would do that:<br>
&gt; <br>
&gt; - Obtain K R-values R1[0], ..., R1[K-1] from the server<br>
&gt; - Let<br>
&gt; R[i] :=3D R1[i] + R2[i] for all i &lt;=3D K-1<br>
&gt; R[K] :=3D R1[0] + ... + R1[K-1]<br>
&gt; c[i] :=3D H(X, R[i], m[i]) for all i &lt;=3D K.<br>
&gt; Using Wagner&#39;s algorithm, choose R2[0], ..., R2[K-1] such that<br>
&gt; c[0] + ... + c[K-1] =3D c[K].<br>
&gt; - Send c[0], ..., c[K-1] to the server to obtain s[0], ..., s[K-1].<br=
>
&gt; - Let<br>
&gt; s[K] =3D s[0] + ... + s[K-1].<br>
&gt; Then (s[K], R[K]) is a valid signature from the server, since<br>
&gt; s[K]G =3D R[K] + c[K]a1X1,<br>
&gt; which the client can complete to a signature for public key X.<br>
&gt; <br>
&gt; What may work in your case is the following scheme:<br>
&gt; - Client sends commitment to the public key X2, nonce R2 and message m=
 to the<br>
&gt; server.<br>
&gt; - Server replies with nonce R1 =3D k1G<br>
&gt; - Client sends c to the server and proves in zero knowledge that c =3D=
<br>
&gt; SHA256(X1 + X2, R1 + R2, m).<br>
&gt; - Server replies with s1 =3D k1 + c*x1<br>
&gt; <br>
&gt; However, this is just some quick intuition and I&#39;m not sure if thi=
s actually<br>
&gt; works, but maybe worth exploring.<br>
&gt; _______________________________________________<br>
&gt; bitcoin-dev mailing list<br>
&gt; <a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_bl=
ank">bitcoin-dev@lists.linuxfoundation.org</a><br>
&gt; <a href=3D"https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-=
dev" rel=3D"noreferrer" target=3D"_blank">https://lists.linuxfoundation.org=
/mailman/listinfo/bitcoin-dev</a><br>
_______________________________________________<br>
bitcoin-dev mailing list<br>
<a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_blank">=
bitcoin-dev@lists.linuxfoundation.org</a><br>
<a href=3D"https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev" =
rel=3D"noreferrer" target=3D"_blank">https://lists.linuxfoundation.org/mail=
man/listinfo/bitcoin-dev</a><br>
</blockquote></div>

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