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From: Tom Trevethan <tom@commerceblock.com>
Date: Wed, 30 Aug 2023 11:52:05 +0100
Message-ID: <CAJvkSsfcp2shLjEdwRKtBJBO+wiV=m5X_Ys1sTwUZKZWg9-HeQ@mail.gmail.com>
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: Re: [bitcoin-dev] Blinded 2-party Musig2
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An update on progress on the development of the blinded two-party Schnorr
scheme for statechains.

As stated previously, we believe that one-more-signature and Wagner attacks
are mitigated by the client committing the values of the blinding nonce
used (labeled f) and the value of R2 used in a signing session to the
server before the server responds with their value of R1. Then each time
the generated signature is verified (in our application this is a new
statecoin owner), the verifier retrieves the commitments and blinded
challenge value from the server (c, SHA256(f) and SHA256(R2)) and f and R2
from the co-signer, and verifies that the blinded challenge value c =3D f +
SHA256(X, R1 + R2 + f.X, m) and the commitments match f,R2. This ensures
the signer cannot have chosen the values of f and R2 after the value of R1
is randomly generated by the server.

This scheme has been implemented in a forked version of the secp256k1-zkp
library: https://github.com/ssantos21/secp256k1-zkp where a new function
has been added secp256k1_blinded_musig_nonce_process (
https://github.com/ssantos21/secp256k1-zkp/blob/ed08ad7603f211fdf39b5f6db9d=
7e99cf048a56c/src/modules/musig/session_impl.h#L580
) which is required for the client generation of the blinded challenge
value.

One issue that came up and had to be solved was ensuring the R (curve
point) is even (in MuSig2 the secret nonce is negated if R is odd) with the
point f.X added (and f committed to). We will add a complete explanation of
this to the updated spec.

The scheme is implemented in a blind server:
https://github.com/ssantos21/blinded-musig-sgx-server

And client:
https://github.com/ssantos21/blinded-musig2-client

Any comments or questions appreciated.

On Mon, Aug 7, 2023 at 1:55=E2=80=AFAM Tom Trevethan <tom@commerceblock.com=
> wrote:

> A follow up to this, I have updated the blinded statechain protocol
> description to include the mitigation to the Wagner attack by requiring t=
he
> server to send R1 values only after commitments made to the server of the
> R2 values used by the user, and that all the previous computed c values a=
re
> verified by each new statecoin owner.
> https://github.com/commerceblock/mercury/blob/master/layer/protocol.md
>
> Essentially, the attack is possible because the server cannot verify that
> the blinded challenge (c) value it has been sent by the user has been
> computed honestly (i.e. c =3D SHA256(X1 + X2, R1 + R2, m) ), however this=
 CAN
> be verified by each new owner of a statecoin for all the previous
> signatures.
>
> Each time an owner cooperates with the server to generate a signature on =
a
> backup tx, the server will require that the owner send a commitment to
> their R2 value: e.g. SHA256(R2). The server will store this value before
> responding with it's R1 value. This way, the owner cannot choose the valu=
e
> of R2 (and hence c).
>
> When the statecoin is received by a new owner, they will receive ALL
> previous signed backup txs for that coin from the sender, and all the
> corresponding R2 values used for each signature. They will then ask the
> server (for each previous signature), the commitments SHA256(R2) and the
> corresponding server generated R1 value and c value used. The new owner
> will then verify that each backup tx is valid, and that each c value was
> computed c =3D SHA256(X1 + X2, R1 + R2, m)  and each commitment equals
> SHA256(R2). This ensures that a previous owner could not have generated
> more valid signatures than the server has partially signed.
>
> On Thu, Jul 27, 2023 at 2:25=E2=80=AFPM Tom Trevethan <tom@commerceblock.=
com>
> wrote:
>
>>
>> On Thu, Jul 27, 2023 at 9:08=E2=80=AFAM Jonas Nick <jonasdnick@gmail.com=
> wrote:
>>
>>> No, proof of knowledge of the r values used to generate each R does not
>>> prevent
>>> Wagner's attack. I wrote
>>>
>>>  >   Using Wagner's algorithm, choose R2[0], ..., R2[K-1] such that
>>>  >    c[0] + ... + c[K-1] =3D c[K].
>>>
>>> You can think of this as actually choosing scalars r2[0], ..., r2[K-1]
>>> and
>>> define R2[i] =3D r2[i]*G. The attacker chooses r2[i]. The attack wouldn=
't
>>> make
>>> sense if he didn't.
>>>
>>

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Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">An update on progress on the development of the blinded tw=
o-party Schnorr scheme for statechains.=C2=A0<div><br></div><div>As stated =
previously, we believe that one-more-signature and Wagner attacks are mitig=
ated by the client=C2=A0committing=C2=A0the values of the blinding nonce us=
ed (labeled f) and the value of R2 used in a signing session to the server =
before the server responds with their value of R1. Then each time the gener=
ated signature is verified (in our application this is a new statecoin owne=
r), the verifier retrieves the commitments and blinded challenge value from=
 the server (c, SHA256(f) and SHA256(R2)) and f and R2 from the co-signer, =
and verifies that the blinded challenge value c =3D f=C2=A0<a class=3D"gmai=
l_plusreply" id=3D"plusReplyChip-0">+</a> SHA256(X, R1 + R2 + f.X, m) and t=
he commitments match f,R2. This ensures the signer cannot have chosen the v=
alues of f and R2 after the value of R1 is randomly generated by the server=
.=C2=A0=C2=A0</div><div><br></div><div>This scheme has been implemented in =
a forked version of the secp256k1-zkp library: <a href=3D"https://github.co=
m/ssantos21/secp256k1-zkp">https://github.com/ssantos21/secp256k1-zkp</a> w=
here a new function has been added secp256k1_blinded_musig_nonce_process ( =
<a href=3D"https://github.com/ssantos21/secp256k1-zkp/blob/ed08ad7603f211fd=
f39b5f6db9d7e99cf048a56c/src/modules/musig/session_impl.h#L580">https://git=
hub.com/ssantos21/secp256k1-zkp/blob/ed08ad7603f211fdf39b5f6db9d7e99cf048a5=
6c/src/modules/musig/session_impl.h#L580</a> ) which is required for the cl=
ient generation of the blinded challenge value.=C2=A0</div><div><br></div><=
div>One issue that came up and had to be solved was ensuring the R (curve p=
oint) is even (in MuSig2 the secret nonce is negated if R is odd) with the =
point f.X added (and f committed to). We will add a complete explanation of=
 this to the updated spec.=C2=A0</div><div><br></div><div>The scheme is imp=
lemented=C2=A0in a blind server:</div><div><a href=3D"https://github.com/ss=
antos21/blinded-musig-sgx-server">https://github.com/ssantos21/blinded-musi=
g-sgx-server</a><br></div><div><br></div><div>And client:</div><div><a href=
=3D"https://github.com/ssantos21/blinded-musig2-client">https://github.com/=
ssantos21/blinded-musig2-client</a><br></div><div><br></div><div>Any commen=
ts or questions appreciated.=C2=A0</div></div><br><div class=3D"gmail_quote=
"><div dir=3D"ltr" class=3D"gmail_attr">On Mon, Aug 7, 2023 at 1:55=E2=80=
=AFAM Tom Trevethan &lt;<a href=3D"mailto:tom@commerceblock.com">tom@commer=
ceblock.com</a>&gt; wrote:<br></div><blockquote class=3D"gmail_quote" style=
=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding=
-left:1ex"><div dir=3D"ltr"><div>A follow up to this, I have updated the bl=
inded statechain protocol description to include the mitigation to the Wagn=
er attack by requiring=C2=A0the server to send R1 values only after commitm=
ents made to the server of the R2 values used by the user, and that all the=
 previous computed c values are verified by each new statecoin=C2=A0owner.=
=C2=A0</div><div><a href=3D"https://github.com/commerceblock/mercury/blob/m=
aster/layer/protocol.md" target=3D"_blank">https://github.com/commerceblock=
/mercury/blob/master/layer/protocol.md</a></div><div><br></div><div>Essenti=
ally, the attack is possible because the server cannot verify that the blin=
ded challenge (c) value it has been sent by the user has been computed hone=
stly=C2=A0(i.e. c =3D SHA256(X1 + X2, R1 + R2, m) ), however this CAN be ve=
rified by each new owner of a statecoin=C2=A0for all the previous signature=
s.=C2=A0</div><div><br></div><div>Each time an owner cooperates with the se=
rver to generate a signature on a backup tx, the server will require that t=
he owner send a commitment to their R2 value: e.g. SHA256(R2). The server w=
ill store this value before responding with it&#39;s R1 value. This way, th=
e owner cannot choose the value of R2 (and hence c).=C2=A0</div><div><br></=
div><div>When the statecoin is received by a new owner, they will receive A=
LL previous signed backup txs for that coin from the sender, and all the co=
rresponding R2 values used for each signature. They will then ask the serve=
r (for each previous signature), the commitments SHA256(R2) and the corresp=
onding server generated R1 value and c value used. The new owner will then =
verify that each backup tx is valid, and that each c value was computed c =
=3D SHA256(X1 + X2, R1 + R2, m)=C2=A0 and each commitment equals SHA256(R2)=
. This ensures that a previous owner could not have generated more valid si=
gnatures than the server has partially signed.=C2=A0</div><div><br></div><d=
iv class=3D"gmail_quote"><div dir=3D"ltr" class=3D"gmail_attr">On Thu, Jul =
27, 2023 at 2:25=E2=80=AFPM Tom Trevethan &lt;<a href=3D"mailto:tom@commerc=
eblock.com" target=3D"_blank">tom@commerceblock.com</a>&gt; wrote:<br></div=
><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border=
-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr"><div cl=
ass=3D"gmail_quote"><div dir=3D"ltr"><div><br></div><div class=3D"gmail_quo=
te"><div dir=3D"ltr" class=3D"gmail_attr">On Thu, Jul 27, 2023 at 9:08=E2=
=80=AFAM Jonas Nick &lt;<a href=3D"mailto:jonasdnick@gmail.com" target=3D"_=
blank">jonasdnick@gmail.com</a>&gt; wrote:<br></div><blockquote class=3D"gm=
ail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,=
204,204);padding-left:1ex">No, proof of knowledge of the r values used to g=
enerate each R does not prevent<br>
Wagner&#39;s attack. I wrote<br>
<br>
=C2=A0&gt;=C2=A0 =C2=A0Using Wagner&#39;s algorithm, choose R2[0], ..., R2[=
K-1] such that<br>
=C2=A0&gt;=C2=A0 =C2=A0 c[0] + ... + c[K-1] =3D c[K].<br>
<br>
You can think of this as actually choosing scalars r2[0], ..., r2[K-1] and<=
br>
define R2[i] =3D r2[i]*G. The attacker chooses r2[i]. The attack wouldn&#39=
;t make<br>
sense if he didn&#39;t.<br>
</blockquote></div></div>
</div></div>
</blockquote></div></div>
</blockquote></div>

--0000000000008280ba060421b835--