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--