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From: Lloyd Fournier <lloyd.fourn@gmail.com>
Date: Mon, 5 Apr 2021 10:27:50 +1000
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To: "David A. Harding" <dave@dtrt.org>, 
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: Re: [bitcoin-dev] PSA: Taproot loss of quantum protections
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On Tue, 16 Mar 2021 at 11:25, David A. Harding via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

>
> I curious about whether anyone informed about ECC and QC
> knows how to create output scripts with lower difficulty that could be
> used to measure the progress of QC-based EC key cracking.  E.g.,
> NUMS-based ECDSA- or taproot-compatible scripts with a security strength
> equivalent to 80, 96, and 112 bit security.


Hi Dave,

This is actually relatively easy if you are willing to use a trusted setup.
The trusted party takes a secp256k1 secret key and verifiably encrypt it
under a NUMS public key from the weaker group. Therefore if you can crack
the weaker group's public key you get the secp256k1 secret key.
Camenisch-Damgard[1] cut-and-choose verifiable encryption works here.
People then pay the secp256k1 public key funds to create the bounty. As
long as the trusted party deletes the secret key afterwards the scheme is
secure.

Splitting the trusted setup among several parties where only one of them
needs to be honest looks doable but would take some engineering and
analysis work.

[1] https://link.springer.com/content/pdf/10.1007/3-540-44448-3_25.pdf

Cheers,

LL

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<div dir=3D"ltr"><div dir=3D"ltr" class=3D"gmail_attr">On Tue, 16 Mar 2021 =
at 11:25, David A. Harding via bitcoin-dev &lt;<a href=3D"mailto:bitcoin-de=
v@lists.linuxfoundation.org">bitcoin-dev@lists.linuxfoundation.org</a>&gt; =
wrote:<br></div><div class=3D"gmail_quote"><blockquote class=3D"gmail_quote=
" style=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);=
padding-left:1ex"><br>I curious about whether anyone informed about ECC and=
 QC<br>
knows how to create output scripts with lower difficulty that could be<br>
used to measure the progress of QC-based EC key cracking.=C2=A0 E.g.,<br>
NUMS-based ECDSA- or taproot-compatible scripts with a security strength<br=
>
equivalent to 80, 96, and 112 bit security.</blockquote><div><br></div><div=
>Hi Dave,</div><div><br></div><div>This is actually relatively easy if you =
are willing to use a trusted setup. The trusted party takes a secp256k1 sec=
ret key and verifiably encrypt it under a NUMS public key from the weaker g=
roup. Therefore if you can crack the weaker group&#39;s public key you get =
the secp256k1 secret key. Camenisch-Damgard[1] cut-and-choose verifiable en=
cryption works here.</div><div>People then pay the secp256k1 public key fun=
ds to create the bounty. As long as the trusted party deletes the secret ke=
y afterwards the scheme is secure.<br></div><div><br></div><div>Splitting t=
he trusted setup among several parties where only one of them needs to be h=
onest looks doable but would take some engineering and analysis work.<br></=
div><div><br></div><div>[1] <a href=3D"https://link.springer.com/content/pd=
f/10.1007/3-540-44448-3_25.pdf">https://link.springer.com/content/pdf/10.10=
07/3-540-44448-3_25.pdf</a></div><div><br></div><div>Cheers,</div><div><br>=
</div><div>LL<br></div><div>=C2=A0<br></div></div></div>

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