Ethash 算法

原文链接:https://github.com/ethereum/wiki/wiki/Ethash

本规范版本 REVISION 23。当你实质性地(即有影响)更新了算法时,请更新本句中的修订号。同样,具体的实现中也请包含相应的修订版本号。

Ethash 基于以太坊 1.0 的 PoW 算法。它是 Dagger-Hashimoto 的最后一个版本,虽然由于两种算法在最后一个月的研究和开发后产生了巨大变化,它已经不应该再叫这个名字了。Dagger-Hashimoto 的算法可以参见这里

算法基于如下流程:

  1. 存在一个种子,可以通过扫描每个区块头部直到该点计算出来。
  2. 从种子中可以算出来一个 16 MB 伪随机缓存。轻量客户端存储该缓存。
  3. 从缓存里可以生成一个 1 GB 数据集,数据集中的每个属性都取决于缓存中的一小部分。全量客户端和矿工存储该数据集。数据集随时间线性增长。
  4. 采矿是收集数据集的随机切片并对其进行散列。验证则可以使用缓存去重新生成数据集中的特别片段,这样只需要使用较少的内存就可以完成,所以你只需要保存缓存。

大型数据集每 30000 个区块更新一次,所以大部分矿工都是去读数据集而不是去修改它。

参见 https://github.com/ethereum/wiki/wiki/Ethash-Design-Rationale 了解设计该算法的基本原则。

定义

我们采用如下定义:

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WORD_BYTES = 4                    # 字长
DATASET_BYTES_INIT = 2**30 # 创世数据集大小
DATASET_BYTES_GROWTH = 2**23 # 每次数据集扩展大小
CACHE_BYTES_INIT = 2**24 # 创世缓存大小
CACHE_BYTES_GROWTH = 2**17 # 每次缓存扩展大小
CACHE_MULTIPLIER=1024 # DAG 相对于缓存的大小
EPOCH_LENGTH = 30000 # 时代跨度
MIX_BYTES = 128 # 混淆宽度
HASH_BYTES = 64 # 散列长度
DATASET_PARENTS = 256 # 数据集元素的父亲数
CACHE_ROUNDS = 3 # 产生缓存的轮数
ACCESSES = 64 # 在松本循环中的访问次数
关于本规范中 “SHA3” 的相关解释

以太坊的开发符合 SHA3 开发的标准,标准处理在最终散列算法的填充中作了一定改动,所以以太坊的 sha3_256 和 sha3_512 并不是标准的 sha3 散列算法,在其他场合里经常被称为 “Keccak-256” 和 “Keccak-512”。参见这里这里这里的讨论。

请记住这一点,下面的算法描述中也提到了 sha3 的散列算法。

参数

Ethash 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是线性增长的,但我们总是采用低于线性增长的大素数,以降低过于规律性导致散列不均匀的风险。

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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

附录提供了数据集和缓存大小值表。

缓存生成

现在,我们定义产生缓存的函数:

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

# 依次产生初始数据集
o = [sha3_512(seed)]
for i in range(1, n):
o.append(sha3_512(o[-1]))

# randmemohash 向下取整
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

缓存产生过程会填满 32 MB 的内存,然后跑两边 Sergio Demian Lerner 的 RandMemoHash 算法(见严格内存硬散列函数 (2014))。输出是 524288 个 64 位字节值。

数据聚合函数

我们使用 FNV 散列 算法来处理某些不适用 XOR 的场景。注意我们乘的素数是 32 位的,FNV-1 则是每轮一个字节(8位)。

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FNV_PRIME = 0x01000193

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

请注意,因为黄皮书定义了 fnv 就是 v1*(FNV_PRIME ^ v2),所以当前实现将一直使用上述定义。

全量数据集计算

1 GB 的全量数据集中每个 64 字节的元素都是如下计算的:

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def calc_dataset_item(cache, i):
n = len(cache)
r = HASH_BYTES // WORD_BYTES
# 初始化混淆值
mix = copy.copy(cache[i % n])
mix[0] ^= i
mix = sha3_512(mix)
# 把基于 i 的随机缓存节点应用 fnv 函数
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)

实际上,我们从缓存里选择了 256 个伪随机结点,散列后计算数据集结点。整个数据集是这样生成的:

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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,我们定义主的“松本”式循环。循环从全量数据集中收集数据,以产生特定头部和一次性随机数的最终值。下面代码中的 headerRLP 用 SHA3-256 _散列_ 算出的截断区块头,不包括 mixHashnoncenonce 是大端序的 8 字节 64 位无符号整数,所以 nonce[::-1] 就是小端序的表示了:

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def hashimoto(header, nonce, full_size, dataset_lookup):
n = full_size / HASH_BYTES
w = MIX_BYTES // WORD_BYTES
mixhashes = MIX_BYTES / HASH_BYTES
# 把 header+nonce 转为 64 字节种子
s = sha3_512(header + nonce[::-1])
# 用一堆 s 填充 mix
mix = []
for _ in range(MIX_BYTES / HASH_BYTES):
mix.extend(s)
# 随机数据集结点的 mix
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)
# 压缩 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])

实际上,我们维护一个 128 字节宽的 mix,并反复依次从全量数据集中获取 128 字节,用 fnv 函数来合并 mix。128 字节的顺序访问,每轮都从内存里获取一个完整的页,从而最大程度地减少集成电路的缓存失效。

如果算法输入低于预期目标,则 nonce 有效。注意最后 sha3_256 的扩展应用保证了存在一个中间值,用以证明最小工作量。这个快速的外部 PoW 验证可以用于防止 DDOS 的目的。它也提供统计功能,结果是一个无偏的 256 位数字。

挖矿

挖矿算法如下定义:

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def mine(full_size, dataset, header, difficulty):
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

定义种子散列

为了计算种子散列,需要对给定的区块进行挖掘,算法如下:

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

注意,为了顺利挖掘和验证,我们建议在另一个线程里预先计算好种子散列和数据集分配表。

附录

如果你有兴趣在 Python 上实现请把下面的代码加在前面:

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import sha3, copy

# 假设为小端序(Intel 体系)
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 散列函数,输出 64 字节
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

下面的表提供了约 2048 个数据集大小和缓存大小的时代值,我们可以用 Mathematica 生成:

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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,
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