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Ethash

Última edição: @MCreimer(opens in a new tab), 6 de março de 2024

Ethash foi o algoritmo de mineração da prova de trabalho do Ethereum. A prova de trabalho foi agora **totalmente desativada** e o Ethereum agora está protegido usando a prova de participação. Leia mais sobre A Fusão (The Merge), prova de participação e participação (stake). Esta página é de interesse histórico!

Ethash(opens in a new tab) é uma versão modificada do algoritmo Dagger-Hashimoto. A prova de trabalho Ethash faz uso de muita memória(opens in a new tab), o que foi pensado para tornar o algoritmo ASIC resistente. Os ASICs Ethash foram eventualmente desenvolvidos, mas a mineração de GPU ainda era uma opção viável até que a prova de trabalho fosse desativada. Ethash ainda é usado para minerar outras moedas em outras redes de prova de trabalho não Ethereum.

Como o Ethash funciona?

Dificuldade de memória é alcançada com um algoritmo de prova de trabalho que requer a escolha de subconjuntos de um recurso fixo dependente do nonce e do cabeçalho do bloco. Este recurso (alguns gigabytes em tamanho) é chamado de DAG. O DAG é alterado a cada 30.000 blocos, uma janela de cerca de 125 horas chamada de período eletrônico (aproximadamente 5,2 dias) e leva um tempo para gerar. Como o DAG depende apenas da altura do bloco, ele pode ser pré-gerado, mas o cliente não precisa esperar até o final deste processo para produzir um bloco. Se os clientes não pré-geraram e armazenaram em cache os DAGs antes, a rede pode sofrer um grande atraso em blocos em cada transição de período eletrônico (epoch). Note que o DAG não precisa ser gerado para verificar a prova de trabalho, permitindo essencialmente a verificação com baixa CPU e pouca memória.

A rota geral que o algoritmo faz é a seguinte:

  1. Existe uma seed que pode ser calculada para cada bloco escaneando os cabeçalhos dos blocos até esse ponto.
  2. Da seed, pode-se calcular um cache pseudo-randômico de 16 MB. Clientes leves armazenam o cache.
  3. A partir do cache, podemos gerar um conjunto de dados de 1 GB, com a propriedade que cada item no conjunto de dados depende de apenas um pequeno número de itens do cache. Clientes e mineradores completos armazenam o conjunto de dados. O conjunto de dados cresce linearmente com o tempo.
  4. Mineração envolve pegar fatias aleatórias do conjunto de dados e fazer hashing deles juntos. A verificação pode ser feita com pouca memória usando o cache para regenerar os pedaços específicos do conjunto de dados que você precisa, então você só precisa armazenar o cache.

O grande conjunto de dados é atualizado uma vez a cada 30.000 blocos, então o maior esforço de um minerador é ler o conjunto de dados, e não fazer alterações nele.

Definições

Nós empregamos as seguintes definições:

1WORD_BYTES = 4 # bytes in word
2DATASET_BYTES_INIT = 2**30 # bytes in dataset at genesis
3DATASET_BYTES_GROWTH = 2**23 # dataset growth per epoch
4CACHE_BYTES_INIT = 2**24 # bytes in cache at genesis
5CACHE_BYTES_GROWTH = 2**17 # cache growth per epoch
6CACHE_MULTIPLIER=1024 # Size of the DAG relative to the cache
7EPOCH_LENGTH = 30000 # blocks per epoch
8MIX_BYTES = 128 # width of mix
9HASH_BYTES = 64 # hash length in bytes
10DATASET_PARENTS = 256 # number of parents of each dataset element
11CACHE_ROUNDS = 3 # number of rounds in cache production
12ACCESSES = 64 # number of accesses in hashimoto loop
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O uso de 'SHA3'

O desenvolvimento do Ethereum coincidiu com o desenvolvimento do padrão SHA3, e o processo de padrões fez uma alteração tardia no preenchimento do algoritmo de hash finalizado, para que os hashes "sha3_256" e "sha3_512" do Ethereum não sejam hashes sha3 padrão, mas uma variante muitas vezes referida como "Keccak-256" e "Keccak-512" em outros contextos. Veja a discussão, por exemplo, aqui(opens in a new tab), aqui(opens in a new tab) ou aqui(opens in a new tab).

Tenha isso em mente, já que hashes "sha3" são referidos na descrição do algoritmo abaixo.

Parâmetros

Os parâmetros do cache Ethash e do conjunto de dados dependem do número do bloco. Tamanho do cache e tamanho do conjunto de dados crescem linearmente; entretanto, sempre tomamos o mais alto prime abaixo do limiar de crescimento linear, a fim de reduzir o risco de regularidades acidentais que conduzem a comportamentos cíclicos.

1def get_cache_size(block_number):
2 sz = CACHE_BYTES_INIT + CACHE_BYTES_GROWTH * (block_number // EPOCH_LENGTH)
3 sz -= HASH_BYTES
4 while not isprime(sz / HASH_BYTES):
5 sz -= 2 * HASH_BYTES
6 return sz
7
8def get_full_size(block_number):
9 sz = DATASET_BYTES_INIT + DATASET_BYTES_GROWTH * (block_number // EPOCH_LENGTH)
10 sz -= MIX_BYTES
11 while not isprime(sz / MIX_BYTES):
12 sz -= 2 * MIX_BYTES
13 return sz
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Tabelas de conjunto de dados e valores de tamanho do cache são fornecidos no apêndice.

Geração de cache

Agora, especificamos a função para produzir um cache:

1def mkcache(cache_size, seed):
2 n = cache_size // HASH_BYTES
3
4 # Sequentially produce the initial dataset
5 o = [sha3_512(seed)]
6 for i in range(1, n):
7 o.append(sha3_512(o[-1]))
8
9 # Use a low-round version of randmemohash
10 for _ in range(CACHE_ROUNDS):
11 for i in range(n):
12 v = o[i][0] % n
13 o[i] = sha3_512(map(xor, o[(i-1+n) % n], o[v]))
14
15 return o
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O processo de produção de cache envolve primeiro preenchimento sequencial de 32 MB de memória e depois executar duas passagens do algoritmo RandMemoHash de Sergio Demian Lerner de Strict Memory Hard Hashing Functions (2014)(opens in a new tab). A saída é um conjunto de 524288 valores de 64-bytes.

Função de agregação de dados

Usamos um algoritmo inspirado no FNV hash(opens in a new tab) em alguns casos como um substituto não associativo para o XOR. Observe que multiplicamos o primo com a entrada completa de 32 bits, em contraste com a especificação FNV-1 que multiplica o primo por um byte (octeto) por sua vez.

1FNV_PRIME = 0x01000193
2
3def fnv(v1, v2):
4 return ((v1 * FNV_PRIME) ^ v2) % 2**32
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Observe que até mesmo o yellow paper especifica fnv como v1*(FNV_PRIME ^ v2). Todas as implementações atuais usam consistentemente a definição acima.

Cálculo completo do conjunto de dados

Cada item de 64 bytes no conjunto de dados completo de 1 GB é calculado da seguinte forma:

1def calc_dataset_item(cache, i):
2 n = len(cache)
3 r = HASH_BYTES // WORD_BYTES
4 # initialize the mix
5 mix = copy.copy(cache[i % n])
6 mix[0] ^= i
7 mix = sha3_512(mix)
8 # fnv it with a lot of random cache nodes based on i
9 for j in range(DATASET_PARENTS):
10 cache_index = fnv(i ^ j, mix[j % r])
11 mix = map(fnv, mix, cache[cache_index % n])
12 return sha3_512(mix)
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Essencialmente, combinamos dados de 256 nós de cache selecionados de maneira pseudo-aleatória e fazemos o hash para calcular o nó do conjunto de dados. Todo o conjunto de dados é então gerado por:

1def calc_dataset(full_size, cache):
2 return [calc_dataset_item(cache, i) for i in range(full_size // HASH_BYTES)]
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Loop principal

Agora, especificamos o loop padrão "hashimoto" principal, onde agregamos dados do conjunto de dados completo para produzir nosso valor final para um cabeçalho em particular ou nonce. No código abaixo, header representa o hash _SHA3-256 da representação RLP de um cabeçalho de bloco _truncado, ou seja, de um cabeçalho excluindo os campos mixHash e nonce. nonce é os oito bytes de um inteiro sem sinal de 64 bits na ordem big-endian. Então nonce[::-1] é a representação little-endian de oito bytes desse valor:

1def hashimoto(header, nonce, full_size, dataset_lookup):
2 n = full_size / HASH_BYTES
3 w = MIX_BYTES // WORD_BYTES
4 mixhashes = MIX_BYTES / HASH_BYTES
5 # combine header+nonce into a 64 byte seed
6 s = sha3_512(header + nonce[::-1])
7 # start the mix with replicated s
8 mix = []
9 for _ in range(MIX_BYTES / HASH_BYTES):
10 mix.extend(s)
11 # mix in random dataset nodes
12 for i in range(ACCESSES):
13 p = fnv(i ^ s[0], mix[i % w]) % (n // mixhashes) * mixhashes
14 newdata = []
15 for j in range(MIX_BYTES / HASH_BYTES):
16 newdata.extend(dataset_lookup(p + j))
17 mix = map(fnv, mix, newdata)
18 # compress mix
19 cmix = []
20 for i in range(0, len(mix), 4):
21 cmix.append(fnv(fnv(fnv(mix[i], mix[i+1]), mix[i+2]), mix[i+3]))
22 return {
23 "mix digest": serialize_hash(cmix),
24 "result": serialize_hash(sha3_256(s+cmix))
25 }
26
27def hashimoto_light(full_size, cache, header, nonce):
28 return hashimoto(header, nonce, full_size, lambda x: calc_dataset_item(cache, x))
29
30def hashimoto_full(full_size, dataset, header, nonce):
31 return hashimoto(header, nonce, full_size, lambda x: dataset[x])
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Essencialmente, mantemos um "mix" de 128 bytes de largura, e de maneira sequencial e repetida buscamos 128 bytes do conjunto de dados completo e usamos a função fnv para combiná-lo com o mix. 128 bytes de acesso sequencial são usados para que cada rodada do algoritmo sempre busque uma página inteira de RAM, minimizando a possibilidade de que o buffer de pesquisa de tradução perca o que os ASICs teoricamente seriam capazes de evitar.

Se a saída deste algoritmo está abaixo do alvo desejado, então o nonce é válido. Observe que a aplicação extra de sha3_256 no final garante que existe um nonce intermediário que pode ser fornecido para provar que pelo menos uma pequena quantidade de trabalho foi feita; esta rápida verificação de prova de trabalho pode ser usada para fins anti-DDoS. Serve também para dar garantias estatísticas de que o resultado é um número imparcial de 256 bits.

Mineração

O algoritmo de mineração é definido da seguinte forma:

1def mine(full_size, dataset, header, difficulty):
2 # zero-pad target to compare with hash on the same digit
3 target = zpad(encode_int(2**256 // difficulty), 64)[::-1]
4 from random import randint
5 nonce = randint(0, 2**64)
6 while hashimoto_full(full_size, dataset, header, nonce) > target:
7 nonce = (nonce + 1) % 2**64
8 return nonce
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Definição do hash seed

Para calcular o hash seed que seria usado para minerar no topo de um determinado bloco, usamos o seguinte algoritmo:

1 def get_seedhash(block):
2 s = '\x00' * 32
3 for i in range(block.number // EPOCH_LENGTH):
4 s = serialize_hash(sha3_256(s))
5 return s
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Observe que, para que a mineração e a verificação aconteçam sem contratempos, recomendamos pré-computar os hashes seed e conjuntos de dados futuros em threads separadas.

Leitura adicional

Conhece algum recurso da comunidade que o ajudou? Edite essa página e adicione!

Apêndice

O código a seguir deve ser precedido se você estiver interessado em executar a especificação python acima como código.

1import sha3, copy
2
3# Assumes little endian bit ordering (same as Intel architectures)
4def decode_int(s):
5 return int(s[::-1].encode('hex'), 16) if s else 0
6
7def encode_int(s):
8 a = "%x" % s
9 return '' if s == 0 else ('0' * (len(a) % 2) + a).decode('hex')[::-1]
10
11def zpad(s, length):
12 return s + '\x00' * max(0, length - len(s))
13
14def serialize_hash(h):
15 return ''.join([zpad(encode_int(x), 4) for x in h])
16
17def deserialize_hash(h):
18 return [decode_int(h[i:i+WORD_BYTES]) for i in range(0, len(h), WORD_BYTES)]
19
20def hash_words(h, sz, x):
21 if isinstance(x, list):
22 x = serialize_hash(x)
23 y = h(x)
24 return deserialize_hash(y)
25
26def serialize_cache(ds):
27 return ''.join([serialize_hash(h) for h in ds])
28
29serialize_dataset = serialize_cache
30
31# sha3 hash function, outputs 64 bytes
32def sha3_512(x):
33 return hash_words(lambda v: sha3.sha3_512(v).digest(), 64, x)
34
35def sha3_256(x):
36 return hash_words(lambda v: sha3.sha3_256(v).digest(), 32, x)
37
38def xor(a, b):
39 return a ^ b
40
41def isprime(x):
42 for i in range(2, int(x**0.5)):
43 if x % i == 0:
44 return False
45 return True
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Tamanho dos dados

As tabelas de pesquisa a seguir fornecem aproximadamente 2.048 períodos eletrônicos (epoch) tabulados de tamanhos de dados e tamanhos de cache.

1def get_datasize(block_number):
2 return data_sizes[block_number // EPOCH_LENGTH]
3
4def get_cachesize(block_number):
5 return cache_sizes[block_number // EPOCH_LENGTH]
6
7data_sizes = [
81073739904, 1082130304, 1090514816, 1098906752, 1107293056,
91115684224, 1124070016, 1132461952, 1140849536, 1149232768,
101157627776, 1166013824, 1174404736, 1182786944, 1191180416,
111199568512, 1207958912, 1216345216, 1224732032, 1233124736,
121241513344, 1249902464, 1258290304, 1266673792, 1275067264,
131283453312, 1291844992, 1300234112, 1308619904, 1317010048,
141325397376, 1333787776, 1342176128, 1350561664, 1358954368,
151367339392, 1375731584, 1384118144, 1392507008, 1400897408,
161409284736, 1417673344, 1426062464, 1434451072, 1442839168,
171451229056, 1459615616, 1468006016, 1476394112, 1484782976,
181493171584, 1501559168, 1509948032, 1518337664, 1526726528,
191535114624, 1543503488, 1551892096, 1560278656, 1568669056,
201577056384, 1585446272, 1593831296, 1602219392, 1610610304,
211619000192, 1627386752, 1635773824, 1644164224, 1652555648,
221660943488, 1669332608, 1677721216, 1686109312, 1694497664,
231702886272, 1711274624, 1719661184, 1728047744, 1736434816,
241744829056, 1753218944, 1761606272, 1769995904, 1778382464,
251786772864, 1795157888, 1803550592, 1811937664, 1820327552,
261828711552, 1837102976, 1845488768, 1853879936, 1862269312,
271870656896, 1879048064, 1887431552, 1895825024, 1904212096,
281912601216, 1920988544, 1929379456, 1937765504, 1946156672,
291954543232, 1962932096, 1971321728, 1979707264, 1988093056,
301996487552, 2004874624, 2013262208, 2021653888, 2030039936,
312038430848, 2046819968, 2055208576, 2063596672, 2071981952,
322080373632, 2088762752, 2097149056, 2105539712, 2113928576,
332122315136, 2130700672, 2139092608, 2147483264, 2155872128,
342164257664, 2172642176, 2181035392, 2189426048, 2197814912,
352206203008, 2214587264, 2222979712, 2231367808, 2239758208,
362248145024, 2256527744, 2264922752, 2273312128, 2281701248,
372290086272, 2298476672, 2306867072, 2315251072, 2323639168,
382332032128, 2340420224, 2348808064, 2357196416, 2365580416,
392373966976, 2382363008, 2390748544, 2399139968, 2407530368,
402415918976, 2424307328, 2432695424, 2441084288, 2449472384,
412457861248, 2466247808, 2474637184, 2483026816, 2491414144,
422499803776, 2508191872, 2516582272, 2524970368, 2533359232,
432541743488, 2550134144, 2558525056, 2566913408, 2575301504,
442583686528, 2592073856, 2600467328, 2608856192, 2617240448,
452625631616, 2634022016, 2642407552, 2650796416, 2659188352,
462667574912, 2675965312, 2684352896, 2692738688, 2701130624,
472709518464, 2717907328, 2726293376, 2734685056, 2743073152,
482751462016, 2759851648, 2768232832, 2776625536, 2785017728,
492793401984, 2801794432, 2810182016, 2818571648, 2826959488,
502835349376, 2843734144, 2852121472, 2860514432, 2868900992,
512877286784, 2885676928, 2894069632, 2902451584, 2910843008,
522919234688, 2927622784, 2936011648, 2944400768, 2952789376,
532961177728, 2969565568, 2977951616, 2986338944, 2994731392,
543003120256, 3011508352, 3019895936, 3028287104, 3036675968,
553045063808, 3053452928, 3061837696, 3070228352, 3078615424,
563087003776, 3095394944, 3103782272, 3112173184, 3120562048,
573128944768, 3137339264, 3145725056, 3154109312, 3162505088,
583170893184, 3179280256, 3187669376, 3196056704, 3204445568,
593212836736, 3221224064, 3229612928, 3238002304, 3246391168,
603254778496, 3263165824, 3271556224, 3279944576, 3288332416,
613296719232, 3305110912, 3313500032, 3321887104, 3330273152,
623338658944, 3347053184, 3355440512, 3363827072, 3372220288,
633380608384, 3388997504, 3397384576, 3405774208, 3414163072,
643422551936, 3430937984, 3439328384, 3447714176, 3456104576,
653464493952, 3472883584, 3481268864, 3489655168, 3498048896,
663506434432, 3514826368, 3523213952, 3531603584, 3539987072,
673548380288, 3556763264, 3565157248, 3573545344, 3581934464,
683590324096, 3598712704, 3607098752, 3615488384, 3623877248,
693632265856, 3640646528, 3649043584, 3657430144, 3665821568,
703674207872, 3682597504, 3690984832, 3699367808, 3707764352,
713716152448, 3724541056, 3732925568, 3741318016, 3749706368,
723758091136, 3766481536, 3774872704, 3783260032, 3791650432,
733800036224, 3808427648, 3816815488, 3825204608, 3833592704,
743841981568, 3850370432, 3858755968, 3867147904, 3875536256,
753883920512, 3892313728, 3900702592, 3909087872, 3917478784,
763925868416, 3934256512, 3942645376, 3951032192, 3959422336,
773967809152, 3976200064, 3984588416, 3992974976, 4001363584,
784009751168, 4018141312, 4026530432, 4034911616, 4043308928,
794051695488, 4060084352, 4068472448, 4076862848, 4085249408,
804093640576, 4102028416, 4110413696, 4118805632, 4127194496,
814135583104, 4143971968, 4152360832, 4160746112, 4169135744,
824177525888, 4185912704, 4194303616, 4202691968, 4211076736,
834219463552, 4227855488, 4236246656, 4244633728, 4253022848,
844261412224, 4269799808, 4278184832, 4286578048, 4294962304,
854303349632, 4311743104, 4320130432, 4328521088, 4336909184,
864345295488, 4353687424, 4362073472, 4370458496, 4378852736,
874387238528, 4395630208, 4404019072, 4412407424, 4420790656,
884429182848, 4437571456, 4445962112, 4454344064, 4462738048,
894471119232, 4479516544, 4487904128, 4496289664, 4504682368,
904513068416, 4521459584, 4529846144, 4538232704, 4546619776,
914555010176, 4563402112, 4571790208, 4580174464, 4588567936,
924596957056, 4605344896, 4613734016, 4622119808, 4630511488,
934638898816, 4647287936, 4655675264, 4664065664, 4672451968,
944680842624, 4689231488, 4697620352, 4706007424, 4714397056,
954722786176, 4731173248, 4739562368, 4747951744, 4756340608,
964764727936, 4773114496, 4781504384, 4789894784, 4798283648,
974806667648, 4815059584, 4823449472, 4831835776, 4840226176,
984848612224, 4857003392, 4865391488, 4873780096, 4882169728,
994890557312, 4898946944, 4907333248, 4915722368, 4924110976,
1004932499328, 4940889728, 4949276032, 4957666432, 4966054784,
1014974438016, 4982831488, 4991221376, 4999607168, 5007998848,
1025016386432, 5024763776, 5033164672, 5041544576, 5049941888,
1035058329728, 5066717056, 5075107456, 5083494272, 5091883904,
1045100273536, 5108662144, 5117048192, 5125436032, 5133827456,
1055142215296, 5150605184, 5158993024, 5167382144, 5175769472,
1065184157568, 5192543872, 5200936064, 5209324928, 5217711232,
1075226102656, 5234490496, 5242877312, 5251263872, 5259654016,
1085268040832, 5276434304, 5284819328, 5293209728, 5301598592,
1095309986688, 5318374784, 5326764416, 5335151488, 5343542144,
1105351929472, 5360319872, 5368706944, 5377096576, 5385484928,
1115393871232, 5402263424, 5410650496, 5419040384, 5427426944,
1125435816576, 5444205952, 5452594816, 5460981376, 5469367936,
1135477760896, 5486148736, 5494536832, 5502925952, 5511315328,
1145519703424, 5528089984, 5536481152, 5544869504, 5553256064,
1155561645696, 5570032768, 5578423936, 5586811264, 5595193216,
1165603585408, 5611972736, 5620366208, 5628750464, 5637143936,
1175645528192, 5653921408, 5662310272, 5670694784, 5679082624,
1185687474048, 5695864448, 5704251008, 5712641408, 5721030272,
1195729416832, 5737806208, 5746194304, 5754583936, 5762969984,
1205771358592, 5779748224, 5788137856, 5796527488, 5804911232,
1215813300608, 5821692544, 5830082176, 5838468992, 5846855552,
1225855247488, 5863636096, 5872024448, 5880411008, 5888799872,
1235897186432, 5905576832, 5913966976, 5922352768, 5930744704,
1245939132288, 5947522432, 5955911296, 5964299392, 5972688256,
1255981074304, 5989465472, 5997851008, 6006241408, 6014627968,
1266023015552, 6031408256, 6039796096, 6048185216, 6056574848,
1276064963456, 6073351808, 6081736064, 6090128768, 6098517632,
1286106906496, 6115289216, 6123680896, 6132070016, 6140459648,
1296148849024, 6157237376, 6165624704, 6174009728, 6182403712,
1306190792064, 6199176064, 6207569792, 6215952256, 6224345216,
1316232732544, 6241124224, 6249510272, 6257899136, 6266287744,
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