From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id 784028B4 for ; Tue, 17 May 2016 13:23:20 +0000 (UTC) X-Greylist: from auto-whitelisted by SQLgrey-1.7.6 Received: from outmail148100.authsmtp.co.uk (outmail148100.authsmtp.co.uk [62.13.148.100]) by smtp1.linuxfoundation.org (Postfix) with ESMTP id F2E80F3 for ; Tue, 17 May 2016 13:23:17 +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 u4HDNGpu014656 for ; Tue, 17 May 2016 14:23:16 +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 u4HDNCjY094815 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO) for ; Tue, 17 May 2016 14:23:13 +0100 (BST) Received: from [127.0.0.1] (localhost [127.0.0.1]) by petertodd.org (Postfix) with ESMTPSA id 4C4674011C for ; Tue, 17 May 2016 13:21:47 +0000 (UTC) Received: by localhost (Postfix, from userid 1000) id 1CF272058A; Tue, 17 May 2016 09:23:11 -0400 (EDT) Date: Tue, 17 May 2016 09:23:11 -0400 From: Peter Todd To: bitcoin-dev@lists.linuxfoundation.org Message-ID: <20160517132311.GA21656@fedora-21-dvm> MIME-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha256; protocol="application/pgp-signature"; boundary="SUOF0GtieIMvvwua" Content-Disposition: inline User-Agent: Mutt/1.5.23 (2014-03-12) X-Server-Quench: 823c4ca8-1c32-11e6-829e-00151795d556 X-AuthReport-Spam: If SPAM / abuse - report it at: http://www.authsmtp.com/abuse X-AuthRoute: OCd2Yg0TA1ZNQRgX IjsJECJaVQIpKltL GxAVJwpGK10IU0Fd P1hyKltILEZaQVBf Ri5dBBEKBAw1ADwr dVUTOktcZVUzDkx1 UkhIREJTEA9qAhYA AlAbUAd3aQROfWBx Z0Z9XHVEXQo/cT4J PD0OfG0PYW9hbS4d WUdcdE1ccgAZekwU Yk1+B3APfGQGM3x9 T1ViMnVpZWwCcXsE Hw1QcAwEZE8IHzgz Dy0+LRJnJkAZDwop KAM6KhY9BlwcNkgs OF09EW0ZLx9aLgpB WmVEHCJfLEhJaycv BBJXUQYiIBo/CQxb BxgpPhpFBCBJMgAA 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 Subject: [bitcoin-dev] Making UTXO Set Growth Irrelevant With Low-Latency Delayed TXO Commitments 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: Tue, 17 May 2016 13:23:20 -0000 --SUOF0GtieIMvvwua Content-Type: text/plain; charset=utf-8 Content-Disposition: inline Content-Transfer-Encoding: quoted-printable # Motivation UTXO growth is a serious concern for Bitcoin's long-term decentralization. = To run a competitive mining operation potentially the entire UTXO set must be = in RAM to achieve competitive latency; your larger, more centralized, competit= ors will have the UTXO set in RAM. Mining is a zero-sum game, so the extra late= ncy of not doing so if they do directly impacts your profit margin. Secondly, having possession of the UTXO set is one of the minimum requirements to run= a full node; the larger the set the harder it is to run a full node. Currently the maximum size of the UTXO set is unbounded as there is no consensus rule that limits growth, other than the block-size limit itself; = as of writing the UTXO set is 1.3GB in the on-disk, compressed serialization, which expands to significantly more in memory. UTXO growth is driven by a number of factors, including the fact that there is little incentive to mer= ge inputs, lost coins, dust outputs that can't be economically spent, and non-btc-value-transfer "blockchain" use-cases such as anti-replay oracles a= nd timestamping. We don't have good tools to combat UTXO growth. Segregated Witness proposes= to give witness space a 75% discount, in part of make reducing the UTXO set si= ze by spending txouts cheaper. While this may change wallets to more often spe= nd dust, it's hard to imagine an incentive sufficiently strong to discourage m= ost, let alone all, UTXO growing behavior. For example, timestamping applications often create unspendable outputs due= to ease of implementation, and because doing so is an easy way to make sure th= at the data required to reconstruct the timestamp proof won't get lost - all Bitcoin full nodes are forced to keep a copy of it. Similarly anti-replay use-cases like using the UTXO set for key rotation piggyback on the uniquely strong security and decentralization guarantee that Bitcoin provides; it's = very difficult - perhaps impossible - to provide these applications with alternatives that are equally secure. These non-btc-value-transfer use-cases can often afford to pay far higher fees per UTXO created than competing btc-value-transfer use-cases; many users could afford to spend $50 to regis= ter a new PGP key, yet would rather not spend $50 in fees to create a standard = two output transaction. Effective techniques to resist miner censorship exist, = so without resorting to whitelists blocking non-btc-value-transfer use-cases as "spam" is not a long-term, incentive compatible, solution. A hard upper limit on UTXO set size could create a more level playing field= in the form of fixed minimum requirements to run a performant Bitcoin node, and make the issue of UTXO "spam" less important. However, making any coins unspendable, regardless of age or value, is a politically untenable economic change. # TXO Commitments A merkle tree committing to the state of all transaction outputs, both spent and unspent, we can provide a method of compactly proving the current state= of an output. This lets us "archive" less frequently accessed parts of the UTXO set, allowing full nodes to discard the associated data, still providing a mechanism to spend those archived outputs by proving to those nodes that the outputs are in fact unspent. Specifically TXO commitments proposes a Merkle Mountain Range=C2=B9 (MMR), a type of deterministic, indexable, insertion ordered merkle tree, which allo= ws new items to be cheaply appended to the tree with minimal storage requireme= nts, just log2(n) "mountain tips". Once an output is added to the TXO MMR it is never removed; if an output is spent its status is updated in place. Both t= he state of a specific item in the MMR, as well the validity of changes to ite= ms in the MMR, can be proven with log2(n) sized proofs consisting of a merkle = path to the tip of the tree. At an extreme, with TXO commitments we could even have no UTXO set at all, entirely eliminating the UTXO growth problem. Transactions would simply be accompanied by TXO commitment proofs showing that the outputs they wanted to spend were still unspent; nodes could update the state of the TXO MMR purely =66rom TXO commitment proofs. However, the log2(n) bandwidth overhead per t= xin is substantial, so a more realistic implementation is be to have a UTXO cache = for recent transactions, with TXO commitments acting as a alternate for the (ra= re) event that an old txout needs to be spent. Proofs can be generated and added to transactions without the involvement of the signers, even after the fact; there's no need for the proof itself to signed and the proof is not part of the transaction hash. Anyone with acces= s to TXO MMR data can (re)generate missing proofs, so minimal, if any, changes a= re required to wallet software to make use of TXO commitments. ## Delayed Commitments TXO commitments aren't a new idea - the author proposed them years ago in response to UTXO commitments. However it's critical for small miners' orphan rates that block validation be fast, and so far it has proven difficult to create (U)TXO implementations with acceptable performance; updating and recalculating cryptographicly hashed merkelized datasets is inherently more work than not doing so. Fortunately if we maintain a UTXO set for recent outputs, TXO commitments are only needed when spending old, archived, outpu= ts. We can take advantage of this by delaying the commitment, allowing it to be calculated well in advance of it actually being used, thus changing a latency-critical task into a much easier average throughput problem. Concretely each block B_i commits to the TXO set state as of block B_{i-n},= in other words what the TXO commitment would have been n blocks ago, if not for the n block delay. Since that commitment only depends on the contents of the blockchain up until block B_{i-n}, the contents of any block after are irrelevant to the calculation. ## Implementation Our proposed high-performance/low-latency delayed commitment full-node implementation needs to store the following data: 1) UTXO set Low-latency K:V map of txouts definitely known to be unspent. Similar to existing UTXO implementation, but with the key difference that old, unspent, outputs may be pruned from the UTXO set. 2) STXO set Low-latency set of transaction outputs known to have been spent by transactions after the most recent TXO commitment, but created prior to= the TXO commitment. 3) TXO journal FIFO of outputs that need to be marked as spent in the TXO MMR. Appends must be low-latency; removals can be high-latency. 4) TXO MMR list Prunable, ordered list of TXO MMR's, mainly the highest pending commitm= ent, backed by a reference counted, cryptographically hashed object store indexed by digest (similar to how git repos work). High-latency ok. We'= ll cover this in more in detail later. ### Fast-Path: Verifying a Txout Spend In a Block When a transaction output is spent by a transaction in a block we have two cases: 1) Recently created output Output created after the most recent TXO commitment, so it should be in= the UTXO set; the transaction spending it does not need a TXO commitment pr= oof. Remove the output from the UTXO set and append it to the TXO journal. 2) Archived output Output created prior to the most recent TXO commitment, so there's no guarantee it's in the UTXO set; transaction will have a TXO commitment proof for the most recent TXO commitment showing that it was unspent. Check that the output isn't already in the STXO set (double-spent), and= if not add it. Append the output and TXO commitment proof to the TXO journ= al. In both cases recording an output as spent requires no more than two key:va= lue updates, and one journal append. The existing UTXO set requires one key:val= ue update per spend, so we can expect new block validation latency to be withi= n 2x of the status quo even in the worst case of 100% archived output spends. ### Slow-Path: Calculating Pending TXO Commitments In a low-priority background task we flush the TXO journal, recording the outputs spent by each block in the TXO MMR, and hashing MMR data to obtain = the TXO commitment digest. Additionally this background task removes STXO's that have been recorded in TXO commitments, and prunes TXO commitment data no lo= nger needed. Throughput for the TXO commitment calculation will be worse than the existi= ng UTXO only scheme. This impacts bulk verification, e.g. initial block downlo= ad. That said, TXO commitments provides other possible tradeoffs that can mitig= ate impact of slower validation throughput, such as skipping validation of old history, as well as fraud proof approaches. ### TXO MMR Implementation Details Each TXO MMR state is a modification of the previous one with most informat= ion shared, so we an space-efficiently store a large number of TXO commitments states, where each state is a small delta of the previous state, by sharing unchanged data between each state; cycles are impossible in merkelized data structures, so simple reference counting is sufficient for garbage collecti= on. Data no longer needed can be pruned by dropping it from the database, and unpruned by adding it again. Since everything is committed to via cryptogra= phic hash, we're guaranteed that regardless of where we get the data, after unpruning we'll have the right data. Let's look at how the TXO MMR works in detail. Consider the following TXO M= MR with two txouts, which we'll call state #0: 0 / \ a b If we add another entry we get state #1: 1 / \ 0 \ / \ \ a b c Note how it 100% of the state #0 data was reused in commitment #1. Let's add two more entries to get state #2: 2 / \ 2 \ / \ \ / \ \ / \ \ 0 2 \ / \ / \ \ a b c d e This time part of state #1 wasn't reused - it's wasn't a perfect binary tree - but we've still got a lot of re-use. Now suppose state #2 is committed into the blockchain by the most recent bl= ock. Future transactions attempting to spend outputs created as of state #2 are obliged to prove that they are unspent; essentially they're forced to provi= de part of the state #2 MMR data. This lets us prune that data, discarding it, leaving us with only the bare minimum data we need to append new txouts to = the TXO MMR, the tips of the perfect binary trees ("mountains") within the MMR: 2 / \ 2 \ \ \ \ \ \ e Note that we're glossing over some nuance here about exactly what data need= s to be kept; depending on the details of the implementation the only data we ne= ed for nodes "2" and "e" may be their hash digest. Adding another three more txouts results in state #3: 3 / \ / \ / \ / \ / \ / \ / \ 2 3 / \ / \ / \ 3 3 / \ / \ e f g h Suppose recently created txout f is spent. We have all the data required to update the MMR, giving us state #4. It modifies two inner nodes and one leaf node: 4 / \ / \ / \ / \ / \ / \ / \ 2 4 / \ / \ / \ 4 3 / \ / \ e (f) g h If an archived txout is spent requires the transaction to provide the merkle path to the most recently committed TXO, in our case state #2. If txout b is spent that means the transaction must provide the following data from state= #2: 2 / 2 / / / 0 \ b We can add that data to our local knowledge of the TXO MMR, unpruning part = of it: 4 / \ / \ / \ / \ / \ / \ / \ 2 4 / / \ / / \ / / \ 0 4 3 \ / \ / \ b e (f) g h Remember, we haven't _modified_ state #4 yet; we just have more data about = it. When we mark txout b as spent we get state #5: 5 / \ / \ / \ / \ / \ / \ / \ 5 4 / / \ / / \ / / \ 5 4 3 \ / \ / \ (b) e (f) g h Secondly by now state #3 has been committed into the chain, and transactions that want to spend txouts created as of state #3 must provide a TXO proof consisting of state #3 data. The leaf nodes for outputs g and h, and the in= ner node above them, are part of state #3, so we prune them: 5 / \ / \ / \ / \ / \ / \ / \ 5 4 / / / / / / 5 4 \ / \ (b) e (f) Finally, lets put this all together, by spending txouts a, c, and g, and creating three new txouts i, j, and k. State #3 was the most recently commi= tted state, so the transactions spending a and g are providing merkle paths up to it. This includes part of the state #2 data: 3 / \ / \ / \ / \ / \ / \ / \ 2 3 / \ \ / \ \ / \ \ 0 2 3 / / / a c g After unpruning we have the following data for state #5: 5 / \ / \ / \ / \ / \ / \ / \ 5 4 / \ / \ / \ / \ / \ / \ 5 2 4 3 / \ / / \ / a (b) c e (f) g That's sufficient to mark the three outputs as spent and add the three new txouts, resulting in state #6: 6 / \ / \ / \ / \ / \ 6 \ / \ \ / \ \ / \ \ / \ \ / \ \ / \ \ / \ \ 6 6 \ / \ / \ \ / \ / \ 6 / \ / \ / \ 6 6 4 6 6 \ / \ / / \ / / \ \ (a) (b) (c) e (f) (g) i j k Again, state #4 related data can be pruned. In addition, depending on how t= he STXO set is implemented may also be able to prune data related to spent txo= uts after that state, including inner nodes where all txouts under them have be= en spent (more on pruning spent inner nodes later). ### Consensus and Pruning It's important to note that pruning behavior is consensus critical: a full = node that is missing data due to pruning it too soon will fall out of consensus,= and a miner that fails to include a merkle proof that is required by the consen= sus is creating an invalid block. At the same time many full nodes will have significantly more data on hand than the bare minimum so they can help wall= ets make transactions spending old coins; implementations should strongly consi= der separating the data that is, and isn't, strictly required for consensus. A reasonable approach for the low-level cryptography may be to actually tre= at the two cases differently, with the TXO commitments committing too what data does and does not need to be kept on hand by the UTXO expiration rules. On = the other hand, leaving that uncommitted allows for certain types of soft-forks where the protocol is changed to require more data than it previously did. ### Consensus Critical Storage Overheads Only the UTXO and STXO sets need to be kept on fast random access storage. Since STXO set entries can only be created by spending a UTXO - and are sma= ller than a UTXO entry - we can guarantee that the peak size of the UTXO and STXO sets combined will always be less than the peak size of the UTXO set alone = in the existing UTXO-only scheme (though the combined size can be temporarily higher than what the UTXO set size alone would be when large numbers of archived txouts are spent). TXO journal entries and unpruned entries in the TXO MMR have log2(n) maximum overhead per entry: a unique merkle path to a TXO commitment (by "unique" we mean that no other entry shares data with it). On a reasonably fast system = the TXO journal will be flushed quickly, converting it into TXO MMR data; the T= XO journal will never be more than a few blocks in size. Transactions spending non-archived txouts are not required to provide any T= XO commitment data; we must have that data on hand in the form of one TXO MMR entry per UTXO. Once spent however the TXO MMR leaf node associated with th= at non-archived txout can be immediately pruned - it's no longer in the UTXO s= et so any attempt to spend it will fail; the data is now immutable and we'll n= ever need it again. Inner nodes in the TXO MMR can also be pruned if all leafs u= nder them are fully spent; detecting this is easy the TXO MMR is a merkle-sum tr= ee, with each inner node committing to the sum of the unspent txouts under it. When a archived txout is spent the transaction is required to provide a mer= kle path to the most recent TXO commitment. As shown above that path is suffici= ent information to unprune the necessary nodes in the TXO MMR and apply the spe= nd immediately, reducing this case to the TXO journal size question (non-conse= nsus critical overhead is a different question, which we'll address in the next section). Taking all this into account the only significant storage overhead of our T= XO commitments scheme when compared to the status quo is the log2(n) merkle pa= th overhead; as long as less than 1/log2(n) of the UTXO set is active, non-archived, UTXO's we've come out ahead, even in the unrealistic case whe= re all storage available is equally fast. In the real world that isn't yet the case - even SSD's significantly slower than RAM. ### Non-Consensus Critical Storage Overheads Transactions spending archived txouts pose two challenges: 1) Obtaining up-to-date TXO commitment proofs 2) Updating those proofs as blocks are mined The first challenge can be handled by specialized archival nodes, not unlike how some nodes make transaction data available to wallets via bloom filters= or the Electrum protocol. There's a whole variety of options available, and the the data can be easily sharded to scale horizontally; the data is self-validating allowing horizontal scaling without trust. While miners and relay nodes don't need to be concerned about the initial commitment proof, updating that proof is another matter. If a node aggressi= vely prunes old versions of the TXO MMR as it calculates pending TXO commitments= , it won't have the data available to update the TXO commitment proof to be agai= nst the next block, when that block is found; the child nodes of the TXO MMR tip are guaranteed to have changed, yet aggressive pruning would have discarded= that data. Relay nodes could ignore this problem if they simply accept the fact that they'll only be able to fully relay the transaction once, when it is initia= lly broadcast, and won't be able to provide mempool functionality after the ini= tial relay. Modulo high-latency mixnets, this is probably acceptable; the author= has previously argued that relay nodes don't need a mempool=C2=B2 at all. For a miner though not having the data necessary to update the proofs as bl= ocks are found means potentially losing out on transactions fees. So how much ex= tra data is necessary to make this a non-issue? Since the TXO MMR is insertion ordered, spending a non-archived txout can o= nly invalidate the upper nodes in of the archived txout's TXO MMR proof (if this isn't clear, imagine a two-level scheme, with a per-block TXO MMRs, committ= ed by a master MMR for all blocks). The maximum number of relevant inner nodes changed is log2(n) per block, so if there are n non-archival blocks between= the most recent TXO commitment and the pending TXO MMR tip, we have to store log2(n)*n inner nodes - on the order of a few dozen MB even when n is a (seemingly ridiculously high) year worth of blocks. Archived txout spends on the other hand can invalidate TXO MMR proofs at any level - consider the case of two adjacent txouts being spent. To guarantee success requires storing full proofs. However, they're limited by the block= size limit, and additionally are expected to be relatively uncommon. For example= , if 1% of 1MB blocks was archival spends, our hypothetical year long TXO commit= ment delay is only a few hundred MB of data with low-IO-performance requirements. ## Security Model Of course, a TXO commitment delay of a year sounds ridiculous. Even the slo= west imaginable computer isn't going to need more than a few blocks of TXO commitment delay to keep up ~100% of the time, and there's no reason why we can't have the UTXO archive delay be significantly longer than the TXO commitment delay. However, as with UTXO commitments, TXO commitments raise issues with Bitcoi= n's security model by allowing relatively miners to profitably mine transactions without bothering to validate prior history. At the extreme, if there was no commitment delay at all at the cost of a bit of some extra network bandwidth "full" nodes could operate and even mine blocks completely statelessly by expecting all transactions to include "proof" that their inputs are unspent= ; a TXO commitment proof for a commitment you haven't verified isn't a proof th= at a transaction output is unspent, it's a proof that some miners claimed the tx= out was unspent. At one extreme, we could simply implement TXO commitments in a "virtual" fashion, without miners actually including the TXO commitment digest in the= ir blocks at all. Full nodes would be forced to compute the commitment from scratch, in the same way they are forced to compute the UTXO state, or total work. Of course a full node operator who doesn't want to verify old history= can get a copy of the TXO state from a trusted source - no different from how y= ou could get a copy of the UTXO set from a trusted source. A more pragmatic approach is to accept that people will do that anyway, and instead assume that sufficiently old blocks are valid. But how old is "sufficiently old"? First of all, if your full node implementation comes "f= rom the factory" with a reasonably up-to-date minimum accepted total-work threshold=E2=81=B1 - in other words it won't accept a chain with less than = that amount of total work - it may be reasonable to assume any Sybil attacker with sufficient hashing power to make a forked chain meeting that threshold with, say, six months worth of blocks has enough hashing power to threaten the ma= in chain as well. That leaves public attempts to falsify TXO commitments, done out in the ope= n by the majority of hashing power. In this circumstance the "assumed valid" threshold determines how long the attack would have to go on before full no= des start accepting the invalid chain, or at least, newly installed/recently re= set full nodes. The minimum age that we can "assume valid" is tradeoff between political/social/technical concerns; we probably want at least a few weeks = to guarantee the defenders a chance to organise themselves. With this in mind, a longer-than-technically-necessary TXO commitment delay= =CA=B2 may help ensure that full node software actually validates some minimum num= ber of blocks out-of-the-box, without taking shortcuts. However this can be achieved in a wide variety of ways, such as the author's prev-block-proof proposal=C2=B3, fraud proofs, or even a PoW with an inner loop dependent on blockchain data. Like UTXO commitments, TXO commitments are also potentially very useful in reducing the need for SPV wallet software to trust third par= ties providing them with transaction data. i) Checkpoints that reject any chain without a specific block are a more common, if uglier, way of achieving this protection. j) A good homework problem is to figure out how the TXO commitment could be designed such that the delay could be reduced in a soft-fork. ## Further Work While we've shown that TXO commitments certainly could be implemented witho= ut increasing peak IO bandwidth/block validation latency significantly with the delayed commitment approach, we're far from being certain that they should = be implemented this way (or at all). 1) Can a TXO commitment scheme be optimized sufficiently to be used directly without a commitment delay? Obviously it'd be preferable to avoid all the a= bove complexity entirely. 2) Is it possible to use a metric other than age, e.g. priority? While this complicates the pruning logic, it could use the UTXO set space more efficiently, especially if your goal is to prioritise bitcoin value-transfer over other uses (though if "normal" wallets nearly never need to use TXO commitments proofs to spend outputs, the infrastructure to actually do this= may rot). 3) Should UTXO archiving be based on a fixed size UTXO set, rather than an age/priority/etc. threshold? 4) By fixing the problem (or possibly just "fixing" the problem) are we encouraging/legitimising blockchain use-cases other than BTC value transfer? Should we? 5) Instead of TXO commitment proofs counting towards the blocksize limit, c= an we use a different miner fairness/decentralization metric/incentive? For instance it might be reasonable for the TXO commitment proof size to be discounted, or ignored entirely, if a proof-of-propagation scheme (e.g. thinblocks) is used to ensure all miners have received the proof in advance. 6) How does this interact with fraud proofs? Obviously furthering dependenc= y on non-cryptographically-committed STXO/UTXO databases is incompatible with the modularized validation approach to implementing fraud proofs. # References 1) "Merkle Mountain Ranges", Peter Todd, OpenTimestamps, Mar 18 2013, https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/= merkle-mountain-range.md 2) "Do we really need a mempool? (for relay nodes)", Peter Todd, bitcoin-dev mailing list, Jul 18th 2015, https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-July/009479= =2Ehtml 3) "Segregated witnesses and validationless mining", Peter Todd, bitcoin-dev mailing list, Dec 23rd 2015, https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-December/01= 2103.html --=20 https://petertodd.org 'peter'[:-1]@petertodd.org --SUOF0GtieIMvvwua Content-Type: application/pgp-signature; name="signature.asc" Content-Description: Digital signature -----BEGIN PGP SIGNATURE----- iQEcBAEBCAAGBQJXOxs6AAoJEGOZARBE6K+yTzIH/1HBOV9Thl+eeXpDXGkUrtjP +qvWvC/fYQVzw3a1Y5FlhlGW0QJ3nEXEEHCdMh0C4GSsOT8ZXWminwKb8NhFZYEl c2RNynGNAhQimnnugvLllxIYzzZZzDPRZ832Wzlskg/XM7exP1BVZQmrh76yT5vn d89TdH9PROcZOp1fI4Bt+nD8SJ/XD8n/bZ+vonj8X8tBPAqaIEaKz+twfxFjvbsg S9+Dj0XKkmLJgKVYfV2lS5YTofyBeEgJzijo87mXMSJXTWF8QomPCnk3vZus8BvV aqfPfo8qoNQ85OKGPZvJdviwUTun/x3RpiVjBxYO9ltL5/TlOO40gbAtRUqJrJk= =i/mM -----END PGP SIGNATURE----- --SUOF0GtieIMvvwua--