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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next prev parent 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 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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