-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 ==Abstract==

In simple payment verification (SPV) proofs it is currently necessary that every intervening block header be provided between two blocks in order to establish both connectivity and proof of work. By committing to a hash tree of past block headers in each block, these back references can be exploited to demonstrate in logarithmic space that an elided sequence of block headers actually represents the claimed work. This is particularly useful in the construction of 2-way pegging between chains, and as an efficiency optimization for SPV clients and headers-first synchronization. ==Overview== The miner of a block is allowed to choose some subset of the block history which it creates direct links back to. These links include the block hash, height, and work distance from the new block, and are organized into a hash tree structure. The root of this hash tree is committed to the coinbase string, or some other identifiable position in the block. Bitcoin is soft-forked to include verification of the accuracy of the contents of this structure - if present - as a validation rule. When constructing an SPV proof, the prover is allowed to choose back-links from this structure whose relative work distance is less than or equal to the apparent work of the proof-of-work which contains the back-link structure. Apparent work in this context means the expected work that would be required to meet or exceed the actual block hash. Since back-links can only be used if the apparent work is greater than or equal to the distance back, constructing such a fraudulent proof is expected to require just as much or more work as recreating the underlying sequence of blocks. The result is skip list structure where "lucky" proofs of work are used to skip back further than a single block (recall that if you search for a 64-bit leading-0 proof of work, half the time you get 65 leading-0's, a quarter of those cases have 66 leading-0's, and so on). When constructing very long proofs, the solver will follow links back to the nearest lucky block, then use the back-links contained within that block to skip back to a prior lucky block, and so on until it reaches a block which points directly to the desired target block. Given the distribution of "lucky" blocks, it is expected that such compact proofs require revelation of log2 N links in order to prove the work required to build a chain of length N. ==Back link selection== In fully general form, this compact SPV proof scheme works no matter the back-links chosen by miners, so long as they are either revealed or selected in a deterministic way such that full nodes can check their validity. In choosing which back-links to include, the primary trade-off is that more back-links results in better connectivity, whereas a limited number of links results in smaller tree structures and therefore fewer hashes. At one extreme you can commit to every single header in the entire history of the block chain, by building an incremental data structure such as a binary heap. Such a structure would require log N storage per chain and log N hash operations per block update, where N is the total number of blocks in the chain. The root hash of this structure is then committed to the block chain in a known location. At the other extreme one could allow the miner instead to commit whatever back-links he or she desires, and force these the hash tree structure to be revealed prior to block validation. This allows the miner to be selective in choosing back-links which provide the most value, although there is not yet a clearly optimal mechanism for choosing these links. This is an area which requires more research with the purpose of determining the best structure for the hash tree of block header commitments, and the selection of back-links. ==Use cases== For SPV clients, a client that has just come online could quickly ascertain which block represents the most work, and retrieve compact proofs-of-inclusion for its transactions without having to download every intervening block header. This further eliminates the need for checkpoints in an SPV client as it can instead obtain very compact proofs back to the genesis block instead of the most recent checkpoint, at a comparable cost. Similar optimizations apply to the initial stages of headers-first synchronization of full nodes. Assuming the availability of (U)TxO hash-tree commitments, a compact SPV proof would allow a mobile client to very quickly fast-forward to the current most-work block from which it could then query the spend status of its wallet outputs. For merged-mined or slow proof-of-work side chains, the savings from not including every intervening block header could be very significant in bandwidth and processing time. Compact SPV proofs allow side chains or private accounting servers to experiment with very short block intervals without having a detrimental effect on SPV proof sizes, as the compact proofs scale logarithmically with the number of blocks. Finally the most important and driving use case: symmetrical two-way pegging between bitcoin and side-chains is made efficient enough to be reduced to practice by the availability of compact SPV proofs[1]. The compact SPV proofs allow both the necessary proofs-of-spend and proofs-of-reorg to fit within current blockchain size limitations, and provide incentives for keeping this data out of the block chain until it is absolutely necessary. ==References== This specific compact SPV proof proposal arose from pegging discussion involving a number of people #bitcoin-wizards: Greg Maxwell, Matt Corallo, Pieter Wuille, Luke-Jr, Jorge Timon, and Mark Friedenbach. It is believed that the first explanation of this general idea is due to Andrew Miller in his 7 Aug 2012 forum post titled "The High-Value-Hash Highway"[2]. [1]http://sourceforge.net/p/bitcoin/mailman/message/32108143/ [2]https://bitcointalk.org/index.php?topic=98986.0 -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.14 (GNU/Linux) Comment: GPGTools - http://gpgtools.org Comment: Using GnuPG with Thunderbird - http://www.enigmail.net/ iQIcBAEBAgAGBQJTJy/eAAoJEAdzVfsmodw4zC4P/izBRTutwypwQ70TxPxxHYfH I4QOpf+MgWHxrD+DKKyqkC2icgUBQz96K1vEhA86PrmK8DITs5yGHLSw7CEF/rlG hZErVY65IpowPt+JnlwOqHcqaoJ277s+4qpd/D9F7L1ROAMUDzzonf7V1Znr/fax lL4b8whfUI5jeRQby/tMiGPUB/1YJcbGmFccTW9gkGWMvoqZiiXcW7ZKuLrq5tbW RFIsrSt7rv3D0Cp2Fiyaxnryr2F0QOTqahHLn50+585eHpVFrA9A5T6xiBcEMzlQ l5cHRZb+lVIktWuYomBiqWljPLo5qercVDrehIq9FFSYuJqzudNx9ZXrpF1ZR4in UfZvlYqMFO/ZOTG33JWeeMonKlVwfHH2WreggzSq/JD/cH8dUj63A266Gaf6cl83 vEfhgVBDTXZnl5H9Z7wymja6R9m9Eo/Xf+GwRV4vyx1b9gcZXML4Zm4bTp4EXFHA StBGrYKmMpEb/gguk/hxJLsm0i9pVaQpMC0u3kClHTA5o0IFF9F5+mVjOb59HlDX AQx96TSwJzhl0l0jcxYye8bXmZFJvpzpsKRPwNISllLEagjplwK2Ub8q5du27lH5 R2qukcso6N5weGggUu1f7NrqcBALdz4E80SSpwu4YtJ6wdI4zsypaq4leqbSRSKh /hLKeOV5fEGNmwTtrDmN =j9cm -----END PGP SIGNATURE----- ------------------------------------------------------------------------------ Learn Graph Databases - Download FREE O'Reilly Book "Graph Databases" is the definitive new guide to graph databases and their applications. 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