diff --git a/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashamoto/index.md b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashamoto/index.md new file mode 100644 index 00000000000..d227087a977 --- /dev/null +++ b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashamoto/index.md @@ -0,0 +1,332 @@ +--- +title: Dagger-Hashamoto +description: A detailed look at the Dagger-Hashamoto algorithm. +lang: en +sidebar: true +incomplete: false +--- + +Dagger-Hashimoto was the original research implementation and specification for Ethereum's mining algorithm. Dagger-Hashimoto was superseded by [Ethash](#ethash). + +## Prerequisites {#prerequisites} + +To better understand this page, we recommend you first read up on [proof-of-work consensus](/developers/docs/consensus-mechanisms/pow), [mining](/developers/docs/consensus-mechanisms/pow/mining), and [mining algorithms](/developers/docs/consensus-mechanisms/pow/mining/mining-algorithms). + +## Dagger-Hashimoto {#dagger-hashimoto} + +Dagger-Hashimoto aims to satisfy two goals: + +1. **ASIC-resistance**: the benefit from creating specialized hardware for the algorithm should be as small as possible +2. **Light client verifiability**: a block should be efficiently verifiable by a light client. + +With an additional modification, we also specify how to fulfill a third goal if desired, but at the cost of additional complexity: + +**Full chain storage**: mining should require storage of the complete blockchain state (due to the irregular structure of the Ethereum state trie, we anticipate that some pruning will be possible, particularly of some often-used contracts, but we want to minimize this). + +## DAG Generation {#dag-generation} + +The code for the algorithm will be defined in Python below. First, we give `encode_int` for marshaling unsigned ints of specified precision to strings. Its inverse is also given: + +```python +NUM_BITS = 512 + +def encode_int(x): + "Encode an integer x as a string of 64 characters using a big-endian scheme" + o = '' + for _ in range(NUM_BITS / 8): + o = chr(x % 256) + o + x //= 256 + return o + +def decode_int(s): + "Unencode an integer x from a string using a big-endian scheme" + x = 0 + for c in s: + x *= 256 + x += ord(c) + return x +``` + +We next assume that `sha3` is a function that takes an integer and outputs an integer, and `dbl_sha3` is a double-sha3 function; if converting this reference code into an implementation use: + +```python +from pyethereum import utils +def sha3(x): + if isinstance(x, (int, long)): + x = encode_int(x) + return decode_int(utils.sha3(x)) + +def dbl_sha3(x): + if isinstance(x, (int, long)): + x = encode_int(x) + return decode_int(utils.sha3(utils.sha3(x))) +``` + +### Parameters {#parameters} + +The parameters used for the algorithm are: + +```python +SAFE_PRIME_512 = 2**512 - 38117 # Largest Safe Prime less than 2**512 + +params = { + "n": 4000055296 * 8 // NUM_BITS, # Size of the dataset (4 Gigabytes); MUST BE MULTIPLE OF 65536 + "n_inc": 65536, # Increment in value of n per period; MUST BE MULTIPLE OF 65536 + # with epochtime=20000 gives 882 MB growth per year + "cache_size": 2500, # Size of the light client's cache (can be chosen by light + # client; not part of the algo spec) + "diff": 2**14, # Difficulty (adjusted during block evaluation) + "epochtime": 100000, # Length of an epoch in blocks (how often the dataset is updated) + "k": 1, # Number of parents of a node + "w": w, # Used for modular exponentiation hashing + "accesses": 200, # Number of dataset accesses during hashimoto + "P": SAFE_PRIME_512 # Safe Prime for hashing and random number generation +} +``` + +`P` in this case is a prime chosen such that `log₂(P)` is just slightly less than 512, which corresponds to the 512 bits we have been using to represent our numbers. Note that only the latter half of the DAG actually needs to be stored, so the de-facto RAM requirement starts at 1 GB and grows by 441 MB per year. + +### Dagger graph building {#dagger-graph-building} + +The dagger graph building primitive is defined as follows: + +```python +def produce_dag(params, seed, length): + P = params["P"] + picker = init = pow(sha3(seed), params["w"], P) + o = [init] + for i in range(1, length): + x = picker = (picker * init) % P + for _ in range(params["k"]): + x ^= o[x % i] + o.append(pow(x, params["w"], P)) + return o +``` + +Essentially, it starts off a graph as a single node, `sha3(seed)`, and from there starts sequentially adding on other nodes based on random previous nodes. When a new node is created, a modular power of the seed is computed to randomly select some indices less than `i` (using `x % i` above), and the values of the nodes at those indices are used in a calculation to generate a new a value for `x`, which is then fed into a small proof of work function (based on XOR) to ultimately generate the value of the graph at index `i`. The rationale behind this particular design is to force sequential access of the DAG; the next value of the DAG that will be accessed cannot be determined until the current value is known. Finally, modular exponentiation hashes the result further. + +This algorithm relies on several results from number theory. See the appendix below for a discussion. + +## Light client evaluation {#light-client-evaluation} + +The above graph construction intends to allow each node in the graph to be reconstructed by computing a subtree of only a small number of nodes and requiring only a small amount of auxiliary memory. Note that with k=1, the subtree is only a chain of values going up to the first element in the DAG. + +The light client computing function for the DAG works as follows: + +```python +def quick_calc(params, seed, p): + w, P = params["w"], params["P"] + cache = {} + + def quick_calc_cached(p): + if p in cache: + pass + elif p == 0: + cache[p] = pow(sha3(seed), w, P) + else: + x = pow(sha3(seed), (p + 1) * w, P) + for _ in range(params["k"]): + x ^= quick_calc_cached(x % p) + cache[p] = pow(x, w, P) + return cache[p] + + return quick_calc_cached(p) +``` + +Essentially, it is simply a rewrite of the above algorithm that removes the loop of computing the values for the entire DAG and replaces the earlier node lookup with a recursive call or a cache lookup. Note that for `k=1` the cache is unnecessary, although a further optimization actually precomputes the first few thousand values of the DAG and keeps that as a static cache for computations; see the appendix for a code implementation of this. + +## Double buffer of DAGs {#double-buffer} + +In a full client, a [_double buffer_](https://wikipedia.org/wiki/Multiple_buffering) of 2 DAGs produced by the above formula is used. The idea is that DAGs are produced every `epochtime` number of blocks according to the params above. Instead of the client using the latest DAG produced, it uses the one previous. The benefit of this is that it allows the DAGs to be replaced over time without needing to incorporate a step where miners must suddenly recompute all of the data. Otherwise, there is the potential for an abrupt temporary slowdown in chain processing at regular intervals and dramatically increasing centralization. Thus 51% attack risks within those few minutes before all data are recomputed. + +The algorithm used to generate the set of DAGs used to compute the work for a block is as follows: + +```python +def get_prevhash(n): + from pyethereum.blocks import GENESIS_PREVHASH + from pyethreum import chain_manager + if num <= 0: + return hash_to_int(GENESIS_PREVHASH) + else: + prevhash = chain_manager.index.get_block_by_number(n - 1) + return decode_int(prevhash) + +def get_seedset(params, block): + seedset = {} + seedset["back_number"] = block.number - (block.number % params["epochtime"]) + seedset["back_hash"] = get_prevhash(seedset["back_number"]) + seedset["front_number"] = max(seedset["back_number"] - params["epochtime"], 0) + seedset["front_hash"] = get_prevhash(seedset["front_number"]) + return seedset + +def get_dagsize(params, block): + return params["n"] + (block.number // params["epochtime"]) * params["n_inc"] + +def get_daggerset(params, block): + dagsz = get_dagsize(params, block) + seedset = get_seedset(params, block) + if seedset["front_hash"] <= 0: + # No back buffer is possible, just make front buffer + return {"front": {"dag": produce_dag(params, seedset["front_hash"], dagsz), + "block_number": 0}} + else: + return {"front": {"dag": produce_dag(params, seedset["front_hash"], dagsz), + "block_number": seedset["front_number"]}, + "back": {"dag": produce_dag(params, seedset["back_hash"], dagsz), + "block_number": seedset["back_number"]}} +``` + +## Hashimoto {#hashimoto} + +The idea behind the original Hashimoto is to use the blockchain as a dataset, performing a computation that selects N indices from the blockchain, gathers the transactions at those indices, performs an XOR of this data, and returns the hash of the result. Thaddeus Dryja's original algorithm, translated to Python for consistency, is as follows: + +```python +def orig_hashimoto(prev_hash, merkle_root, list_of_transactions, nonce): + hash_output_A = sha256(prev_hash + merkle_root + nonce) + txid_mix = 0 + for i in range(64): + shifted_A = hash_output_A >> i + transaction = shifted_A % len(list_of_transactions) + txid_mix ^= list_of_transactions[transaction] << i + return txid_max ^ (nonce << 192) +``` + +Unfortunately, while Hashimoto is considered RAM hard, it relies on 256-bit arithmetic, which has considerable computational overhead. However, Dagger-Hashimoto only uses the least significant 64 bits when indexing its dataset to address this issue. + +```python +def hashimoto(dag, dagsize, params, header, nonce): + m = dagsize / 2 + mix = sha3(encode_int(nonce) + header) + for _ in range(params["accesses"]): + mix ^= dag[m + (mix % 2**64) % m] + return dbl_sha3(mix) +``` + +The use of double SHA3 allows for a form of zero-data, near-instant pre-verification, verifying only that a correct intermediate value was provided. This outer layer of proof-of-work is highly ASIC-friendly and fairly weak, but exists to make DDoS even more difficult since that small amount of work must be done in order to produce a block that will not be rejected immediately. Here is the light-client version: + +```python +def quick_hashimoto(seed, dagsize, params, header, nonce): + m = dagsize // 2 + mix = sha3(nonce + header) + for _ in range(params["accesses"]): + mix ^= quick_calc(params, seed, m + (mix % 2**64) % m) + return dbl_sha3(mix) +``` + +## Mining and verifying {#mining-and-verifying} + +Now, let us put it all together into the mining algorithm: + +```python +def mine(daggerset, params, block): + from random import randint + nonce = randint(0, 2**64) + while 1: + result = hashimoto(daggerset, get_dagsize(params, block), + params, decode_int(block.prevhash), nonce) + if result * params["diff"] < 2**256: + break + nonce += 1 + if nonce >= 2**64: + nonce = 0 + return nonce +``` + +Here is the verification algorithm: + +```python +def verify(daggerset, params, block, nonce): + result = hashimoto(daggerset, get_dagsize(params, block), + params, decode_int(block.prevhash), nonce) + return result * params["diff"] < 2**256 +``` + +Light-client friendly verification: + +```python +def light_verify(params, header, nonce): + seedset = get_seedset(params, block) + result = quick_hashimoto(seedset["front_hash"], get_dagsize(params, block), + params, decode_int(block.prevhash), nonce) + return result * params["diff"] < 2**256 +``` + +Also, note that Dagger-Hashimoto imposes additional requirements on the block header: + +- For two-layer verification to work, a block header must have both the nonce and the middle value pre-sha3 +- Somewhere, a block header must store the sha3 of the current seedset + +## Further reading {#further-reading} + +_Know of a community resource that helped you? Edit this page and add it!_ + +## Appendix {#appendix} + +As noted above, the RNG used for DAG generation relies on some results from number theory. First, we provide assurance that the Lehmer RNG that is the basis for the `picker` variable has a wide period. Second, we show that `pow(x,3,P)` will not map `x` to `1` or `P-1` provided `x ∈ [2,P-2]` to start. Finally, we show that `pow(x,3,P)` has a low collision rate when treated as a hashing function. + +### Lehmer random number generator {#lehmer-random-number} + +While the `produce_dag` function does not need to produce unbiased random numbers, a potential threat is that `seed**i % P` only takes on a handful of values. This could provide an advantage to miners recognizing the pattern over those that do not. + +To avoid this, a result from number theory is appealed to. A [_Safe Prime_](https://en.wikipedia.org/wiki/Safe_prime) is defined to be a prime `P` such that `(P-1)/2` is also prime. The _order_ of a member `x` of the [multiplicative group](https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n) `ℤ/nℤ` is defined to be the minimal `m` such that 
xᵐ mod P ≡ 1
+Given these definitions, we have: + +> Observation 1. Let `x` be a member of the multiplicative group `ℤ/Pℤ` for a safe prime `P`. If `x mod P ≠ 1 mod P` and `x mod P ≠ P-1 mod P`, then the order of `x` is either `P-1` or `(P-1)/2`. + +_Proof_. Since `P` is a safe prime, then by [Lagrange's Theorem][lagrange] we have that the order of `x` is either `1`, `2`, `(P-1)/2`, or `P-1`. + +The order of `x` cannot be `1`, since by Fermat's Little Theorem we have: + +
xP-1 mod P ≡ 1
+Hence `x` must be a multiplicative identity of `ℤ/nℤ`, which is unique. Since we assumed that `x ≠ 1` by assumption, this is not possible. + +The order of `x` cannot be `2` unless `x = P-1`, since this would violate that `P` is prime. + +From the above proposition, we can recognize that iterating `(picker * init) % P` will have a cycle length of at least `(P-1)/2`. This is because we selected `P` to be a safe prime approximately equal to be a higher power of two, and `init` is in the interval `[2,2**256+1]`. Given the magnitude fo `P`, we should never expect a cycle from modular exponentiation. + +When we are assigning the first cell in the DAG (the variable labeled `init`), we compute `pow(sha3(seed) + 2, 3, P)`. At first glance, this does not guarantee that the result is neither `1` nor `P-1`. However, since `P-1` is a safe prime, we have the following additional assuance, which is a corollary of Observation 1: + +> Observation 2. Let `x` be a member of the multiplicative group `ℤ/Pℤ` for a safe prime `P`, and let `w` be a natural number. If `x mod P ≠ 1 mod P` and `x mod P ≠ P-1 mod P`, as well as `w mod P ≠ P-1 mod P` and `w mod P ≠ 0 mod P`, then `xʷ mod P ≠ 1 mod P` and `xʷ mod P ≠ P-1 mod P` + + +### Modular exponentiation as a hash function {#modular-exponentiation} + +For certain values of `P` and `w`, the function `pow(x, w, P)` may have many collisions. For instance, `pow(x,9,19)` only takes on values `{1,18}`. + +Given that `P` is prime, then an appropriate `w` for a modular exponentation hashing function can be chosen using the following result: + +> Observation 3. Let `P` be a prime; `w` and `P-1` are relatively prime if and only if for all `a` and `b` in `ℤ/Pℤ`:
`aʷ mod P ≡ bʷ mod P` if and only if `a mod P ≡ b mod P`
+ +Thus, given that `P` is prime and `w` is relatively prime to `P-1`, we have that `|{pow(x, w, P) : x ∈ ℤ}| = P`, implying that the hashing function has the minimal collision rate possible. + +In the special case that `P` is a safe prime as we have selected, then `P-1` only has factors 1, 2, `(P-1)/2` and `P-1`. Since `P` > 7, we know that 3 is relatively prime to `P-1`, hence `w=3` satisfies the above proposition. + +## More efficient cache-based evaluation algorithm {#cache-based-evaluation} + +```python +def quick_calc(params, seed, p): + cache = produce_dag(params, seed, params["cache_size"]) + return quick_calc_cached(cache, params, p) + +def quick_calc_cached(cache, params, p): + P = params["P"] + if p < len(cache): + return cache[p] + else: + x = pow(cache[0], p + 1, P) + for _ in range(params["k"]): + x ^= quick_calc_cached(cache, params, x % p) + return pow(x, params["w"], P) + +def quick_hashimoto(seed, dagsize, params, header, nonce): + cache = produce_dag(params, seed, params["cache_size"]) + return quick_hashimoto_cached(cache, dagsize, params, header, nonce) + +def quick_hashimoto_cached(cache, dagsize, params, header, nonce): + m = dagsize // 2 + mask = 2**64 - 1 + mix = sha3(encode_int(nonce) + header) + for _ in range(params["accesses"]): + mix ^= quick_calc_cached(cache, params, m + (mix & mask) % m) + return dbl_sha3(mix) +``` diff --git a/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/ethash/index.md b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/ethash/index.md new file mode 100644 index 00000000000..9fa431de23a --- /dev/null +++ b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/ethash/index.md @@ -0,0 +1,1011 @@ +--- +title: Ethash +description: A detailed look at the Ethash algorithm. +lang: en +sidebar: true +incomplete: false +--- + +[Ethash](https://github.com/ethereum/wiki/wiki/Ethash) is a modified version of the [Dagger-Hashimoto](/developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashamoto) algorithm. Ethash proof-of-work is [memory hard](https://wikipedia.org/wiki/Memory-hard_function), which was thought to make the algorithm ASIC resistant, but ASIC Ethash-mining has since been shown to be possible. Memory hardness is achieved with a proof of work algorithm that requires choosing subsets of a fixed resource dependent on the nonce and block header. This resource (a few gigabytes in size) is called a DAG. The DAG is changed every 30000 blocks, a 125-hour window called an epoch (roughly 5.2 days) and takes a while to generate. Since the DAG only depends on block height, it can be pre-generated but if it's not, the client needs to wait until the end of this process to produce a block. If clients do not pre-generate and cache DAGs ahead of time the network may experience massive block delay on each epoch transition. Note that the DAG does not need to be generated for verifying the proof-of-work essentially allowing for verification with both low CPU and small memory. + +The general route that the algorithm takes is as follows: + +1. There exists a **seed** which can be computed for each block by scanning through the block headers up until that point. +2. From the seed, one can compute a **16 MB pseudorandom cache**. Light clients store the cache. +3. From the cache, we can generate a **1 GB dataset**, with the property that each item in the dataset depends on only a small number of items from the cache. Full clients and miners store the dataset. The dataset grows linearly with time. +4. Mining involves grabbing random slices of the dataset and hashing them together. Verification can be done with low memory by using the cache to regenerate the specific pieces of the dataset that you need, so you only need to store the cache. + +The large dataset is updated once every 30000 blocks, so the vast majority of a miner's effort will be reading the dataset, not making changes to it. + +## Definitions {#definitions} + +We employ the following definitions: + +``` +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 +``` + +### The use of 'SHA3' {#sha3} + +Ethereum's development coincided with the development of the SHA3 standard, and the +standards process made a late change in the padding of the finalized hash algorithm, so that Ethereum's +"sha3_256" and "sha3_512" hashes are not standard sha3 hashes, but a variant often referred +to as "Keccak-256" and "Keccak-512" in other contexts. See discussion, e.g. [here](https://github.com/ethereum/EIPs/issues/59), [here](http://ethereum.stackexchange.com/questions/550/which-cryptographic-hash-function-does-ethereum-use), or [here](http://bitcoin.stackexchange.com/questions/42055/what-is-the-approach-to-calculate-an-ethereum-address-from-a-256-bit-private-key/42057#42057). + +Please keep that in mind as "sha3" hashes are referred to in the description of the algorithm below. + +## Parameters {#parameters} + +The parameters for Ethash's cache and dataset depend on the block number. The cache size and dataset size both grow linearly; however, we always take the highest prime below the linearly growing threshold in order to reduce the risk of accidental regularities leading to cyclic behavior. + +```python +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 +``` + +Tables of dataset and cache size values are provided in the appendix. + +## Cache generation {#cache-generation} + +Now, we specify the function for producing a cache: + +```python +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 +``` + +The cache production process involves first sequentially filling up 32 MB of memory, then performing two passes of Sergio Demian Lerner's _RandMemoHash_ algorithm from [_Strict Memory Hard Hashing Functions_ (2014)](http://www.hashcash.org/papers/memohash.pdf). The output is a set of 524288 64-byte values. + +## Data aggregation function {#date-aggregation-function} + +We use an algorithm inspired by the [FNV hash](https://en.wikipedia.org/wiki/Fowler%E2%80%93Noll%E2%80%93Vo_hash_function) in some cases as a non-associative substitute for XOR. Note that we multiply the prime with the full 32-bit input, in contrast with the FNV-1 spec which multiplies the prime with one byte (octet) in turn. + +```python +FNV_PRIME = 0x01000193 + +def fnv(v1, v2): + return ((v1 * FNV_PRIME) ^ v2) % 2**32 +``` + +Please note, even the yellow paper specifies fnv as v1\*(FNV_PRIME ^ v2), all current implementations consistently use the above definition. + +## Full dataset calculation {#full-dataset-calculation} + +Each 64-byte item in the full 1 GB dataset is computed as follows: + +```python +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) +``` + +Essentially, we combine data from 256 pseudorandomly selected cache nodes, and hash that to compute the dataset node. The entire dataset is then generated by: + +```python +def calc_dataset(full_size, cache): + return [calc_dataset_item(cache, i) for i in range(full_size // HASH_BYTES)] +``` + +## Main loop {#main-loop} + +Now, we specify the main "hashimoto"-like loop, where we aggregate data from the full dataset in order to produce our final value for a particular header and nonce. In the code below, `header` represents the SHA3-256 _hash_ of the RLP representation of a _truncated_ block header, that is, of a header excluding the fields **mixHash** and **nonce**. `nonce` is the eight bytes of a 64 bit unsigned integer in big-endian order. So `nonce[::-1]` is the eight-byte little-endian representation of that value: + +```python +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]) +``` + +Essentially, we maintain a "mix" 128 bytes wide, and repeatedly sequentially fetch 128 bytes from the full dataset and use the `fnv` function to combine it with the mix. 128 bytes of sequential access are used so that each round of the algorithm always fetches a full page from RAM, minimizing translation lookaside buffer misses which ASICs would theoretically be able to avoid. + +If the output of this algorithm is below the desired target, then the nonce is valid. Note that the extra application of `sha3_256` at the end ensures that there exists an intermediate nonce which can be provided to prove that at least a small amount of work was done; this quick outer PoW verification can be used for anti-DDoS purposes. It also serves to provide statistical assurance that the result is an unbiased, 256-bit number. + +## Mining {#mining} + +The mining algorithm is defined as follows: + +```python +def mine(full_size, dataset, header, difficulty): + # zero-pad target to compare with hash on the same digit + 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 +``` + +## Defining the seed hash {#seed-hash} + +In order to compute the seed hash that would be used to mine on top of a given block, we use the following algorithm: + +```python + def get_seedhash(block): + s = '\x00' * 32 + for i in range(block.number // EPOCH_LENGTH): + s = serialize_hash(sha3_256(s)) + return s +``` + +Note that for smooth mining and verifying, we recommend pre-computing future seedhashes and datasets in a separate thread. + +## Further reading {#further-reading} + +_Know of a community resource that helped you? Edit this page and add it!_ + +## Appendix {#appendix} + +The following code should be prepended if you are interested in running the above python spec as code. + +```python +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 +``` + +### Data Sizes {#data-sizes} + +The following lookup tables provide approximately 2048 tabulated epochs of data sizes and cache sizes. + +```python +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, 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272498368, 272629568, 272759488, 272891456, 273022784, +273153856, 273284672, 273415616, 273547072, 273677632, 273808448, +273937088, 274071488, 274200896, 274332992, 274463296, 274595392, +274726208, 274857536, 274988992, 275118656, 275250496, 275382208, +275513024, 275643968, 275775296, 275906368, 276037184, 276167872, +276297664, 276429376, 276560576, 276692672, 276822976, 276955072, +277085632, 277216832, 277347008, 277478848, 277609664, 277740992, +277868608, 278002624, 278134336, 278265536, 278395328, 278526784, +278657728, 278789824, 278921152, 279052096, 279182912, 279313088, +279443776, 279576256, 279706048, 279838528, 279969728, 280099648, +280230976, 280361408, 280493632, 280622528, 280755392, 280887104, +281018176, 281147968, 281278912, 281411392, 281542592, 281673152, +281803712, 281935552, 282066496, 282197312, 282329024, 282458816, +282590272, 282720832, 282853184, 282983744, 283115072, 283246144, +283377344, 283508416, 283639744, 283770304, 283901504, 284032576, +284163136, 284294848, 284426176, 284556992, 284687296, 284819264, +284950208, 285081536] +``` diff --git a/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/index.md b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/index.md new file mode 100644 index 00000000000..a5c7632d2f6 --- /dev/null +++ b/src/content/developers/docs/consensus-mechanisms/pow/mining-algorithms/index.md @@ -0,0 +1,38 @@ +--- +title: Mining algorithms +description: A detailed look at the algorithms used for Ethereum mining. +lang: en +sidebar: true +incomplete: false +--- + +Ethereum mining has used two mining algorithms, Dagger Hashimoto and Ethash. Dagger Hashimoto was never used to to mine Ethereum, being superseded by Ethash before mainet launched. It was a R&D minign algorithm that paved the way for Ethash. However, it has historical significance as an important innovation in Ethereum's development. Proof-of-work mining itself will be deprecated in favor of proof-of-stake during [The Merge](/merge/), which is forecast to happen in Q3-Q4 2022. + +The fundamental idea of both mining algorithms is that a miner tries to find a nonce input using brute force computation so that the result is below a certain difficulty threshold. This difficulty threshold can be dynamically adjusted, allowing block production to happen at a regular interval. + +## Prerequisites {#prerequisites} + +To better understand this page, we recommend you first read up on [proof-of-work consensus](/pow) and [mining](/mining). + +## Dagger Hashimoto {#dagger-hashimoto} + +Dagger Hashimoto was a precursor research algorithm for Ethereum mining that Ethash superseded. It was an amalgamation of two different algorithms: Dagger and Hashimoto. + +[Dagger](http://www.hashcash.org/papers/dagger.html) involves the generation of a [Directed Acyclic Graph](https://en.wikipedia.org/wiki/Directed_acyclic_graph), random slices of which get hashed together. The core principle is that each nonce only requires a small portion of a large total data tree. Recomputing the subtree for each nonce is prohibitive for mining - hence the need to store the tree - but okay for a single nonce’s worth of verification. Dagger was designed to be an alternative to existing algorithms like Scrypt, which are memory-hard but difficult to verify when their memory-hardness increases to genuinely secure levels. However, Dagger was vulnerable to shared memory hardware acceleration and dropped in favor of other avenues of research. + +[Hashimoto](http://diyhpl.us/%7Ebryan/papers2/bitcoin/meh/hashimoto.pdf) is an algorithm that adds ASIC-resistance by being I/O bound (i.e. memory reads are the limiting factor in the mining process). The theory is that RAM is more available than computation; billions of dollars worth of research have already investigated optimizing RAM for different use cases, which often involve near-random access patterns (hence “random access memory”). As a result, existing RAM is likely to be moderately close to optimal for evaluating the algorithm. Hashimoto uses the blockchain as a source of data, simultaneously satisfying (1) and (3) above. + +Dagger-Hashimoto used amended versions of the Dagger and Hashimoto algorithms. The difference between Dagger Hashimoto and Hashimoto is that, instead of using the blockchain as a data source, Dagger Hashimoto uses a custom-generated data set, which updates based on block data every N blocks. The data set is generated using the Dagger algorithm, allowing for efficiently calculating a subset specific to every nonce for the light client verification algorithm. The difference between Dagger Hashimoto and Dagger is that, unlike in the original Dagger, the dataset used to query the block is semi-permanent, only being updated at occasional intervals (e.g. once per week). This means that the portion of the effort of generating the dataset is close to zero, so Sergio Lerner’s arguments regarding shared memory speedups become negligible. + +More on [Dagger-Hashimoto](/developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashimoto). + +## Ethash {#ethash} + +Ethash is Ethereum's current mining algorithm. Ethash was effectively a new name given to a specific version of Dagger-Hashimoto after the algorithm got significantly updated, whilst still inheriting the fundamental principles of its predecessor. Ethereum mainnet has only ever used Ethash - Dagger Hashimoto was an R&D version of the mining algorithm that was superseded before mining started on Ethereum mainnet. + +[More on Ethash](/developers/docs/consensus-mechanisms/pow/mining-algorithms/ethash). + +## Further reading {#further-reading} + +_Know of a community resource that helped you? Edit this page and add it!_ + diff --git a/src/content/developers/docs/consensus-mechanisms/pow/mining/index.md b/src/content/developers/docs/consensus-mechanisms/pow/mining/index.md index bce4a453689..da7b25254a1 100644 --- a/src/content/developers/docs/consensus-mechanisms/pow/mining/index.md +++ b/src/content/developers/docs/consensus-mechanisms/pow/mining/index.md @@ -3,7 +3,7 @@ title: Mining description: An explanation of how mining works in Ethereum and how it helps keep Ethereum secure and decentralized. lang: en sidebar: true -incomplete: true +incomplete: false --- ## Prerequisites {#prerequisites} @@ -14,6 +14,10 @@ To better understand this page, we recommend you first read up on [transactions] Mining is the process of creating a block of transactions to be added to the Ethereum blockchain. +The word mining originates in the context of the gold analogy for crypto currencies. Gold or precious metals are scarce, so are digital tokens, and the only way to increase the total volume is through mining. This is appropriate to the extent that in Ethereum too, the only mode of issuance post launch is via mining. Unlike these examples however, mining is also the way to secure the network by creating, verifying, publishing and propagating blocks in the blockchain. + +Mining ether = Securing the Network + Ethereum, like Bitcoin, currently uses a [proof-of-work (PoW)](/developers/docs/consensus-mechanisms/pow/) consensus mechanism. Mining is the lifeblood of proof-of-work. Ethereum miners - computers running software - using their time and computation power to process transactions and produce blocks. @@ -60,6 +64,12 @@ Watch Austin walk you through mining and the proof-of-work blockchain. +## The mining algorithm {#mining-algorithm} + +The Ethereum mining algorithm has undergone several upgrades since its inception. The original algorithm, "Dagger Hashimoto" was based around the provision of a large, transient, randomly generated dataset which forms a [Directed Acyclic Graph](https://en.wikipedia.org/wiki/Directed_acyclic_graph) (the Dagger-part), with miners attempting to solve a particular constraint on it, partly determined through a block’s header-hash. This algorithm was novel because it had high memory-access bandwidth requirements but could be run using a modest processor, making it GPU-friendly but resistant to the type of ASIC-driven hardware arms race that could pose a centralization risk (more on [problems with ASICS](https://www.investopedia.com/investing/why-centralized-crypto-mining-growing-problem/)). After substantial upgrades to the algorithm, it was renamed to "Ethash". This renaming happened before mining began on Ethereum mainnet. Dagger-Hashimoto was a precursor, research algorithm that was not used on Ethereum mainnet. + +More information on these mining algorithms is available at our [mining algorithms page](/developers/docs/consensus-mechanisms/pow/mining-algorithms/). + ## Further reading {#further-reading} - [What does it mean to mine Ethereum?](https://docs.ethhub.io/using-ethereum/mining/) _EthHub_ diff --git a/src/data/developer-docs-links.yaml b/src/data/developer-docs-links.yaml index 1ba59bac1de..830784a452e 100644 --- a/src/data/developer-docs-links.yaml +++ b/src/data/developer-docs-links.yaml @@ -60,6 +60,14 @@ items: - id: docs-nav-mining to: /developers/docs/consensus-mechanisms/pow/mining/ + items: + - id: docs-nav-mining-algorithms + to: /developers/docs/consensus-mechanisms/pow/mining-algorithms/ + items: + - id: docs-nav-dagger-hashamoto + to: /developers/docs/consensus-mechanisms/pow/mining-algorithms/dagger-hashamoto + - id: docs-nav-ethash + to: /developers/docs/consensus-mechanisms/pow/mining-algorithms/ethash - id: docs-nav-proof-of-stake to: /developers/docs/consensus-mechanisms/pos/ - id: docs-nav-ethereum-stack diff --git a/src/intl/en/page-developers-docs.json b/src/intl/en/page-developers-docs.json index ea46a01a1e0..a8ba560e92d 100644 --- a/src/intl/en/page-developers-docs.json +++ b/src/intl/en/page-developers-docs.json @@ -50,6 +50,9 @@ "docs-nav-mev": "Miner extractable value (MEV)", "docs-nav-mev-description": "How value is extracted from the Ethereum blockchain beyond the block reward", "docs-nav-mining": "Mining", + "docs-nav-mining-algorithms": "Mining algorithms", + "docs-nav-dagger-hashamoto": "Dagger-Hashamoto", + "docs-nav-ethash": "Ethash", "docs-nav-networks": "Networks", "docs-nav-networks-description": "Implementations of Ethereum including test networks", "docs-nav-nodes-and-clients": "Nodes and clients", diff --git a/src/intl/en/page-developers-index.json b/src/intl/en/page-developers-index.json index 3cbda339ac8..d88acef8863 100644 --- a/src/intl/en/page-developers-index.json +++ b/src/intl/en/page-developers-index.json @@ -54,6 +54,8 @@ "page-developers-mev-link": "Miner extractable value (MEV)", "page-developers-mining-desc": "How new blocks are created and consensus is reached", "page-developers-mining-link": "Mining", + "page-developers-mining-algorithms-desc": "Information on Ethereum's mining algorithms", + "page-developers-mining-algorithms-link": "Mining algorithms", "page-developers-networks-desc": "An overview of Mainnet and the test networks", "page-developers-networks-link": "Networks", "page-developers-node-clients-desc": "How blocks and transactions are verified in the network", diff --git a/src/pages/developers/index.js b/src/pages/developers/index.js index d1a20b9bc4d..33b9080aced 100644 --- a/src/pages/developers/index.js +++ b/src/pages/developers/index.js @@ -423,6 +423,13 @@ const DevelopersPage = ({ data }) => {

+ + + + +

+ +