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From: Erik Aronesty <erik@q32.com>
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Multiparty signatures
Date: Mon, 9 Jul 2018 11:02:30 -0400	[thread overview]
Message-ID: <CAJowKgJ3K=wmCEtoZXJZhrnnA8XJcHYg788KP+7MCeP4Mxf-0w@mail.gmail.com> (raw)
In-Reply-To: <CAJowKg+=7nS4gNmtc8a4-2cu1uCOPqxjfchFwDVqUciKNMUYWQ@mail.gmail.com>

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Actually, it looks like in order to compute a multiparty signature you will
need to broadcast shares of r first, so it's not offline :(

It is still seems, to me, to be a simpler mechanism than musig - with
security assumptions that match the original Schnorr construction more
closely, and should therefore be easier to prove secure in a multiparty
context.

Shamir/Schnorr threshold multi-signature scheme:

Each party:

- Has a public key g*x', where x' is their private key, and where H(g*x)
can be considered their public index for the purposes of Shamir polynomial
interpolation
- Rolls a random k' and compute r' = g*k'
- Broadcast r' as a share
- Computes g*k, via lagrange interpolation across shares.   At this point k
is not known to any party unless Shamir is vulnerable or DL is not hard
- Computes e' = H(M) * r'
- Computes s' = k'-x*e'
- Share of signature is (s', e')

Verification is the same as Scnhorr, but only after using interpolation to
get the needed (s, e, g*x) from shares of s', e' and g*x':

- Using lagrange interpolation, compute the public key g*x
- Again, using lagrange interpolation, compute (s, e)
- Verify the signature as per standard Schnorr

Security assumptions:

 - Because this is not additive, and instead we are using Shamir
combination, the additional blinding and masking steps of musig are not
needed to create a secure scheme.
 - The scheme is the same as Schnorr otherwise
 - The only thing to prove is that H(M) * r does not reveal any information
about k ... which relies on the same DL assumptions as Bitcoin itself
 - Overall, this seems, to me at least, to have a smaller attack surface
because there's fewer moving parts


On Mon, Jul 9, 2018 at 8:24 AM, Erik Aronesty <erik@q32.com> wrote:

> I was hoping that nobody in this group saw an obvious problem with it then
> I'd sit down and try to write up a paper.
>
> Not that hard to just reuse the work done on schnorr.   And demonstrate
> that there are no additional assumptions.
>
> On Mon, Jul 9, 2018, 12:40 AM Pieter Wuille <pieter.wuille@gmail.com>
> wrote:
>
>> On Sun, Jul 8, 2018, 21:29 Erik Aronesty <erik@q32.com> wrote:
>>
>>> Because it's non-interactive, this construction can produce multisig
>>> signatures offline.   Each device produces a signature using it's own
>>> k-share and x-share.   It's only necessary to interpolate M of n shares.
>>>
>>> There are no round trips.
>>>
>>> The security is Shamir + discrete log.
>>>
>>> it's just something I've been tinkering with and I can't see an obvious
>>> problem.
>>>
>>> It's basically the same as schnorr, but you use a threshold hash to fix
>>> the need to be online.
>>>
>>> Just seems more useful to me.
>>>
>>
>> That sounds very useful if true, but I don't think we should include
>> novel cryptography in Bitcoin based on your not seeing an obvious problem
>> with it.
>>
>> I'm looking forward to seeing a more complete writeup though.
>>
>> Cheers,
>>
>> --
>> Pieter
>>
>>
>>

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  parent reply	other threads:[~2018-07-09 15:02 UTC|newest]

Thread overview: 26+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2018-07-08 14:19 [bitcoin-dev] Multiparty signatures Erik Aronesty
2018-07-08 15:16 ` Tim Ruffing
2018-07-08 18:23   ` Erik Aronesty
2018-07-08 21:01   ` Gregory Maxwell
2018-07-09  0:27     ` Erik Aronesty
2018-07-09  2:33       ` Pieter Wuille
2018-07-09  4:29         ` Erik Aronesty
2018-07-09  4:39           ` Pieter Wuille
     [not found]             ` <CAJowKg+=7nS4gNmtc8a4-2cu1uCOPqxjfchFwDVqUciKNMUYWQ@mail.gmail.com>
2018-07-09 15:02               ` Erik Aronesty [this message]
2018-07-09 15:57                 ` Dan Robinson
2018-07-09 15:59                 ` Gregory Maxwell
2018-07-09 16:33                   ` Erik Aronesty
2018-07-09 16:58                     ` Gregory Maxwell
2018-07-09 17:59                       ` Erik Aronesty
2018-07-10 11:46                         ` Erik Aronesty
2018-07-11 10:35                           ` Adam Back
2018-07-11 14:45                             ` Erik Aronesty
2018-07-19 12:16                               ` Erik Aronesty
2018-07-19 12:24                                 ` Erik Aronesty
2018-07-19 13:11                                 ` Russell O'Connor
2018-07-20 16:25                                   ` Erik Aronesty
2018-07-20 17:34                                     ` Erik Aronesty
2018-07-20 20:18                                       ` Erik Aronesty
2018-07-26  2:05                                         ` Erik Aronesty
2018-07-09 16:21                 ` Gregory Maxwell
2018-07-09  2:29 ` Pieter Wuille

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