[Chinese Simplified] Ethash中文翻译

Corey Lin edited this page Nov 2, 2018 · 4 revisions

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目录

此规范是修订版23.如果你在实质上(比如,未澄清)更新算法,请更新此句中的修订号。此外,在所有实现中,请包括规范修订号

Ethash是Ethereum 1.0计划的PoW算法。它是Dagger-Hashimoto的最新版本,虽然它不能再适当地被称为Dagger-Hashimoto,因为在上个月的研究和开发中,两种算法的许多原始特征都发生了巨大的变化。有关原始版本,请参阅 https://github.com/ethereum/wiki/wiki/Dagger-Hashimoto

算法采用的基本路径如下:

  1. 存在一个种子(seed),这个种子可以通过扫描区块头部直到该点为每个区块计算。
  2. 从种子中,可以计算出16 MB的伪随机缓存。轻客户端存储缓存。
  3. 从缓存中,我们可以生成1 GB的数据集,其属性是数据集中的每个项仅依赖于缓存中的少量项。完整客户端和矿工存储数据集。数据集随时间线性增长。
  4. 挖矿涉及抓取数据集的随机切片并将它们一起哈希。通过使用缓存重新生成所需数据集的特定部分,可以使用低内存进行验证,因此你只需要存储缓存。

大型数据集每30000个块更新一次,因此绝大多数矿工的工作将是读取数据集,而不是对其进行更改。

有关此算法的设计原理方面的考虑,请参阅 https://github.com/ethereum/wiki/wiki/Ethash-Design-Rationale

定义

我们采用以下定义:

WORD_BYTES = 4                    # bytes in word
DATASET_BYTES_INIT = 2**30        # bytes in dataset at genesis
DATASET_BYTES_GROWTH = 2**23      # dataset growth per epoch
CACHE_BYTES_INIT = 2**24          # bytes in cache at genesis
CACHE_BYTES_GROWTH = 2**17        # cache growth per epoch
CACHE_MULTIPLIER=1024             # Size of the DAG relative to the cache
EPOCH_LENGTH = 30000              # blocks per epoch
MIX_BYTES = 128                   # width of mix
HASH_BYTES = 64                   # hash length in bytes
DATASET_PARENTS = 256             # number of parents of each dataset element
CACHE_ROUNDS = 3                  # number of rounds in cache production
ACCESSES = 64                     # number of accesses in hashimoto loop
关于本规范中描述的“SHA3”哈希的注释

以太坊的开发与SHA3标准的发展相吻合,标准流程对最终哈希算法的填充进行了后期更改,因此以太坊的“sha3_256”和“sha3_512”哈希不是标准的sha3哈希,而是经常提到的在其他环境中作为“Keccak-256”和“Keccak-512”的变体。参见讨论,例如 here, here, 或 here

请记住这一点,因为“sha3”哈希在下面的算法描述中被引用。

参数

Ethash缓存和数据集的参数取决于区块编号。缓存大小和数据集大小都呈线性增长;然而,我们总是采用低于线性增长阈值的最高素数,以降低导致循环行为的偶然规律性的风险。

def get_cache_size(block_number):
    sz = CACHE_BYTES_INIT + CACHE_BYTES_GROWTH * (block_number // EPOCH_LENGTH)
    sz -= HASH_BYTES
    while not isprime(sz / HASH_BYTES):
        sz -= 2 * HASH_BYTES
    return sz

def get_full_size(block_number):
    sz = DATASET_BYTES_INIT + DATASET_BYTES_GROWTH * (block_number // EPOCH_LENGTH)
    sz -= MIX_BYTES
    while not isprime(sz / MIX_BYTES):
        sz -= 2 * MIX_BYTES
    return sz

附录中提供了数据集和缓存大小值的表。

缓存生成

现在,我们指定用于生成缓存的函数:

def mkcache(cache_size, seed):
    n = cache_size // HASH_BYTES

    # Sequentially produce the initial dataset
    o = [sha3_512(seed)]
    for i in range(1, n):
        o.append(sha3_512(o[-1]))

    # Use a low-round version of randmemohash
    for _ in range(CACHE_ROUNDS):
        for i in range(n):
            v = o[i][0] % n
            o[i] = sha3_512(map(xor, o[(i-1+n) % n], o[v]))

    return o

缓存生产过程包括首先顺序填充32 MB内存,然后执行来自 Strict Memory Hard Hashing Functions (2014) 的两次Sergio Demian Lerner的RandMemoHash算法。输出是一组524288 64字节值。

数据聚合函数

在某些情况下,我们使用受 FNV hash 启发的算法作为XOR的非关联替代。请注意,我们将素数与完整的32位输入相乘,而FNV-1规范则将素数乘以一个字节(八位字节)。

FNV_PRIME = 0x01000193

def fnv(v1, v2):
    return ((v1 * FNV_PRIME) ^ v2) % 2**32

请注意,即使黄皮书指定fnv为v1*(FNV_PRIME ^ v2),所有当前实现都始终使用上述定义。

完整的数据集计算

完整1 GB数据集中的每个64字节项计算如下:

def calc_dataset_item(cache, i):
    n = len(cache)
    r = HASH_BYTES // WORD_BYTES
    # initialize the mix
    mix = copy.copy(cache[i % n])
    mix[0] ^= i
    mix = sha3_512(mix)
    # fnv it with a lot of random cache nodes based on i
    for j in range(DATASET_PARENTS):
        cache_index = fnv(i ^ j, mix[j % r])
        mix = map(fnv, mix, cache[cache_index % n])
    return sha3_512(mix)

本质上,我们组合来自256个伪随机选择的缓存节点的数据,并对其进行哈希以计算数据集节点。然后通过以下方式生成整个数据集:

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

主循环

现在,我们指定主类似“hashimoto”的循环,我们从完整数据集聚合数据,以便为特定的头和随机数生成最终值。在下面的代码中,header表示截断的区块头的 RLP 表示的SHA3-256哈希,即不包括字段mixHashnonce的区块头。 nonce是big-endian顺序的64位无符号整数的八个字节。所以nonce[::-1]是该值的八字节little-endian表示:

def hashimoto(header, nonce, full_size, dataset_lookup):
    n = full_size / HASH_BYTES
    w = MIX_BYTES // WORD_BYTES
    mixhashes = MIX_BYTES / HASH_BYTES
    # combine header+nonce into a 64 byte seed
    s = sha3_512(header + nonce[::-1])
    # start the mix with replicated s
    mix = []
    for _ in range(MIX_BYTES / HASH_BYTES):
        mix.extend(s)
    # mix in random dataset nodes
    for i in range(ACCESSES):
        p = fnv(i ^ s[0], mix[i % w]) % (n // mixhashes) * mixhashes
        newdata = []
        for j in range(MIX_BYTES / HASH_BYTES):
            newdata.extend(dataset_lookup(p + j))
        mix = map(fnv, mix, newdata)
    # compress mix
    cmix = []
    for i in range(0, len(mix), 4):
        cmix.append(fnv(fnv(fnv(mix[i], mix[i+1]), mix[i+2]), mix[i+3]))
    return {
        "mix digest": serialize_hash(cmix),
        "result": serialize_hash(sha3_256(s+cmix))
    }

def hashimoto_light(full_size, cache, header, nonce):
    return hashimoto(header, nonce, full_size, lambda x: calc_dataset_item(cache, x))

def hashimoto_full(full_size, dataset, header, nonce):
    return hashimoto(header, nonce, full_size, lambda x: dataset[x])

本质上,我们维持一个128字节宽的“混合”,并从整个数据集中重复顺序获取128个字节,并使用fnv函数将其与“混合”组合。使用128字节的顺序访问,以便每轮算法总是从RAM中获取一整页,从而最小化ASIC在理论上能够避免的转换后备缓冲器未命中。

如果此算法的输出低于所需目标,则nonce有效。请注意,sha3_256最后的额外应用确保存在一个中间的nonce,可用于证明至少完成了少量的工作;这种快速外部PoW验证可用于防DDoS目的。它还用于提供统计保证,结果是无偏见的256位数。

挖矿

挖矿算法定义如下:

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

定义种子哈希

为了计算将被用于在给定区块之上挖矿的种子哈希,我们使用以下算法:

 def get_seedhash(block):
     s = '\x00' * 32
     for i in range(block.number // EPOCH_LENGTH):
         s = serialize_hash(sha3_256(s))
     return s

请注意,为了平滑挖矿和验证,我们建议在单独的线程中预先计算未来的种子哈希和数据集。

附录

如果你有兴趣将上述python规范作为代码运行,则应该预先添加以下代码。

import sha3, copy

# Assumes little endian bit ordering (same as Intel architectures)
def decode_int(s):
    return int(s[::-1].encode('hex'), 16) if s else 0

def encode_int(s):
    a = "%x" % s
    return '' if s == 0 else ('0' * (len(a) % 2) + a).decode('hex')[::-1]

def zpad(s, length):
    return s + '\x00' * max(0, length - len(s))

def serialize_hash(h):
    return ''.join([zpad(encode_int(x), 4) for x in h])
  
def deserialize_hash(h):
    return [decode_int(h[i:i+WORD_BYTES]) for i in range(0, len(h), WORD_BYTES)]
  
def hash_words(h, sz, x):
    if isinstance(x, list):
        x = serialize_hash(x)
    y = h(x)
    return deserialize_hash(y)

def serialize_cache(ds):
    return ''.join([serialize_hash(h) for h in ds])
  
serialize_dataset = serialize_cache

# sha3 hash function, outputs 64 bytes
def sha3_512(x):
    return hash_words(lambda v: sha3.sha3_512(v).digest(), 64, x)

def sha3_256(x):
    return hash_words(lambda v: sha3.sha3_256(v).digest(), 32, x)

def xor(a, b):
    return a ^ b

def isprime(x):
    for i in range(2, int(x**0.5)):
         if x % i == 0:
             return False
    return True

数据大小

以下查找表提供大约2048个列表的数据大小和缓存大小的时期。它们是使用此处提供的Mathematica函数生成的:

def get_datasize(block_number):
    return data_sizes[block_number // EPOCH_LENGTH]

def get_cachesize(block_number):
    return cache_sizes[block_number // EPOCH_LENGTH]

data_sizes = [
1073739904, 1082130304, 1090514816, 1098906752, 1107293056, 
1115684224, 1124070016, 1132461952, 1140849536, 1149232768, 
1157627776, 1166013824, 1174404736, 1182786944, 1191180416, 
1199568512, 1207958912, 1216345216, 1224732032, 1233124736, 
1241513344, 1249902464, 1258290304, 1266673792, 1275067264, 
1283453312, 1291844992, 1300234112, 1308619904, 1317010048, 
1325397376, 1333787776, 1342176128, 1350561664, 1358954368, 
1367339392, 1375731584, 1384118144, 1392507008, 1400897408, 
1409284736, 1417673344, 1426062464, 1434451072, 1442839168, 
1451229056, 1459615616, 1468006016, 1476394112, 1484782976, 
1493171584, 1501559168, 1509948032, 1518337664, 1526726528, 
1535114624, 1543503488, 1551892096, 1560278656, 1568669056, 
1577056384, 1585446272, 1593831296, 1602219392, 1610610304, 
1619000192, 1627386752, 1635773824, 1644164224, 1652555648, 
1660943488, 1669332608, 1677721216, 1686109312, 1694497664, 
1702886272, 1711274624, 1719661184, 1728047744, 1736434816, 
1744829056, 1753218944, 1761606272, 1769995904, 1778382464, 
1786772864, 1795157888, 1803550592, 1811937664, 1820327552, 
1828711552, 1837102976, 1845488768, 1853879936, 1862269312, 
1870656896, 1879048064, 1887431552, 1895825024, 1904212096, 
1912601216, 1920988544, 1929379456, 1937765504, 1946156672, 
1954543232, 1962932096, 1971321728, 1979707264, 1988093056, 
1996487552, 2004874624, 2013262208, 2021653888, 2030039936, 
2038430848, 2046819968, 2055208576, 2063596672, 2071981952, 
2080373632, 2088762752, 2097149056, 2105539712, 2113928576, 
2122315136, 2130700672, 2139092608, 2147483264, 2155872128, 
2164257664, 2172642176, 2181035392, 2189426048, 2197814912, 
2206203008, 2214587264, 2222979712, 2231367808, 2239758208, 
2248145024, 2256527744, 2264922752, 2273312128, 2281701248, 
2290086272, 2298476672, 2306867072, 2315251072, 2323639168, 
2332032128, 2340420224, 2348808064, 2357196416, 2365580416, 
2373966976, 2382363008, 2390748544, 2399139968, 2407530368, 
2415918976, 2424307328, 2432695424, 2441084288, 2449472384, 
2457861248, 2466247808, 2474637184, 2483026816, 2491414144, 
2499803776, 2508191872, 2516582272, 2524970368, 2533359232, 
2541743488, 2550134144, 2558525056, 2566913408, 2575301504, 
2583686528, 2592073856, 2600467328, 2608856192, 2617240448, 
2625631616, 2634022016, 2642407552, 2650796416, 2659188352, 
2667574912, 2675965312, 2684352896, 2692738688, 2701130624, 
2709518464, 2717907328, 2726293376, 2734685056, 2743073152, 
2751462016, 2759851648, 2768232832, 2776625536, 2785017728, 
2793401984, 2801794432, 2810182016, 2818571648, 2826959488, 
2835349376, 2843734144, 2852121472, 2860514432, 2868900992, 
2877286784, 2885676928, 2894069632, 2902451584, 2910843008, 
2919234688, 2927622784, 2936011648, 2944400768, 2952789376, 
2961177728, 2969565568, 2977951616, 2986338944, 2994731392, 
3003120256, 3011508352, 3019895936, 3028287104, 3036675968, 
3045063808, 3053452928, 3061837696, 3070228352, 3078615424, 
3087003776, 3095394944, 3103782272, 3112173184, 3120562048, 
3128944768, 3137339264, 3145725056, 3154109312, 3162505088, 
3170893184, 3179280256, 3187669376, 3196056704, 3204445568, 
3212836736, 3221224064, 3229612928, 3238002304, 3246391168, 
3254778496, 3263165824, 3271556224, 3279944576, 3288332416, 
3296719232, 3305110912, 3313500032, 3321887104, 3330273152, 
3338658944, 3347053184, 3355440512, 3363827072, 3372220288, 
3380608384, 3388997504, 3397384576, 3405774208, 3414163072, 
3422551936, 3430937984, 3439328384, 3447714176, 3456104576, 
3464493952, 3472883584, 3481268864, 3489655168, 3498048896, 
3506434432, 3514826368, 3523213952, 3531603584, 3539987072, 
3548380288, 3556763264, 3565157248, 3573545344, 3581934464, 
3590324096, 3598712704, 3607098752, 3615488384, 3623877248, 
3632265856, 3640646528, 3649043584, 3657430144, 3665821568, 
3674207872, 3682597504, 3690984832, 3699367808, 3707764352, 
3716152448, 3724541056, 3732925568, 3741318016, 3749706368, 
3758091136, 3766481536, 3774872704, 3783260032, 3791650432, 
3800036224, 3808427648, 3816815488, 3825204608, 3833592704, 
3841981568, 3850370432, 3858755968, 3867147904, 3875536256, 
3883920512, 3892313728, 3900702592, 3909087872, 3917478784, 
3925868416, 3934256512, 3942645376, 3951032192, 3959422336, 
3967809152, 3976200064, 3984588416, 3992974976, 4001363584, 
4009751168, 4018141312, 4026530432, 4034911616, 4043308928, 
4051695488, 4060084352, 4068472448, 4076862848, 4085249408, 
4093640576, 4102028416, 4110413696, 4118805632, 4127194496, 
4135583104, 4143971968, 4152360832, 4160746112, 4169135744, 
4177525888, 4185912704, 4194303616, 4202691968, 4211076736, 
4219463552, 4227855488, 4236246656, 4244633728, 4253022848, 
4261412224, 4269799808, 4278184832, 4286578048, 4294962304, 
4303349632, 4311743104, 4320130432, 4328521088, 4336909184, 
4345295488, 4353687424, 4362073472, 4370458496, 4378852736, 
4387238528, 4395630208, 4404019072, 4412407424, 4420790656, 
4429182848, 4437571456, 4445962112, 4454344064, 4462738048, 
4471119232, 4479516544, 4487904128, 4496289664, 4504682368, 
4513068416, 4521459584, 4529846144, 4538232704, 4546619776, 
4555010176, 4563402112, 4571790208, 4580174464, 4588567936, 
4596957056, 4605344896, 4613734016, 4622119808, 4630511488, 
4638898816, 4647287936, 4655675264, 4664065664, 4672451968, 
4680842624, 4689231488, 4697620352, 4706007424, 4714397056, 
4722786176, 4731173248, 4739562368, 4747951744, 4756340608, 
4764727936, 4773114496, 4781504384, 4789894784, 4798283648, 
4806667648, 4815059584, 4823449472, 4831835776, 4840226176, 
4848612224, 4857003392, 4865391488, 4873780096, 4882169728, 
4890557312, 4898946944, 4907333248, 4915722368, 4924110976, 
4932499328, 4940889728, 4949276032, 4957666432, 4966054784, 
4974438016, 4982831488, 4991221376, 4999607168, 5007998848, 
5016386432, 5024763776, 5033164672, 5041544576, 5049941888, 
5058329728, 5066717056, 5075107456, 5083494272, 5091883904, 
5100273536, 5108662144, 5117048192, 5125436032, 5133827456, 
5142215296, 5150605184, 5158993024, 5167382144, 5175769472, 
5184157568, 5192543872, 5200936064, 5209324928, 5217711232, 
5226102656, 5234490496, 5242877312, 5251263872, 5259654016, 
5268040832, 5276434304, 5284819328, 5293209728, 5301598592, 
5309986688, 5318374784, 5326764416, 5335151488, 5343542144, 
5351929472, 5360319872, 5368706944, 5377096576, 5385484928, 
5393871232, 5402263424, 5410650496, 5419040384, 5427426944, 
5435816576, 5444205952, 5452594816, 5460981376, 5469367936, 
5477760896, 5486148736, 5494536832, 5502925952, 5511315328, 
5519703424, 5528089984, 5536481152, 5544869504, 5553256064, 
5561645696, 5570032768, 5578423936, 5586811264, 5595193216, 
5603585408, 5611972736, 5620366208, 5628750464, 5637143936, 
5645528192, 5653921408, 5662310272, 5670694784, 5679082624, 
5687474048, 5695864448, 5704251008, 5712641408, 5721030272, 
5729416832, 5737806208, 5746194304, 5754583936, 5762969984, 
5771358592, 5779748224, 5788137856, 5796527488, 5804911232, 
5813300608, 5821692544, 5830082176, 5838468992, 5846855552, 
5855247488, 5863636096, 5872024448, 5880411008, 5888799872, 
5897186432, 5905576832, 5913966976, 5922352768, 5930744704, 
5939132288, 5947522432, 5955911296, 5964299392, 5972688256, 
5981074304, 5989465472, 5997851008, 6006241408, 6014627968, 
6023015552, 6031408256, 6039796096, 6048185216, 6056574848, 
6064963456, 6073351808, 6081736064, 6090128768, 6098517632, 
6106906496, 6115289216, 6123680896, 6132070016, 6140459648, 
6148849024, 6157237376, 6165624704, 6174009728, 6182403712, 
6190792064, 6199176064, 6207569792, 6215952256, 6224345216, 
6232732544, 6241124224, 6249510272, 6257899136, 6266287744, 
6274676864, 6283065728, 6291454336, 6299843456, 6308232064, 
6316620928, 6325006208, 6333395584, 6341784704, 6350174848, 
6358562176, 6366951296, 6375337856, 6383729536, 6392119168, 
6400504192, 6408895616, 6417283456, 6425673344, 6434059136, 
6442444672, 6450837376, 6459223424, 6467613056, 6476004224, 
6484393088, 6492781952, 6501170048, 6509555072, 6517947008, 
6526336384, 6534725504, 6543112832, 6551500672, 6559888768, 
6568278656, 6576662912, 6585055616, 6593443456, 6601834112, 
6610219648, 6618610304, 6626999168, 6635385472, 6643777408, 
6652164224, 6660552832, 6668941952, 6677330048, 6685719424, 
6694107776, 6702493568, 6710882176, 6719274112, 6727662976, 
6736052096, 6744437632, 6752825984, 6761213824, 6769604224, 
6777993856, 6786383488, 6794770816, 6803158144, 6811549312, 
6819937664, 6828326528, 6836706176, 6845101696, 6853491328, 
6861880448, 6870269312, 6878655104, 6887046272, 6895433344, 
6903822208, 6912212864, 6920596864, 6928988288, 6937377152, 
6945764992, 6954149248, 6962544256, 6970928768, 6979317376, 
6987709312, 6996093824, 7004487296, 7012875392, 7021258624, 
7029652352, 7038038912, 7046427776, 7054818944, 7063207808, 
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