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Block verification consumes a lot of time and processing power because the source code causes superlinear transaction confirmation times. This can be solved with new transaction formats, but we should also do something about it, especially since bigger blocks mean more transactions and the number of transactions increases exponentially (in English, it means all equations containing exponents, not just e^x in mathematics). Bitcoin Unlimited will incorporate a technique we call "parallel validation" that allows small or fast-validating member blocks to replace large or slow-validating blocks. This competitive technical approach will cause large blocks to be isolated, and miners will instead favor smaller blocks. However, it is very meaningful and can prevent extremely large blocks and "extremely costly transactions" (Translator's note: The extremely costly transactions here are costly transactions in the original text, meaning that the verification and broadcasting costs are very high, such as someone once maliciously constructed transactions with very large input and output quantities) through emergent consensus. Current software attempts to solve this problem using Sigops. However, sigops cannot be used in this way. Let's use Bitcoin's RPC "Create Raw Transaction" API to construct two transactions to illustrate. The first has one input and 10,000 outputs, and the second has 10,000 inputs and one output. The statistics for transaction 1 are as follows: Input: 1, Output: 10000
Size: 340126 bytes
Calculated sigops: 10000
Actual sigops: 1
sighash: 340092
Confirmation time: 125ms
Transaction 2 is completely different Input 10000, Output: 1 Size: 1474955 bytes Calculated sigops: 1 Actual sigops: 10000 sighash: 4100750000 Confirmation time: 394725 ms
It can be seen that the calculated sigops is exactly the opposite of the actual sigops, and the confirmation time is longer than the transaction with a calculated sigop of 1, and shorter than the transaction with a calculated sigops of 10,000. When confirming a transaction, the Bitcoin client first uses the input and then the output of the previous transaction (called unspent output). In other words, this input is the output of the previous transaction. The signature instruction needs to ensure that the signature confirmation is valid when the previous output is confirmed (unless you are using P2SH-STYLE TX-THE 3XXXADDRESSES). Of course, the outputs of the signature operation in this transaction are not used in the confirmation of this transaction. They will be used in the next transaction output. Therefore, the signop calculation code includes irrelevant signature operations and ignores relevant signature operations. What is the cost of transaction verification? The following graph depicts the confirmation time for different values of inputs and outputs in a "normal" transaction. The data was collected using an AMD 6-core 3.2 Ghz (red) and Intel 6-core 4.0 Ghz (green). The vertical axis represents the confirmation time in milliseconds, the left horizontal axis represents the output amount, and the right horizontal axis (depth) represents the input amount. Transaction confirmation time for transactions from 1-2000 inputs and outputs
To make the superlinear rise more obvious, the following figure shows a transaction with N inputs and one output (blue), and one input and N outputs (orange) Obviously it is the inputs that cause the nonlinear behavior, not the outputs. But we can fill in a curve based on this data. Now let's assume a quadratic mathematical model (ie ax² + by² + cxy + dx + ey + f): The results are as follows X= # inputs, Y= # outputs The model is: 0.004174*x^2 + 0.000008*y^2 + 2.435706*x +0.136400*y + 0.001659*x*y + 879.778020
-0.000008 is pretty close to zero in this data collection (0-2000 output). So both from the data analysis and the graph, the data looks very much like a quadratic equation in the input and a straight line in the output. I won't do a formal error analysis in this informal report, since we won't be using these constants directly, but in the 3D graph, you can see that Model 1 (red) explains the trend of the actual data (green) reasonably well. The second guess in the N case limit 1 seems to jump out because of the constant. How do we solve this problem? From the above graph we should clearly understand that input value is better than signops in transactions as an estimate. But this data is limited to simple transactions. We know that some inputs require multiple signatures. In theory, we must calculate sigops. However, to do so we need to enter all previous transactions. And from a practical standpoint, these transactions are difficult to enter Satoshi's client source code. Satoshi is just more comfortable with the UTXO on top of the existing active blockchain. But we need to be able to estimate any block or transaction. Therefore we cannot look at previous outputs to determine the correct signops. However, since the Bitcoin script language does not allow loop closures, each signature must be in the input script. This means that the length of the input script is a proxy for sigops. We also know how transactions are confirmed, each OP-CHECKSIG signs a complete transaction (inputs and outputs) and checks the competition between the signature and the hash data. So a reasonable prediction is Transaction effort = length of all inputs * total length Block effort = SUM(transaction effort)
(Translator's note: The word effort appears frequently in this article. I am not sure what it should be translated as, so I will temporarily translate it as "cost". From the context, I guess the original word "length" refers to the number of inputs and outputs, so I will translate it as "volume size" instead of the literal "length") Of course, the total volume is the sum of the input and output volumes. So this equation can also be rewritten as transaction effort = len(inputs)^2 * len(outputs)
So this estimate is very similar to the model we extracted from the data. It extracts the quadratic input characteristics and the XY terms. It also ignores linear effects, but these are not important. I am going to use the metric "Bigger Blocks" (EB) to calculate the block size and the number of transactions in blocks larger than 1MB. We will provide a configuration parameter "Cost per MB". Blocks with a cost per MB greater than this parameter will be considered large blocks. For blocks of 1M or less, Bitcoin Unlimited will continue to enforce the current rules. After this divergence, we will continue to allow blocks smaller than 1MB to adapt to the old rules by maintaining compatibility with old transactions. That is, transactions that have not yet been submitted can still be submitted. This also simplifies the code. The block/transaction size estimation code does not require external information and blockchain description tables. It can be obtained by a block or large transaction or by observing the object. Let me explain this rule just in terms of block size. This is not a traditional fork consensus rule, so if the rule is broken or other clients use a different standard, there will be no blockchain forks. So it uses the "emergent consensus" algorithm. This algorithm has many advantages: This can make it easier to change the rules in the future, that is, old blocks do not need to follow this rule, but only need to strictly follow the rule of a Bitcoin blockchain. However, the details of the emergent consensus algorithm are beyond the scope of this article. The final question is how do the defaults reflect the “greater cost” of Bitcoin Unlimited? In the following description, I will quote a value of 150,000,000,000 per MB. The size of this number doesn’t mean much, but it will result in a confirmation time of about 10 seconds per MB on modern processors. It will be longer on ARM processors, but the estimate will be preserved. As I explain below, the confirmation time will also be less than the worst case block confirmation time on today’s blockchain. What does this mean for blockchain? We can calculate all the blocks currently in the Bitcoin blockchain and retrieve them from the highest to the lowest “cost” (see the appendix at the end of this article). All of these blocks contain a transaction that is difficult to confirm. These transactions range from 350KB to 1MB, so not many transactions can fit into a block. This means that a block with 350KB transactions will take a high but reasonable 30 seconds per MB to confirm. So if we block transactions like 100/175, 100/195, 100/742 in the future (00005708% of them), we can solve this problem ourselves. These higher-cost transactions seem to be more like "junk dust" transactions (I checked many but not all transactions, please contact me if there are any discrepancies). However, as far as I know, splitting a dust transaction into several small transactions is fine. Appendix: The most expensive blocks block hash, # transactions, max tx length, max # vin, max # vout, block cost, max tx cost block hash, # transactions, max tx length, max # vin, max # vout, block cost, max tx cost
('00000000000000003dd2fdbb484d6d9c349d644d8bbb3cbfa5e67f639a465fe', 2, 999657, 5569, 1, 999268159512, 999268133427)
('00000000000000000283e9409575c2426cd72fcb722065431c52b5083e5bb58', 2, 999651, 5569, 1, 999243168477, 999243142392)
('0000000000000000d63417949af6653756d975f5e60cacff162303efcc41f3e', 2, 999622, 7350, 1, 999222177285, 999222151200)
('0000000000000000671d60be5c9439be636a4e00f50c33141ded6a29f816cbc', 2, 999621, 7350, 1, 999221177685, 999221151600)
('00000000000000003104258b4af9f6362b9e37cff80a25f521ee222a393330c', 2, 999634, 5569, 1, 999209181635, 999209155550)
('0000000000000000058319fa2282779aada74b249369ecf9baa7ffaed3e11fb0', 2, 999611, 5569, 1, 999163200357, 999163174272)
('0000000000000000030efd6441dc3520878727dc7c195aa3a268f33f41a344e4', 2, 999608, 5569, 1, 999157202877, 999157176792)
('0000000000000000c17f800899d77056a61e0ec5a47402e61eba00ee621ba9f', 235, 926262, 5160, 6, 857932538512, 857906643186)
('0000000000000000094b3d68fe7004b683c55aa40b6fb0e633d3f31105bf0831', 346, 897599, 5000, 20, 805660561281, 805631006460)
('000000000000000008360c45209d17a47fc4ae9c580e519323c4c7b9b2a6ab58', 371, 897564, 5000, 9, 805603866660, 805568177820)
('0000000000000000286409e3efb3e7c0653be26472f19089dbee4861f08e0ad', 119, 886617, 4925, 9, 786424716789, 785988630351)
('0000000000000000113ba2a64fdfd175223ba3c3fccd02f3673a92d2303d4d3b', 165, 883773, 4909, 11, 780984714454, 780953965407)
('0000000000000000117527da7d5c18cb03e3486b40409acef382be70a7480d69', 207, 854331, 4746, 12, 730140672352, 729813111081)
('00000000000000000efc700678729b24309c9a5dfae8c6965c3a493b690f531c', 338, 842481, 4680, 74, 709740975337, 709706836881)
('00000000000000003777900d8512b213aa30c1f830c867bc0b09d55796a6041', 489, 842079, 4691, 51, 709127971391, 709047359580)
('00000000000000000528f81f5641d0c240176fbfe2a9bc5e92ce06124bfc5224', 279, 840022, 20000, 39, 705963364464, 705618480000)
('0000000000000000008368a5c59bf755abd9d967370fe7c7a1c2929684e7e8a2', 273, 840022, 20000, 13, 705918102321, 705618480000)
('000000000000000011c34837a74038b730edeaefd3a158d0ba0e1e1390f5c220', 281, 840219, 4667, 10, 705914181075, 705872182995)
('0000000000000000053bceb058c6e8fae9efd0c17746e6c845f89ef1d97893f8', 260, 840022, 20000, 51, 705859962311, 705618480000)
('00000000000000000bef938ebe4f04049206995fca611c78692606db3871b04c', 376, 840022, 20000, 21, 705810617110, 705618480000)
('00000000000000000b8d631639b0dd7ea223f2efc46fc9ab0992f7d612e29c25', 368, 840022, 20000, 101, 705791298560, 705618480000)
('0000000000000000e17bc7ba14fc16897a41cb1b2f0b89ddbad2cfe30184a61', 423, 840022, 20000, 16, 705790914100, 705618480000)
('00000000000000005780446bbdddfff6e547ab83d39b237ec0f1440ff9af45f', 346, 840022, 20000, 16, 705743934757, 705618480000)
('000000000000000096aa43cd0d602b704bfa23f620141eea4006f179d40ce08', 477, 840022, 20000, 11, 705720326435, 705618480000)
('000000000000000012ea0ca9579299ec120e3f57e7c309216884872592b29970', 420, 840022, 20000, 6, 705681723837, 705618480000)
('00000000000000007c5ace173341f0bcdfe3a8edcecfb7c23d3336829a2bf80', 253, 839406, 4663, 74, 704772458086, 704535280356)
('0000000000000000063e5b9d30e49596fe2219b0decfcf694f00653fc661fa38', 266, 837794, 4654, 21, 701945523339, 701831762916)
('0000000000000000d86f6cc57eae1f167321c3650bb238944712dd4e2a1efb0', 188, 832508, 4625, 8, 693811660588, 692974664152)
('0000000000000000ec68dc67c0bde9fab8502f95c2bc8894f42959ddffb179a', 278, 831095, 4617, 36, 690825131965, 690652411425)
('0000000000000000d60936f7885c4407e0e18a4a9e02bfc97b417d06637f2e0', 394, 828552, 4603, 14, 686526538402, 686432132544)
('00000000000000002d10761a51dd948b52af03cc758aa37f15dd14761968a86', 45, 811536, 4507, 5, 659541991519, 658442979744)
('00000000000000009327d9cd32c82b78b23f877c82587cfb4d1142e6433cd57', 224, 796238, 4423, 21, 634073229246, 633931253604)
('000000000000000009a07b761b0239baf86a3449e25f842a37bc604628e7e87a', 509, 789537, 4386, 13, 623377439128, 623305511409)
('000000000000000002a8571bee11074e33021e594b8909d23f28aa2ec6a03d92', 527, 787898, 4377, 12, 620771768498, 620720226564)
('0000000000000000d9fa4313b005a54db9242295b5c4ca193f6b676b6069295', 323, 782696, 4348, 151, 613085446559, 612550412736)
('00000000000000008fc403e02c73b32a5b6139bd2e4debabdc8df9ba180232d', 299, 773527, 4297, 16, 598527747893, 598308437487)
('00000000000000000872231d0d3d402e5dddd30711fdb19f242fd7c59a7f57c6', 430, 772964, 4294, 15, 597485956914, 597411508176)
('00000000000000000596cff56060b95758fb6e77f5d0fbf87e5b83989e76be45', 370, 761938, 4233, 9, 582014941473, 580488560804)
('0000000000000000ad13642532640c520abfede7f16d80922277471013abb09', 421, 761037, 4227, 12, 579504571396, 579116432409)
('000000000000000008cb5666ad253b9308c0c11a581b354f25a76d0effe94f35', 208, 755955, 4199, 21, 571719356275, 571330378215)
('0000000000000000063649fc8894f697fc58c7b7d87918c47f462ad8833e5db1', 198, 737559, 5000, 35, 567077766234, 543959350767)
('000000000000000000747e3d8314a3e3d21ed2f44d94e256f50b49e741e1fac4', 73, 745449, 4141, 4, 557346698144, 555634575681)
('000000000000000007eee2a2844312f5718db70dc3ec6263017ab3e2823c4384', 539, 742362, 4124, 50, 551332389904, 551041950084)
('000000000000000015c89ab74c296908c9e5f269508ee410293983b12619085f', 235, 737510, 5000, 7, 546642860065, 543890024680)
('00000000000000000c251056710cd5ae9855f8373b64675ada89d96e3292395d', 220, 737548, 5000, 18, 544198251563, 543946075288)
('0000000000000000116e7371b8a7c35834d2b62a5806bd04c16bc3474a72cc26', 109, 724941, 4027, 15, 526338649627, 525481458201)
('000000000000000085412139c377478b8a7ff7d31caa35ac160251f411f8d8b', 628, 718410, 3991, 17, 516990431986, 516055455300)
('0000000000000000013ec024ffc51a6d87c30362bf6c41b9290fb3db9e2ac508', 171, 701117, 3895, 58, 501481440693, 491508958329)
('0000000000000000088ab3a8a791419bfc88b854571894d7dfd7b225e0980a63', 320, 692557, 3847, 151, 483406043326, 479556246751)
('0000000000000000ede556711a82f88d1d8669da648a92de134d1f32463da53', 666, 694193, 3856, 19, 482008798325, 481848385809)
('0000000000000000e5c87d568324ba252550a4cb02b7279cf398b9994c0c39f', 409, 691939, 3844, 12, 478795452118, 478724224601)
('000000000000000093d5e21b67b8febbf067a538fb6193a4fc0d6948346f24a', 800, 682650, 3792, 167, 466126999742, 465956410500)
('000000000000000013bee13c13c8408e72e75b78800b6493a71fd56f5d975b8', 1032, 655425, 3651, 58, 432757522025, 429543260550)
('000000000000000015a382acfc08bd42952fef355b66c9c9e6550353b6c167d0', 663, 655438, 3651, 22, 429664524420, 429560301002)
('00000000000000004e568e462c0acf1843ca5dd15bc356a921729cd33b8ae71', 377, 632404, 3513, 54, 413502951557, 399884226896)
('000000000000000054790aa56d6ca30b033233a133d02d308878b719f711b41', 641, 612356, 3411, 18, 412788257766, 374943741732)
('0000000000000000bfbefddfe17466b9cbe7dcfec7833f3be1fd5738e964944', 530, 634422, 3524, 2418, 403053803050, 402440520324)
('00000000000000007a7648870dbaa5668a6f9307e99060cc7c0703945e098bd', 821, 613585, 3418, 102, 376639652381, 376458327315)
('0000000000000000d62348cd0bde52e8cf8aa85df3b0b0d23594565667f58d9', 161, 596708, 3314, 15, 356255535628, 355992412552)
('0000000000000000b3424dade9b0402fe56db61c6c7de15c440772c18e7ec0f', 177, 585148, 3250, 8, 342439831082, 342331475032)
('000000000000000004bf023e5fe85087d01f1c345de703489b89a429d525c65a', 252, 418687, 2325, 8, 315137532937, 175236838293)
('0000000000000000c94ca4441d4f2470188dcb8845820d818cbfaf9f0c838e9', 388, 559319, 3116, 154, 314660386656, 312812015087)
('000000000000023d9a3ee2714f4365b2d312700ba113af23084104319133c6c0', 725, 465554, 2585, 24, 295090009096, 216639967252)
('00000000000000002ac55f2ada57d8f6034bf079fc3c16cdd961531650045db', 283, 500012, 3390, 22, 294403660972, 249990999640)
('0000000000000000120f31d6e21a8976066f1ea8e3652a144d99d3fe10ba461e', 377, 500028, 3390, 15, 293764638072, 250006999608)
('000000000000000010889bb61503de0bbcd225c4b57ea0c709f5f6403962ca08', 439, 500048, 3390, 22, 293677436332, 250027000288)
('000000000000000077c1da70b544d3b401805ee4f0f8da8433212049194cb8b', 552, 499992, 3390, 15, 293644521158, 249971000400)
('0000000000000000bdf286d03caf440c81c0a49503be628a6ab784b813ab745', 523, 531058, 3600, 101, 288542881258, 282000294928)
('0000000000000000ca5400a9d607c7e6cdf95aded1681f043f0e7528ad13a5c', 582, 512204, 2853, 20, 287517152285, 262322717580)
('0000000000000000de35723889e1c31ca66d527c4d72ccb726a9841c924c082', 1173, 535796, 2976, 74, 287366298960, 287034489936)
('000000000000000006a53e8e9dc2be33f91bf04a3cea4c4cff8a47c1b6520dd8', 1094, 531061, 3600, 30, 286421196770, 282003481159)
('00000000000000001474b9a66f8f8b6c890135ae2074ef767493d3f60d0c0044', 705, 500032, 3390, 175, 272044428303, 250010999680)
('000000000000000011418703f3e6674e1a19cdfd9955f76ffd646bf2dedcfda3', 515, 486870, 2704, 21, 267978654435, 236986893720)
('0000000000000000126b5419f9d31f64fe9e91640b5fc383af629828bbae0fd', 254, 505880, 2810, 74, 256576274071, 255874104000)
('000000000000000001dcb26d9a6786955cfdfd94e368c5ca25ae672233823c7d', 1491, 500057, 3390, 41, 251089361416, 250036000855)
('00000000000000008686f8ee926d297063471f15693530de1b59393dd5a95cf', 607, 500022, 3390, 3846, 250537960825, 250000999560)
('000000000000000001e23249369c26abdd142b506c1796934f2e1780bd15a216', 1481, 500073, 3390, 77, 250227656361, 250052002263)
('0000000000000000e700a9de911a57ae5c3ac4238530878ebf18f2cba7d2bb4', 586, 500073, 3390, 102, 250210561024, 250052002263)
('000000000000000011bae3d44a6f198f4670bc2502b6cc725f28d9fe04dec5db', 439, 500063, 3390, 102, 250139971582, 250042001323)
('000000000000000007b4bd703d1ca95a51b3d70f2b74ddf09942f95cc3a5128b', 474, 500018, 3390, 102, 250096537199, 249996999568)
('0000000000000000afa83a2bef7bf2c7c4b055554dc64b31c5f71ddecd9d4e6', 461, 496472, 2758, 21, 246697639731, 246461609072)
('000000000000000003d9e27c8aa6b846b1db19df2db50373c643542c62725363', 769, 491111, 2728, 151, 241290452375, 241150725441)
('00000000000000000c840c9855a79d9e629d2b4357136df495966b960ec8ff25', 228, 483953, 2688, 11, 234545821649, 234171789969)
('00000000000000008fa8784a8921bd64983f60c8daea41b74197ac1921edee9', 740, 471876, 2621, 179, 224194921204, 222613165512)
('00000000000000000087036d230bed40f5c74f8c4aa0800c0b4bec183110b773', 372, 469724, 2609, 21, 221870040189, 220603058256)
('000000000000000000812d4b59c826bd2047e72e01c3ba3f3ad517c63e7de64', 714, 464554, 2580, 229, 217097056954, 215773254596)
('0000000000000000101c965a762eb6ff0d541a3b03dd96130851d7efee9f57c7', 140, 463683, 2575, 21, 215429176215, 214933299405)
('0000000000000001052a4c9af72f80c634e0da86733c1aeca3a206cf1662ccc', 366, 457507, 2541, 60, 211799631965, 209276054489)
('000000000000000021b72ac222d06f424902454c86748f096119ec81e8aeebd', 306, 456711, 2537, 12, 208676485402, 208532872467)
('00000000000000001098af47793a0094c310e089efcc81d0ef6dc6cc53b2c198', 1057, 451541, 2508, 61, 204827126763, 203837799007)
('00000000000000001196412df6f4d90e1c773a2fc4cb4d4d6b1d1360f5e62438', 1390, 439184, 2439, 74, 193164601772, 192802654368)
('00000000000000450634d2a059e1a154cfd5783872ff9c7e788524e81fa163a1', 358, 369986, 2055, 41, 183989940557, 136860041316)
('0000000000000000ce1f56134e7d27eee5db75466723e21655e478028fe2576', 491, 425781, 2365, 56, 181738057055, 181255397481)
('0000000000000000816cabe4571b0b665993e637d00dba8ac45222b1712a83c', 526, 419896, 9997, 151, 180245981292, 176303413104)
('00000000000000006c2664614dacb672c47a42a6ab270d1bdd01abc837c7f6d', 1040, 412318, 2290, 251, 170842082052, 169973147684)
('0000000000000000b7df7d919db2b73c23d6c016acae098778ea70c9095e00c', 979, 368776, 2500, 468, 159134078850, 135978774480)
('00000000000000000d710f3876a7b235aab173042cfe77ff7d0d1972bc279465', 416, 388415, 2157, 151, 153639042348, 150821932915)
('0000000000000000e7c7050d8e8546c1db61a064f2cc6ce5c60f009dde8a875', 1061, 338825, 1882, 142, 141730172877, 114775274625)
('0000000000000000a9cd67f563169d5f1452a305d6e311e822e4f9ffc88ca9a', 548, 364589, 2025, 134, 135044516959, 132895971801)
('000000000000000009cd352daf6ab3edeceefd21838028d20ea60d0ef282afa8', 387, 359854, 1999, 22, 131024341095, 129453877960)
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