updated hashimoto (Heiko)
This commit is contained in:
Vitalik Buterin
parent
e25467da56
commit
d4a36a28c4
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@ -6,8 +6,8 @@ hashpower = [float(x) for x in open('hashpower.csv').readlines()]
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target = 12
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seconds_in_day = 8640
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ema_factor = 0.005
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f = 30
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threshold = 1.5
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f = 80
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threshold = 1.3
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maxadjust = 0.1
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@ -1,15 +1,51 @@
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#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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"""
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Requirements:
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- I/O bound: cycles spent on I/O ≫ cycles spent in cpu
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- no sharding: impossible to implement data locality strategy
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- easy verification
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Thoughts:
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Efficient implementations will not switch context (threading) when waiting for data.
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But they would leverage all fill buffers and have concurrent memory accesses.
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It can be assumed, that code can be written in a way to calculate N (<10)
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nonces in parallel (on a single core).
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So, after all maybe memory bandwidth rather than latency is the actual bottleneck.
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Can this be solved in a way that aligns with hashing nonces and allows
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for a quick verification? Probably not.
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Loop unrolling:
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Initially proposed dagger sets offer data locality which allows to scale the algo
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on multiple cores/l2chaches. 320MB / 40sets = 8MB (< L2 cache)
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A solution is to make accessed mem location depended on the value of the
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previous access.
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Partitial Memory:
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If a users only keeps e.g. one third of each DAG in memory (i.e. to
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have in L3 cache), he still can answer ~0.5**k of accesses by substituting
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them through previous node lookups.
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This can be mitigated by
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a) making each node deterministically depend on the value of at
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least one close high memory node. Optionally for quick validation, select
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the 2nd dependency for the lower (cached) memory. see produce_dag_k2dr
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b) for DAG creation, using a hashing function which needs more cycles
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than multiple memory lookups would - even for GPUs/FPGAs/ASICs.
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"""
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try:
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shathree = __import__('sha3')
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except:
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shathree = __import__('python_sha3')
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import random
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import time
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def sha3(x):
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return decode_int(shathree.sha3_256(x).digest()) #
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def decode_int(s):
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o = 0
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for i in range(len(s)):
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@ -19,110 +55,225 @@ def decode_int(s):
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def encode_int(x):
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o = ''
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for _ in range(32):
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for _ in range(64):
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o = chr(x % 256) + o
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x //= 256
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return o
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P = 2**256 - 4294968273
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def get_daggerset(params, seedset):
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return [produce_dag(params, i) for i in seedset]
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def update_daggerset(params, daggerset, seedset, seed):
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idx = decode_int(seed) % len(daggerset)
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seedset[idx] = seed
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daggerset[idx] = produce_dag(params, seed)
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P = (2**256 - 4294968273)**2
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def produce_dag(params, seed):
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o = [sha3(seed)]
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k, w, d = params.k, params.w, params.d
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o = [sha3(seed)**2]
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init = o[0]
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picker = 1
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for i in range(1, params["n"]):
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for i in range(1, params.dag_size):
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x = 0
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picker = (picker * init) % P
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#assert picker == pow(init, i, P)
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curpicker = picker
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for j in range(k): # can be flattend if params are known
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pos = curpicker % i
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x |= o[pos]
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curpicker >>= 10
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o.append(pow(x, w, P)) # use any "hash function" here
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return o
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def quick_calc(params, seed, pos, known={}):
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init = sha3(seed)**2
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k, w, d = params.k, params.w, params.d
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known[0] = init
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def calc(i):
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if i not in known:
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curpicker = pow(init, i, P)
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x = 0
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for j in range(k):
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pos = curpicker % i
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x |= calc(pos)
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curpicker >>= 10
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known[i] = pow(x, w, P)
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return known[i]
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o = calc(pos)
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return o
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def produce_dag_k2dr(params, seed):
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"""
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# k=2 and dependency ranges d [:i/d], [-i/d:]
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Idea is to prevent partitial memory availability in
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which a significant part of the higher mem acesses
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can be substituted by two low mem accesses, plus some calc.
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"""
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w, d = params.w, params.d
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o = [sha3(seed)**2]
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init = o[0]
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picker = 1
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for i in range(1, params.dag_size):
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x = 0
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picker = (picker * init) % P
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curpicker = picker
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for j in range(params["k"]):
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x |= o[curpicker % i]
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# higher end
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f = i/d + 1
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pos = i - f + curpicker % f
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x |= o[pos]
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curpicker >>= 10
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o.append((x * x) % P) # use any "hash function" here
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# lower end
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pos = f - curpicker % f - 1
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x |= o[pos]
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o.append(pow(x, w, P)) # use any "hash function" here
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return o
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def quick_calc(params, seed, pos):
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init = sha3(seed)
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known = {0: init}
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def calc(p):
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if p not in known:
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picker = pow(init, p, P)
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def quick_calc_k2dr(params, seed, pos, known={}):
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# k=2 and dependency ranges d [:i/d], [-i/d:]
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init = sha3(seed) ** 2
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k, w, d = params.k, params.w, params.d
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known[0] = init
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def calc(i):
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if i not in known:
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curpicker = pow(init, i, P)
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x = 0
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for j in range(params["k"]):
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x |= calc(picker % p)
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picker >>= 10
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known[p] = (x * x) % P
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return known[p]
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# higher end
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f = i/d + 1
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pos = i - f + curpicker % f
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x |= calc(pos)
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curpicker >>= 10
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# lower end
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pos = f - curpicker % f - 1
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x |= calc(pos)
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known[i] = pow(x, w, P)
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return known[i]
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o = calc(pos)
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print 'Calculated pos %d with %d accesses' % (pos, len(known))
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return o
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produce_dag = produce_dag_k2dr
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quick_calc = quick_calc_k2dr
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def hashimoto(daggerset, params, header, nonce):
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rand = sha3(header+encode_int(nonce))
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mix = 0
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for i in range(40):
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shifted_A = rand >> i
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dag = daggerset[shifted_A % params["numdags"]]
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mix ^= dag[(shifted_A // params["numdags"]) % params["n"]]
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return mix ^ rand
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def hashimoto(daggerset, lookups, header, nonce):
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"""
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Requirements:
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- I/O bound: cycles spent on I/O ≫ cycles spent in cpu
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- no sharding: impossible to implement data locality strategy
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# I/O bound:
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e.g. lookups = 16
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sha3: 12 * 32 ~384 cycles
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lookups: 16 * 160 ~2560 cycles # if zero cache
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loop: 16 * 3 ~48 cycles
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I/O / cpu = 2560/432 = ~ 6/1
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# no sharding
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lookups depend on previous lookup results
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impossible to route computation/lookups based on the initial sha3
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"""
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num_dags = len(daggerset)
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dag_size = len(daggerset[0])
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mix = sha3(header + encode_int(nonce)) ** 2
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# loop, that can not be unrolled
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# dag and dag[pos] depended on previous lookup
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for i in range(lookups):
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dag = daggerset[mix % num_dags] # modulo
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pos = mix % dag_size # modulo
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mix ^= dag[pos] # xor
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return mix
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def light_hashimoto(params, seedset, header, nonce):
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lookups = params.lookups
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dag_size = params.dag_size
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known = dict((s, {}) for s in seedset) # cache results for each dag
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mix = sha3(header + encode_int(nonce)) ** 2
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for i in range(lookups):
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seed = seedset[mix % len(seedset)]
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pos = mix % dag_size
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mix ^= quick_calc(params, seed, pos, known[seed])
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num_accesses = sum(len(known[s]) for s in seedset)
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print 'Calculated %d lookups with %d accesses' % (lookups, num_accesses)
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return mix
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def light_verify(params, seedset, header, nonce):
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return light_hashimoto(params, seedset, header, nonce) \
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<= 2**512 / params.diff
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def get_daggerset(params, block):
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if block.number == 0:
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return [produce_dag(params, i) for i in range(params["numdags"])]
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elif block.number % params["epochtime"]:
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return get_daggerset(block.parent)
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else:
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o = get_daggerset(block.parent)
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o[sha3(block.parent.nonce) % params["numdags"]] = \
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produce_dag(params, sha3(block.parent.nonce))
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return o
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def mine(daggerset, params, header):
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nonce = random.randrange(2**50)
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def mine(daggerset, params, header, nonce=0):
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orignonce = nonce
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origtime = time.time()
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while 1:
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h = hashimoto(daggerset, params, header, nonce)
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if h <= 2**256 / params["diff"]:
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h = hashimoto(daggerset, params.lookups, header, nonce)
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if h <= 2**512 / params.diff:
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noncediff = nonce - orignonce
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timediff = time.time() - origtime
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print 'Found nonce: %d, tested %d nonces in %f seconds (%f per sec)' % \
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print 'Found nonce: %d, tested %d nonces in %.2f seconds (%d per sec)' % \
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(nonce, noncediff, timediff, noncediff / timediff)
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return nonce
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nonce += 1
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def verify(daggerset, params, header, nonce):
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return hashimoto(daggerset, params, header, nonce) \
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<= 2**256 / params["diff"]
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class params(object):
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"""
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=== tuning ===
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memory: memory requirements ≫ L2/L3/L4 cache sizes
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lookups: hashes_per_sec(lookups=0) ≫ hashes_per_sec(lookups_mem_hard)
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k: ?
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d: higher values enfore memory availability but require more quick_calcs
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numdags: so that a dag can be updated in reasonable time
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"""
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memory = 512 * 1024**2 # memory usage
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numdags = 128 # number of dags
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dag_size = memory /numdags / 64 # num 64byte values per dag
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lookups = 512 # memory lookups per hash
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diff = 2**14 # higher is harder
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k = 2 # num dependecies of each dag value
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d = 8 # max distance of first dependency (1/d=fraction of size)
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w = 2
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def light_hashimoto(seedset, params, header, nonce):
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rand = sha3(header+encode_int(nonce))
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mix = 0
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for i in range(40):
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shifted_A = rand >> i
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seed = seedset[shifted_A % params["numdags"]]
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# can further optimize with cross-round memoization
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mix ^= quick_calc(params, seed,
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(shifted_A // params["numdags"]) % params["n"])
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return mix ^ rand
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if __name__ == '__main__':
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print dict((k,v) for k,v in params.__dict__.items() if isinstance(v,int))
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# odds of a partitial storage attack
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missing_mem = 0.01
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P_partitial_mem_success = (1-missing_mem) ** params.lookups
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print 'P success per hash with %d%% mem missing: %d%%' %(missing_mem*100, P_partitial_mem_success*100)
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# which actually only results in a slower mining, as more hashes must be tried
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slowdown = 1/ P_partitial_mem_success
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print 'x%.1f speedup required to offset %d%% missing mem' % (slowdown, missing_mem*100)
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# create set of DAGs
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st = time.time()
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seedset = [str(i) for i in range(params.numdags)]
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daggerset = get_daggerset(params, seedset)
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print 'daggerset with %d dags' % len(daggerset), 'size:', 64*params.dag_size*params.numdags / 1024**2 , 'MB'
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print 'creation took %.2fs' % (time.time() - st)
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# update DAG
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st = time.time()
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update_daggerset(params, daggerset, seedset, seed='new')
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print 'updating 1 dag took %.2fs' % (time.time() - st)
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# Mine
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for i in range(10):
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header = 'test%d' % i
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print '\nmining', header
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nonce = mine(daggerset, params, header)
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# verify
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st = time.time()
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assert light_verify(params, seedset, header, nonce)
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print 'verification took %.2fs' % (time.time() - st)
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def light_verify(seedset, params, header, nonce):
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return light_hashimoto(seedset, params, header, nonce) \
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<= 2**256 / params["diff"]
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params = {
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"numdags": 40,
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"n": 250000,
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"diff": 2**14,
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"epochtime": 100,
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"k": 3
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}
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