یک الگوریتم اثبات انجام کار برای اتریوم ۱. ۰
آخرین ویرایش: @sharifi.masoud(opens in a new tab), ۱۶ اسفند ۱۴۰۲
Ethash(opens in a new tab) نسخه اصلاح شده الگوریتم Dagger-Hashimoto است. اثبات کار Ethash نیازمند حافظه سخت(opens in a new tab) است که تصور میشد این الگوریتم را در برابر دستگاههای ASIC مقاوم میکند. در نهایت، دستگاههای Ethash ASIC توسعه یافتند، اما تا زمانی که اثبات کار خاموش شد، استخراج با GPU همچنان یک گزینه قابل اجرا بود. Ethash هنوز برای استخراج سکه های دیگر در سایر شبکه های اثبات کار غیر اتریوم استفاده می شود.
Ethash چگونه کار می کند؟
سختی حافظه با الگوریتم اثبات کار به دست می آید که مستلزم انتخاب زیر مجموعه های یک منبع ثابت وابسته به سر نانس و بلوک است. این منبع (به اندازه چند گیگابایت) DAG نامیده می شود. DAG هر 30000 بلوک تغییر می کند، یعنی یک پنجره حدودا 125 ساعته به نام ایپوک (تقریباً 5.2 روز) و مدتی طول می کشد تا تولید شود. از آنجا که DAG فقط به ارتفاع بلوک بستگی دارد، میتوان آن را از پیش تولید کرد، اما اگر تولید نشده باشد، کاربر باید تا پایان این فرآیند منتظر بماند تا بتواند بلوک تولید کند. اگر کاربرها DAGها را از قبل تولید و ذخیره نکنند، ممکن است شبکه در هر انتقال دوره با تأخیر عظیم در بلوک مواجه شود. توجه داشته باشید که برای تأیید اثبات کار نیازی به تولید DAG نیست و این امکان را میدهد که تأیید با پردازنده کم مصرف و حافظه کم انجام شود.
مسیر کلی که الگوریتم طی می کند به شرح زیر است:
- برای هر بلوک یک بذر وجود دارد که با اسکن کردن سرهای بلوک تا آن نقطه قابل محاسبه است.
- از روی این بذر، میتوان یک حافظه پنهان شبهتصادفی ۱۶ مگابایتی محاسبه کرد. کاربرهای سبک، حافظه پنهان را ذخیره میکنند.
- از حافظه پنهان، میتوانیم یک مجموعه داده یک گیگابایتی تولید کنیم، طوری که هر آیتم در این مجموعه داده فقط به تعداد کمی از آیتمهای حافظه پنهان وابسته است. کاربرهای کامل و استخراجگرها مجموعه داده را ذخیره میکنند. مجموعه داده به صورت خطی با زمان رشد می کند.
- استخراج شامل گرفتن برشهای تصادفی از مجموعه داده و هش کردن آنها با هم است. تأیید را میتوان با استفاده از حافظه پنهان برای بازسازی قطعات خاص مجموعه داده مورد نیاز با حافظه کم انجام داد، بنابراین فقط نیاز به ذخیره حافظه پنهان دارید.
مجموعه داده بزرگ هر 30000 بلوک یک بار بهروزرسانی میشود، بنابراین اکثر تلاشهای یک استخراجگر صرف خواندن مجموعه داده میشود، نه ایجاد تغییر در آن.
تعاریف
ما از تعاریف زیر استفاده می کنیم:
1WORD_BYTES = 4 # bytes in word2DATASET_BYTES_INIT = 2**30 # bytes in dataset at genesis3DATASET_BYTES_GROWTH = 2**23 # dataset growth per epoch4CACHE_BYTES_INIT = 2**24 # bytes in cache at genesis5CACHE_BYTES_GROWTH = 2**17 # cache growth per epoch6CACHE_MULTIPLIER=1024 # Size of the DAG relative to the cache7EPOCH_LENGTH = 30000 # blocks per epoch8MIX_BYTES = 128 # width of mix9HASH_BYTES = 64 # hash length in bytes10DATASET_PARENTS = 256 # number of parents of each dataset element11CACHE_ROUNDS = 3 # number of rounds in cache production12ACCESSES = 64 # number of accesses in hashimoto loopنمایش همه
استفاده از 'SHA3'
توسعه اتریوم همزمان با توسعه استاندارد SHA3 انجام شد و فرآیند استانداردسازی تغییری دیرهنگام در پرکردن الگوریتم هش نهایی ایجاد کرد، طوری که هشهای "sha3_256" و "sha3_512" اتریوم هشهای استاندارد sha3 نیستند، بلکه نوعی متفاوت هستند که اغلب در زمینههای دیگر به عنوان "Keccak-256" و "Keccak-512" شناخته میشوند. برای اطلاعات بیشتر، به بحثهای انجام شده در اینجا(opens in a new tab)، اینجا(opens in a new tab)، یا اینجا(opens in a new tab) مراجعه کنید.
لطفا این نکته را در نظر داشته باشید که در توضیحات الگوریتم زیر به هشهای "sha3" اشاره شده است.
پارامترها
پارامترهای حافظه پنهان و مجموعه داده Ethash وابسته به شماره بلوک هستند. اندازه حافظه پنهان و اندازه مجموعه داده هر دو به صورت خطی رشد میکنند؛ با این حال، برای کاهش خطر ایجاد الگوهای تکراری منجر به رفتار چرخهای، همیشه بزرگترین عدد اول کمتر از آستانه رشد خطی را انتخاب میکنیم.
1def get_cache_size(block_number):2 sz = CACHE_BYTES_INIT + CACHE_BYTES_GROWTH * (block_number // EPOCH_LENGTH)3 sz -= HASH_BYTES4 while not isprime(sz / HASH_BYTES):5 sz -= 2 * HASH_BYTES6 return sz78def get_full_size(block_number):9 sz = DATASET_BYTES_INIT + DATASET_BYTES_GROWTH * (block_number // EPOCH_LENGTH)10 sz -= MIX_BYTES11 while not isprime(sz / MIX_BYTES):12 sz -= 2 * MIX_BYTES13 return szنمایش همهکپی
جدولهای مقادیر اندازه حافظه پنهان و مجموعه داده در ضمیمه ارائه شده است.
تولید حافظه پنهان
اکنون تابع تولید حافظه پنهان را مشخص می کنیم:
1def mkcache(cache_size, seed):2 n = cache_size // HASH_BYTES34 # Sequentially produce the initial dataset5 o = [sha3_512(seed)]6 for i in range(1, n):7 o.append(sha3_512(o[-1]))89 # Use a low-round version of randmemohash10 for _ in range(CACHE_ROUNDS):11 for i in range(n):12 v = o[i][0] % n13 o[i] = sha3_512(map(xor, o[(i-1+n) % n], o[v]))1415 return oنمایش همهکپی
فرآیند تولید حافظه پنهان شامل پر کردن متوالی 32 مگابایت حافظه میشود، سپس دو پاس از الگوریتم RandMemoHash سرجیو دمیان لرنر از Strict Memory Hard Hashing Functions (2014) انجام میشود(opens in a new tab). خروجی، یک مجموعه شامل ۵۲۴۲۸۸ مقدار ۶۴ بایتی است.
تابع تجمیع داده ها
در برخی موارد از یک الگوریتم الهام گرفته از هش FNV(opens in a new tab) به عنوان جایگزینی غیر تداعی برای XOR استفاده میکنیم. توجه داشته باشید که ما عدد اول را در کل ورودی ۳۲ بیتی ضرب میکنیم، برخلاف مشخصات FNV-1 که عدد اول را با هر بایت (octet) به نوبت ضرب میکند.
1FNV_PRIME = 0x0100019323def fnv(v1, v2):4 return ((v1 * FNV_PRIME) ^ v2) % 2**32کپی
لطفا توجه داشته باشید که حتی وایتپیپر نیز fnv را به عنوان v1*(FNV_PRIME ^ v2) مشخص میکند، اما تمام اجراهای فعلی به طور مداوم از تعریف بالا استفاده میکنند.
محاسبه کامل مجموعه داده
هر آیتم ۶۴ بایتی در کل مجموعه داده ۱ گیگابایتی به شرح زیر محاسبه میشود:
1def calc_dataset_item(cache, i):2 n = len(cache)3 r = HASH_BYTES // WORD_BYTES4 # initialize the mix5 mix = copy.copy(cache[i % n])6 mix[0] ^= i7 mix = sha3_512(mix)8 # fnv it with a lot of random cache nodes based on i9 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)نمایش همهکپی
در اصل، ما دادهها را از ۲۵۶ گره حافظه پنهان انتخاب شده به صورت شبهتصادفی ترکیب میکنیم و آن را هش میکنیم تا گره مجموعه داده را محاسبه کنیم. کل مجموعه داده سپس با استفاده از روش زیر تولید میشود:
1def calc_dataset(full_size, cache):2 return [calc_dataset_item(cache, i) for i in range(full_size // HASH_BYTES)]کپی
حلقه اصلی
حالا حلقه اصلی شبیه به "hashimoto" را مشخص میکنیم که در آن دادهها را از کل مجموعه داده جمعآوری میکنیم تا مقدار نهایی خود را برای یک سر و نانسِ خاص تولید کنیم. در کد زیر، header
نشان دهنده هش SHA3-256 از نمایش RLP یک سر بلوک بریده شده است، یعنی سر بدون فیلدهای mixHash و nonce. نانس
هشت بایت از یک عدد صحیح بدون علامت ۶۴ بیتی با ترتیب بزرگ به کوچک است. پس nonce[::-1]
نمایش هشت بایتی با ترتیب کوچک به بزرگ little-endian از آن مقدار است:
1def hashimoto(header, nonce, full_size, dataset_lookup):2 n = full_size / HASH_BYTES3 w = MIX_BYTES // WORD_BYTES4 mixhashes = MIX_BYTES / HASH_BYTES5 # combine header+nonce into a 64 byte seed6 s = sha3_512(header + nonce[::-1])7 # start the mix with replicated s8 mix = []9 for _ in range(MIX_BYTES / HASH_BYTES):10 mix.extend(s)11 # mix in random dataset nodes12 for i in range(ACCESSES):13 p = fnv(i ^ s[0], mix[i % w]) % (n // mixhashes) * mixhashes14 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 mix19 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 }2627def hashimoto_light(full_size, cache, header, nonce):28 return hashimoto(header, nonce, full_size, lambda x: calc_dataset_item(cache, x))2930def hashimoto_full(full_size, dataset, header, nonce):31 return hashimoto(header, nonce, full_size, lambda x: dataset[x])نمایش همهکپی
در اصل، ما یک "میکس" ۱۲۸ بایتی را حفظ میکنیم و به طور متوالی ۱۲۸ بایت را از کل مجموعه داده دریافت کرده و از تابع fnv
برای ترکیب آن با میکس استفاده میکنیم. از ۱۲۸ بایت دسترسی متوالی استفاده میشود تا هر دور از الگوریتم همیشه یک صفحه کامل را از رم دریافت کند و خطای حافظه پنهان ترجمه را به حداقل برساند که از نظر تئوری ASICها میتوانند از آن جلوگیری کنند.
اگر خروجی این الگوریتم کمتر از هدف مورد نظر باشد، پس نانس معتبر است. توجه داشته باشید که اعمال اضافی sha3_256
در انتها تضمین میکند که یک نانس میانی وجود دارد که میتواند برای اثبات انجام حداقل مقدار کار ارائه شود؛ این تأیید سریع PoW خارجی میتواند برای اهداف ضد DDoS استفاده شود. همچنین برای ارائه اطمینان آماری از اینکه نتیجه یک عدد ۲۵۶ بیتی بدون سوگیری است، عمل میکند.
استخراج
الگوریتم استخراج به صورت زیر تعریف شده است:
1def mine(full_size, dataset, header, difficulty):2 # zero-pad target to compare with hash on the same digit3 target = zpad(encode_int(2**256 // difficulty), 64)[::-1]4 from random import randint5 nonce = randint(0, 2**64)6 while hashimoto_full(full_size, dataset, header, nonce) > target:7 nonce = (nonce + 1) % 2**648 return nonceکپی
تعریف هش بذر
برای محاسبه هش بذر که برای استخراج در بالای یک بلوک مورد استفاده قرار می گیرد، از الگوریتم زیر استفاده می کنیم:
1 def get_seedhash(block):2 s = '\x00' * 323 for i in range(block.number // EPOCH_LENGTH):4 s = serialize_hash(sha3_256(s))5 return sکپی
توجه داشته باشید که برای استخراج و تأیید روان، توصیه میشود که seedhashها و مجموعه دادههای آینده را در یک رشته جداگانه از قبل محاسبه کنید.
بیشتر بخوانید
آیا میخواهید در مورد منابع جامعه که به شما کمک کرده بدانید؟ این صفحه را ویرایش کنید و آن را اضافه کنید!
پیوست
در صورتی که علاقهمند به اجرای مشخصات پایتون بالا به عنوان کد هستید، باید کد زیر را در ابتدای آن قرار دهید.
1import sha3, copy23# Assumes little endian bit ordering (same as Intel architectures)4def decode_int(s):5 return int(s[::-1].encode('hex'), 16) if s else 067def encode_int(s):8 a = "%x" % s9 return '' if s == 0 else ('0' * (len(a) % 2) + a).decode('hex')[::-1]1011def zpad(s, length):12 return s + '\x00' * max(0, length - len(s))1314def serialize_hash(h):15 return ''.join([zpad(encode_int(x), 4) for x in h])1617def deserialize_hash(h):18 return [decode_int(h[i:i+WORD_BYTES]) for i in range(0, len(h), WORD_BYTES)]1920def hash_words(h, sz, x):21 if isinstance(x, list):22 x = serialize_hash(x)23 y = h(x)24 return deserialize_hash(y)2526def serialize_cache(ds):27 return ''.join([serialize_hash(h) for h in ds])2829serialize_dataset = serialize_cache3031# sha3 hash function, outputs 64 bytes32def sha3_512(x):33 return hash_words(lambda v: sha3.sha3_512(v).digest(), 64, x)3435def sha3_256(x):36 return hash_words(lambda v: sha3.sha3_256(v).digest(), 32, x)3738def xor(a, b):39 return a ^ b4041def isprime(x):42 for i in range(2, int(x**0.5)):43 if x % i == 0:44 return False45 return Trueنمایش همهکپی
اندازه داده ها
جدولهای جستجوی زیر تقریباً ۲۰۴۸ دوره محاسباتی جدولبندی شده از اندازههای دادهها و اندازههای کش را ارائه میدهند.
1def get_datasize(block_number):2 return data_sizes[block_number // EPOCH_LENGTH]34def get_cachesize(block_number):5 return cache_sizes[block_number // EPOCH_LENGTH]67data_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, 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