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From: Adam Back <adam.back@gmail.com>
To: Erik Aronesty <erik@q32.com>,
	Bitcoin Dev <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Multiparty signatures
Date: Wed, 11 Jul 2018 11:35:08 +0100	[thread overview]
Message-ID: <CALqxMTHYaspkn8JupaHBeLDxLOfZbnwcne2AVeFZe2ADOefktA@mail.gmail.com> (raw)
In-Reply-To: <CAJowKg+UaMsY_nL6SBfb20Ltki+LdhXOwwvG_mAsUq_ww3Tesg@mail.gmail.com>

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On Wed, Jul 11, 2018, 02:42 Erik Aronesty via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:
> Basically you're just replacing addition with interpolation everywhere in
the musig construction

Yes, but you can't do that without a delinearization mechanism to prevent
adaptive public key choice being used to break the scheme using Wagner's
attack. It is not specific to addition, it is a generalized birthday attack.

Look at the delinearization mechanism for an intuition, all public keys are
hashed along with per value hash, so that pre-commits and forces the public
keys to be non-adaptively chosen.

Adaptively chosen public keys are dangerous and simple to exploit for
example pub keys A+B, add party C' he chooses C=C'-A-B, now we can sign for
A+B+C using adaptively chose public key C.

Btw Wagner also breaks this earlier delinearization scheme
S=H(A)*A+H(B)*B+H(C)*C

Adam

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  reply	other threads:[~2018-07-11 10:35 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
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 [this message]
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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