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Ethash

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Ethash 是以太坊的工作量证明挖矿算法。 工作量证明现在已经被 **完全关闭**,取而代之,以太坊现在使用 [proof-of-stake](/developers/docs/consensus-mechanisms/pos) 来保证安全。 阅读更多关于合并权益证明质押的信息。 此页面是为了满足对历史的兴趣!

EthashDagger-Hashimoto 算法的修改版。 Ethash 工作量证明是内存密集型算法,这被认为使算法可抵御专用集成电路。 Ethash 专用集成电路最终被开发出来,但在工作量证明被关闭之前,图形处理单元挖矿仍然是一个可行的选择。 Ethash 仍然用于在其他非以太坊工作量证明网络上挖掘其他币。

Ethash 是如何工作的?

内存硬度通过工作量证明算法实现,需要根据随机数和区块头选择固定资源子集。 该资源(大小为几 GB)称为有向无环图。 有向无环图每 30000 个区块更改一次(大约 125 小时的窗口,称为一个时段(大约 5.2 天)),需要一段时间才能生成。 由于有向无环图仅依赖于区块高度,因此可以预先生成,但如果没有,则客户端需要等到此过程结束才能生成区块。 如果客户端没有提前预生成和缓存有向无环图,网络可能会在每个时段过渡时遇到严重的区块延迟。 请注意,不需要生成有向无环图即可验证,工作量证明本质上允许使用低端中央处理器和小内存进行验证。

该算法采取的一般路线如下:

  1. 有一个种子,可以通过扫描区块头直到该点来为每个区块计算种子。
  2. 从种子中可以计算出 16 MB 的伪随机缓存。 轻量级客户端存储缓存。
  3. 我们可以从缓存中生成一个 1 GB 数据集,数据集中每个项目仅依赖于一小部分缓存中的项目。 全客户端和矿工存储数据集。 数据集随着时间的流逝而呈线性增长。
  4. 采矿会抢走数据集的随机片段并将它们散列在一起。 可以通过使用缓存来重新生成您需要的数据集中的特定区块,以较低的内存进行验证,以使您只需要存储缓存。

每隔 30000 个区块更新一次大数据集,因此,矿工的绝大部分工作都是读取数据集,而不是对其进行修改。

定义

我们采用以下定义:

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
13
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使用“SHA3”

以太坊的开发恰逢 SHA3 标准的制定, 标准进程对最终确定的哈希算法的填充做了后期改动,使得以太坊的 “sha3_256”和“sha3_512”哈希值不是标准的 sha3 哈希值,而是在其他情况下 常被称为“Keccak-256”和“Keccak-512”的变量。 讨论请见此处此处此处

请记住这一点,因为下面的算法描述中提到了“sha3”哈希值。

参数

Ethash 的缓存和数据集的参数取决于区块号。 缓存大小和数据集大小都呈线性增长;然而,我们总是取低于线性增长阈值的最高素数,以降低意外规律导致循环行为的风险。

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
14
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附录中提供了数据集和缓存大小值表。

缓存生成

现在,我们来指定生成缓存的函数:

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
16
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缓存生成过程中,先按顺序填充 32 MB 内存,然后从严格内存硬哈希函数 (2014) 执行两次 Sergio Demian Lerner 的 RandMemoHash 算法。 输出一组 524288 个 64 字节值。

数据聚合函数

我们使用灵感来自 FNV 哈希的算法,在部分情况下,这种算法可用作逻辑异或的不相关替代。 请注意,我们使用全 32 位输入乘以素数,与之相对地,FNV-1 spec 用 1 个字节(8 个字节)依次乘以素数。

1FNV_PRIME = 0x01000193
2
3def fnv(v1, v2):
4 return ((v1 * FNV_PRIME) ^ v2) % 2**32
5
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请注意,即使黄皮书也指出 fnv 为 v1*(FNV_PRIME ^ v2),所有当前实现始终采用上述定义。

完整数据集计算

整个 1 GB 数据集中每个 64 字节项目的计算如下:

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)
13
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基本上,我们将来自 256 个伪随机选择的缓存节点的数据聚集起来求哈希值,以计算数据集节点。 然后生成整个数据集:

1def calc_dataset(full_size, cache):
2 return [calc_dataset_item(cache, i) for i in range(full_size // HASH_BYTES)]
3
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主循环

现在,我们指定了类似“hashimoto”的主要循环。在此循环中,我们聚合整个数据集的数据,以生成特定区块头和随机数的最终值。 在下面的代码中,header 代表一个被截断区块头的递归长度前缀表示的 SHA3-256 哈希值。被截断是指区块头被截去了 mixHash随机数字段。 nonce 是指一个 64 位无符号整数的八个字节,按大端序排列。 因此 nonce[::-1] 是上述值的八字节小端序表示:

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])
32
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基本上,我们保持着一个宽 128 字节的“混合物”,并多次按顺序从整个数据集中获取 128 字节,并使用 fnv 函数将其与混合物结合起来。 使用 128 字节的序列访问,以便每轮算法总是能从随机访问内存获取完整的页面,从而尽量减少转译后备缓冲区的疏忽,而专用集成电路在理论上能够避免这些疏忽。

如果此算法的输出低于所需目标,即证明随机数是有效的。 请注意,在最后额外应用 sha3_256 将确保中间随机数的存在。提供此证据可以证明至少做了少量工作;而且此快速外部工作量证明验证可以用于反分布式拒绝服务目的。 也可提供统计保证,说明结果是一个无偏 256 位数字。

挖矿

挖矿算法定义如下:

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
9
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定义种子哈希

为了计算用于在给定区块上挖掘的种子哈希值,我们使用以下算法:

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
6
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请注意,为了顺利挖矿和验证,我们建议在单个线程中预先计算未来的种子哈希值和数据集。

延伸阅读

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附录

如果您有兴趣将上述 python spec 作为代码运行,则应在头部添加以下代码。

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
46
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数据大小

以下查找表列表显示了大约 2048 个数据大小和缓存大小时段。

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,
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