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
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
Return-Path: <pete@petertodd.org>
Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org
[172.17.192.35])
by mail.linuxfoundation.org (Postfix) with ESMTPS id 7B37840A
for <bitcoin-dev@lists.linuxfoundation.org>;
Sat, 27 May 2017 18:16:57 +0000 (UTC)
X-Greylist: from auto-whitelisted by SQLgrey-1.7.6
Received: from outmail149056.authsmtp.com (outmail149056.authsmtp.com
[62.13.149.56])
by smtp1.linuxfoundation.org (Postfix) with ESMTPS id C79E613D
for <bitcoin-dev@lists.linuxfoundation.org>;
Sat, 27 May 2017 18:16:56 +0000 (UTC)
Received: from mail-c232.authsmtp.com (mail-c232.authsmtp.com [62.13.128.232])
by punt21.authsmtp.com (8.14.2/8.14.2/) with ESMTP id v4RIGs7f092826;
Sat, 27 May 2017 19:16:54 +0100 (BST)
Received: from petertodd.org (ec2-52-5-185-120.compute-1.amazonaws.com
[52.5.185.120]) (authenticated bits=0)
by mail.authsmtp.com (8.14.2/8.14.2/) with ESMTP id v4RIGqVV077514
(version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO);
Sat, 27 May 2017 19:16:53 +0100 (BST)
Received: from [127.0.0.1] (localhost [127.0.0.1])
by petertodd.org (Postfix) with ESMTPSA id B0EA84008E;
Sat, 27 May 2017 18:16:51 +0000 (UTC)
Received: by localhost (Postfix, from userid 1000)
id 633CE20611; Sat, 27 May 2017 13:41:38 -0400 (EDT)
Date: Sat, 27 May 2017 13:41:38 -0400
From: Peter Todd <pete@petertodd.org>
To: "Russell O'Connor" <roconnor@blockstream.io>
Message-ID: <20170527174138.GA7610@fedora-23-dvm>
References: <CAMZUoK=f3hXHkqJBDfiLGSrgXi_ppgyH6+XWD9W54EYFWLm1+Q@mail.gmail.com>
<20170522140548.GA17732@fedora-23-dvm>
<CAMZUoKk1fxOLgBfuxqXpxG-M5ZCPHZBb62_LZF7H4syQ-L7tCg@mail.gmail.com>
MIME-Version: 1.0
Content-Type: multipart/signed; micalg=pgp-sha256;
protocol="application/pgp-signature"; boundary="VbJkn9YxBvnuCH5J"
Content-Disposition: inline
In-Reply-To: <CAMZUoKk1fxOLgBfuxqXpxG-M5ZCPHZBb62_LZF7H4syQ-L7tCg@mail.gmail.com>
User-Agent: Mutt/1.5.23 (2014-03-12)
X-Server-Quench: a9397a06-4308-11e7-829f-00151795d556
X-AuthReport-Spam: If SPAM / abuse - report it at:
http://www.authsmtp.com/abuse
X-AuthRoute: OCd2Yg0TA1ZNQRgX IjsJECJaVQIpKltL GxAVKBZePFsRUQkR
aAdMdAUUFVQNAgsB AmEbWl1eUVt7XGA7 bghPaBtcak9QXgdq
T0pMXVMcUgEKeGtA YHgeVR53dgEIfX9x YwgzV3NSWxV6c1t5
QU5cCGwHMGB9YGIW Bl1YdwJRcQRDe0tA b1YxNiYHcQ5VPz4z
GA41ejw8IwAXAWxw Tx0NKl5aT0ERVhU7 QggfATQpEgUgSj8w
KxFuEFkbAF1ZNUt6 GF0nXk4RLxIeaEV0 HkdEGj4RG0MMSjFD
X-Authentic-SMTP: 61633532353630.1037:706
X-AuthFastPath: 0 (Was 255)
X-AuthSMTP-Origin: 52.5.185.120/25
X-AuthVirus-Status: No virus detected - but ensure you scan with your own
anti-virus system.
X-Spam-Status: No, score=-2.6 required=5.0 tests=BAYES_00,RCVD_IN_DNSWL_LOW
autolearn=ham version=3.3.1
X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on
smtp1.linux-foundation.org
Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] A Method for Computing Merkle Roots of Annotated
Binary Trees
X-BeenThere: bitcoin-dev@lists.linuxfoundation.org
X-Mailman-Version: 2.1.12
Precedence: list
List-Id: Bitcoin Protocol Discussion <bitcoin-dev.lists.linuxfoundation.org>
List-Unsubscribe: <https://lists.linuxfoundation.org/mailman/options/bitcoin-dev>,
<mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=unsubscribe>
List-Archive: <http://lists.linuxfoundation.org/pipermail/bitcoin-dev/>
List-Post: <mailto:bitcoin-dev@lists.linuxfoundation.org>
List-Help: <mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=help>
List-Subscribe: <https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev>,
<mailto:bitcoin-dev-request@lists.linuxfoundation.org?subject=subscribe>
X-List-Received-Date: Sat, 27 May 2017 18:16:57 -0000
--VbJkn9YxBvnuCH5J
Content-Type: text/plain; charset=utf-8
Content-Disposition: inline
Content-Transfer-Encoding: quoted-printable
On Mon, May 22, 2017 at 06:32:38PM -0400, Russell O'Connor wrote:
> On May 22, 2017 23:05, "Peter Todd" <pete@petertodd.org> wrote:
>=20
> On Mon, May 22, 2017 at 03:05:49AM -0400, Russell O'Connor via bitcoin-dev
> wrote:
> > MerkleRoot :=3D SHA256(SHA256(LeftRoot =E2=8B=85 RightRoot))
> > sha256Compress : Word256 =C3=97 Word512 -> Word256
>=20
> To be clear, what math operations do you mean by "=E2=8B=85" and "=C3=97"?
>=20
>=20
> By "=E2=8B=85", I usually mean concatenation (though I also use it for fu=
nction
> composition in one instance). By "=C3=97", I mean the Cartesian product.
Cartesian product can mean a lot of things.
What specifically do you mean by "cartesian product" here?
--=20
https://petertodd.org 'peter'[:-1]@petertodd.org
--VbJkn9YxBvnuCH5J
Content-Type: application/pgp-signature; name="signature.asc"
Content-Description: Digital signature
-----BEGIN PGP SIGNATURE-----
iQEcBAEBCAAGBQJZKbpPAAoJECSBQD2l8JH7/tUIAJ0kRv96NqGScFfATsYh3+kU
zNaSF6I5n+topmlQz7x3w63IsY2iP51rZJDnuVZyOAhauNSLXPreHM01rSpKCssE
Sit4QVXUX9kiR7Vc8Ge2J8EamGliTZq5DWETjjMRYn/EYvNpwskXmkaDaYP9YAGn
HvkvqiMSHKKvH6O6U1wmQR9I9o+ENjg4qjHw++YuM0jY+k5QtP6xiT5YI88HF4j/
YCzIOrOkeMuAtjlrD6/BJfmrUC/NRaHqVX6xDQDzaaWEQ4c1duH4vKaXhCKvVKDM
DgSags9LaINxV+e2ShpeIu0UZfUFSotx05aJuq/fHsFTzJtsyptXiMtDNhOw49o=
=+51f
-----END PGP SIGNATURE-----
--VbJkn9YxBvnuCH5J--
|