Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 12E23BC7 for ; Fri, 24 Feb 2017 04:36:20 +0000 (UTC) X-Greylist: from auto-whitelisted by SQLgrey-1.7.6 Received: from outmail149095.authsmtp.com (outmail149095.authsmtp.com [62.13.149.95]) by smtp1.linuxfoundation.org (Postfix) with ESMTP id 076B413C for ; Fri, 24 Feb 2017 04:36:18 +0000 (UTC) Received: from mail-c232.authsmtp.com (mail-c232.authsmtp.com [62.13.128.232]) by punt24.authsmtp.com (8.14.2/8.14.2/) with ESMTP id v1O4aGV0093206; Fri, 24 Feb 2017 04:36:16 GMT 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 v1O4aEPH042689 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Fri, 24 Feb 2017 04:36:15 GMT Received: from [127.0.0.1] (localhost [127.0.0.1]) by petertodd.org (Postfix) with ESMTPSA id 0E3E740014; Fri, 24 Feb 2017 04:36:14 +0000 (UTC) Received: by localhost (Postfix, from userid 1000) id 3FE91204AB; Thu, 23 Feb 2017 23:36:13 -0500 (EST) Date: Thu, 23 Feb 2017 23:36:13 -0500 From: Peter Todd To: Bram Cohen Message-ID: <20170224043613.GA32502@savin.petertodd.org> References: <20170223235105.GA28497@savin.petertodd.org> <20170224010943.GA29218@savin.petertodd.org> <20170224025811.GA31911@savin.petertodd.org> <20170224031531.GA32118@savin.petertodd.org> MIME-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="5mCyUwZo2JvN/JJP" Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.5.23 (2014-03-12) X-Server-Quench: c7576ddb-fa4a-11e6-829f-00151795d556 X-AuthReport-Spam: If SPAM / abuse - report it at: http://www.authsmtp.com/abuse X-AuthRoute: OCd2Yg0TA1ZNQRgX IjsJECJaVQIpKltL GxAVKBZePFsRUQkR aQdMdAYUHlAWAgsB AmEbW1BeU1t7WGU7 bghPaBtcak9QXgdq T0pMXVMcUgQXBU10 ZmYeVht0fwwIen94 YkAsDXdeW0IuIRRg FB9QRHAHZDJmdWgd WRZFdwNVdQJNdxoR b1V5GhFYa3VsNCMk FAgyOXU9MCtqYA0d aAwRMV8ICWMuJHYQ Sh4DGzQzHEoDLwAA 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 Subject: Re: [bitcoin-dev] A Better MMR Definition X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Fri, 24 Feb 2017 04:36:20 -0000 --5mCyUwZo2JvN/JJP Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Content-Transfer-Encoding: quoted-printable On Thu, Feb 23, 2017 at 07:32:43PM -0800, Bram Cohen wrote: > On Thu, Feb 23, 2017 at 7:15 PM, Peter Todd wrote: >=20 > > > > Glad we're on the same page with regard to what's possible in TXO > > commitments. > > > > Secondly, am I correct in saying your UTXO commitments scheme requires > > random > > access? While you describe it as a "merkle set", obviously to be merkel= ized > > it'll have to have an ordering of some kind. What do you propose that > > ordering > > to be? > > >=20 > The ordering is by the bits in the hash. Technically it's a Patricia Trie. > I'm using 'merkle tree' to refer to basically anything with a hash root. The hash of what? The values in the set? > > Maybe more specifically, what exact values do you propose to be in the = set? > > > > > That is unspecified in the implementation, it just takes a 256 bit value > which is presumably a hash of something. The intention is to nail down a > simple format and demonstrate good performance and leave those semantics = to > a higher layer. The simplest thing would be to hash together the txid and > output number. Ok, so let's assume the values in the set are the unspent outpoints. Since we're ordering by the hash of the values in the set, outpoints will be distributed uniformly in the set, and thus the access pattern of data in the set is uniform. Now let's fast-forward 10 years. For the sake of argument, assume that for every 1 UTXO in the set that corresponds to funds in someone's wallet that = are likely to be spent, there are 2^12 =3D 4096 UTXO's that have been permanent= ly lost (and/or created in spam attacks) and thus will never be spent. Since lost UTXO's are *also* uniformly distributed, if I'm processing a new block that spends 2^12 =3D 4096 UTXO's, on average for each UTXO spent, I'll have to update log2(4096) =3D 12 more digests than I would have had those "= dead" UTXO's not existed. Concretely, imagine our UTXO set had just 8 values in it, and we were updat= ing two of them: # / \ / \ / \ / \ / \ # # / \ / \ / \ / \ # . . # / \ / \ / \ / \ . X . . . . X . To mark two coins as spent, we've had to update 5 inner nodes. Now let's look at what happens in an insertion-ordered TXO commitment schem= e. For sake of argument, let's assume the best possible case, where every UTXO spent in that same block was recently created. Since the UTXO's are recently created, chances are almost every single one of those "dead" UTXO's will ha= ve been created in the past. Thus, since this is an insertion-ordered data structure, those UTXO's exist in an older part of the data structure that o= ur new block doesn't need to modify at all. Concretely, again let's imagine a TXO commitment with 8 values in it, and t= wo of them being spent: # / \ / \ / \ / \ / \ . # / \ / \ / \ / \ . . . # / \ / \ / \ / \ . . . . . . X X To mark two coins as spent, we've only had to update 3 inner nodes; while o= ur tree is higher with those lost coins, those extra inner nodes are amortised across all the coins we have to update. The situation gets even better when we look at the *new* UTXO's that our bl= ock creates. Suppose our UTXO set has size n. To mark a single coin as spent, we have to update log2(n) inner nodes. We do get to amortise this a bit at the= top levels in the tree, but even if we assume the amortisation is totally free, we're updating at least log2(n) - log2(m) inner nodes "under" the amortised nodes at the top of the tree for *each* new node. Meanwhile with an insertion-ordered TXO commitment, each new UTXO added to = the data set goes in the same place - the end. So almost none of the existing d= ata needs to be touched to add the new UTXOs. Equally, the hashing required for= the new UTXO's can be done in an incremental fashion that's very L1/L2 cache friendly. tl;dr: Precisely because access patterns in TXO commitments are *not* unifo= rm, I think we'll find that from a L1/L2/etc cache perspective alone, TXO commitments will result in better performance than UTXO commitments. Now it is true that Bitcoin's current design means we'll need a map of confirmed outpoints to TXO insertion order indexes. But it's not particular= ly hard to add that "metadata" to transactions on the P2P layer in the same way that segwit added witnesses to transactions without modifying how txids were calculated; if you only connect to peers who provide you with TXO index information in blocks and transactions, you don't need to keep that map yourself. Finally, note how this makes transactions *smaller* in many circumstances: = it's just a 8-byte max index rather than a 40 byte outpoint. --=20 https://petertodd.org 'peter'[:-1]@petertodd.org --5mCyUwZo2JvN/JJP Content-Type: application/pgp-signature; name="signature.asc" Content-Description: Digital signature -----BEGIN PGP SIGNATURE----- iQEcBAEBCAAGBQJYr7g2AAoJECSBQD2l8JH7cP4H/2rxlMxRuSpOHm3yH3NhX6Q1 +7bKiis07RYfTO5c8IaGqUqHorqDLXAQI2hXx37FyeE90H/u12Ev7PiZfVst6qgD aqGSSaBQIvPVzhh3EBhTAmokHXQMucWt5Ibx8zJecYbGz6AWWR89jsBIfh5nPSnC pEpfOmT5WUQNEhL1M9HN0m/phXcmr2+NgqjopyQGl7nxuy+2V99zHRn1gHU7o4QS UWOyRMQidlGoi/nqm2XBO3jZmySlVs6w/RPReSZEw0rYcJVaw3NCZcr5UCCxiznd qfulbhOf0dx5BpdPnqngMfteUMlVeXinUlOmJ1q1NXkrhOvEX5qgnvI34PHKrDk= =6ew2 -----END PGP SIGNATURE----- --5mCyUwZo2JvN/JJP--