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From: Erik Aronesty <erik@q32.com>
Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Multiparty signatures
Date: Fri, 20 Jul 2018 13:34:29 -0400	[thread overview]
Message-ID: <CAJowKgKB1GDxvpQt1JjPr+cgyM8yztLtgJ_mZ8vsoCHyBdqkVA@mail.gmail.com> (raw)
In-Reply-To: <CAJowKgJBVdJbRvf5Y6dV4o5Jf1XyELNsT+vCrp4b-86ZYr+LYQ@mail.gmail.com>

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 Hi, thanks for all the help.   I'm going to summarize again, and see if
we've arrived at the correct solution for an M of N "single sig" extension
of MuSig, which I think we have.

- Using MuSig's solution for the blinding to solve the Wagner attack
- Using interpolation to enhance MuSig to be M of N instead of M of M

References:

 - MuSig
https://blockstream.com/2018/01/23/musig-key-aggregation-schnorr-signatures.html
 - HomPrf http://crypto.stanford.edu/~dabo/papers/homprf.pdf (sections 7.1
and 7.4)

Each party:

1. Publishes public key G*xi
3. Xi = H(G*xi) ... Xi is the parties x coordinate, for the purposes of
interpolation
3. r = G*x = via interpolation of Gx1, Gx2... (see HomPrf)
4. L = H(X1,X2,…) (see MuSig)
5. X = sum of all H(L,Xi)Xi (see MuSig)
6. Computes e = H(r | M | X) .... standard schnorr e... not a share
7. Computes si = xi - xe ... where si is a "share" of the sig, and xi is
the private data
8. Publishes (si, e, G*Xi)

Any party can then derive s from m of n shares, by interpolating, not
adding.

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  reply	other threads:[~2018-07-20 17:34 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
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 [this message]
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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