1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
|
Received: from sog-mx-2.v43.ch3.sourceforge.com ([172.29.43.192]
helo=mx.sourceforge.net)
by sfs-ml-1.v29.ch3.sourceforge.com with esmtp (Exim 4.76)
(envelope-from <bip@mattwhitlock.name>) id 1WTwuu-0003qG-5O
for bitcoin-development@lists.sourceforge.net;
Sat, 29 Mar 2014 17:19:36 +0000
X-ACL-Warn:
Received: from qmta01.westchester.pa.mail.comcast.net ([76.96.62.16])
by sog-mx-2.v43.ch3.sourceforge.com with esmtp (Exim 4.76)
id 1WTwut-0005x1-3m for bitcoin-development@lists.sourceforge.net;
Sat, 29 Mar 2014 17:19:36 +0000
Received: from omta15.westchester.pa.mail.comcast.net ([76.96.62.87])
by qmta01.westchester.pa.mail.comcast.net with comcast
id jUQS1n0021swQuc51VKVNR; Sat, 29 Mar 2014 17:19:29 +0000
Received: from crushinator.localnet ([IPv6:2601:6:4800:47f:219:d1ff:fe75:dc2f])
by omta15.westchester.pa.mail.comcast.net with comcast
id jVKV1n0074VnV2P3bVKV1z; Sat, 29 Mar 2014 17:19:29 +0000
From: Matt Whitlock <bip@mattwhitlock.name>
To: Alan Reiner <etotheipi@gmail.com>
Date: Sat, 29 Mar 2014 13:19:29 -0400
Message-ID: <15872432.k8h0hUxqlf@crushinator>
User-Agent: KMail/4.12.3 (Linux/3.12.13-gentoo; KDE/4.12.3; x86_64; ; )
In-Reply-To: <5336FBE7.7030209@gmail.com>
References: <CACsn0ckScTWG4YxNCscxvtdsmcUkxtR2Gi-rdBs2HCkirPz5rA@mail.gmail.com>
<4906130.DUyjhm1C93@crushinator> <5336FBE7.7030209@gmail.com>
MIME-Version: 1.0
Content-Transfer-Encoding: 7Bit
Content-Type: text/plain; charset="us-ascii"
X-Spam-Score: 0.0 (/)
X-Spam-Report: Spam Filtering performed by mx.sourceforge.net.
See http://spamassassin.org/tag/ for more details.
-0.0 RCVD_IN_DNSWL_NONE RBL: Sender listed at http://www.dnswl.org/,
no trust [76.96.62.16 listed in list.dnswl.org]
0.1 DKIM_SIGNED Message has a DKIM or DK signature,
not necessarily valid
-0.1 DKIM_VALID Message has at least one valid DKIM or DK signature
X-Headers-End: 1WTwut-0005x1-3m
Cc: bitcoin-development@lists.sourceforge.net
Subject: Re: [Bitcoin-development] Presenting a BIP for Shamir's Secret
Sharing of Bitcoin private keys
X-BeenThere: bitcoin-development@lists.sourceforge.net
X-Mailman-Version: 2.1.9
Precedence: list
List-Id: <bitcoin-development.lists.sourceforge.net>
List-Unsubscribe: <https://lists.sourceforge.net/lists/listinfo/bitcoin-development>,
<mailto:bitcoin-development-request@lists.sourceforge.net?subject=unsubscribe>
List-Archive: <http://sourceforge.net/mailarchive/forum.php?forum_name=bitcoin-development>
List-Post: <mailto:bitcoin-development@lists.sourceforge.net>
List-Help: <mailto:bitcoin-development-request@lists.sourceforge.net?subject=help>
List-Subscribe: <https://lists.sourceforge.net/lists/listinfo/bitcoin-development>,
<mailto:bitcoin-development-request@lists.sourceforge.net?subject=subscribe>
X-List-Received-Date: Sat, 29 Mar 2014 17:19:36 -0000
On Saturday, 29 March 2014, at 12:59 pm, Alan Reiner wrote:
> I won't lie, there's a lot of work that goes into making an interface
> that makes this feature "usable." The user needs clear ways to identify
> which fragments are associated with which wallet, and which fragments
> are compatible with each other.
The same is true of the multiple private keys involved in a multi-signature addresses.
> They need a way to save some fragments
> to file, print them, or simply write them down.
I proposed a share encoding scheme for exactly this purpose.
> They need a way to
> re-enter fragment, reject duplicates, identify errors, etc. Without it,
> the math fails silently, and you end up restoring a different wallet.
I intentionally omitted the parameter M (minimum subset size) from the shares because including it would give an adversary a vital piece of information. Likewise, including any kind of information that would allow a determination of whether the secret has been correctly reconstituted would give an adversary too much information. Failing silently when given incorrect shares or an insufficient number of shares is intentional.
> Also I put the secret in the highest-order coefficient of the
> polynomial,
Does it make any difference which coefficient holds the secret? It's convenient to put it in the lowest-order coefficient to simply the recovery code.
> and made sure that the other coefficients were
> deterministic. This meant that if print out an M-of-N wallet, I can
> later print out an M-of-(N+1) wallet and the first N fragments will be
> the same. I'm not sure how many users would trust this, but we felt it
> was important in case a user needs to export some fragments, even if
> they don't increase N.
My BIP likewise deterministically chooses the coefficients so that the shares of a secret are consistent across all runs of the algorithm having the same M. As I'm sure you're aware, N (the number of shares to output) plays no part in the calculation and merely controls how many times the outermost loop is executed. My BIP doesn't even mention this parameter.
|
