Some updates
This commit is contained in:
Vitalik Buterin
parent
d4a36a28c4
commit
e41f3f15dd
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@ -36,15 +36,10 @@ 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 time
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from pyethereum import utils
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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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@ -61,107 +56,76 @@ def encode_int(x):
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return o
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def sha3(x):
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return decode_int(utils.sha3(x))
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def cantor_pair(x, y, p):
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return ((x+y) * (x+y+1) / 2 + y) % p
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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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k, w, d = params.k, params.w, params.d
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o = [sha3(seed)**2]
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k, hk, w, hw, n, p, t = params.k, params.hk, params.w, \
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params.hw, params.dag_size, params.p, params.h_threshold
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print 'Producing dag of size %d (%d memory)' % (n, n * params.wordsz)
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o = [sha3(seed)]
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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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for i in range(1, n):
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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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picker = (picker * init) % p
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curpicker = picker
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if i < t:
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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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x ^= o[curpicker % i]
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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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else:
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for j in range(hk):
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x ^= o[curpicker % t]
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curpicker >>= 10
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o.append(pow(x, w if i < t else hw, 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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def quick_calc(params, seed, pos, known=None):
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k, hk, w, hw, p, t = params.k, params.hk, params.w, \
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params.hw, params.p, params.h_threshold
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init = sha3(seed) % p
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if known is None:
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known = {}
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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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curpicker = pow(init, i, p)
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x = 0
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if i < t:
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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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x ^= calc(curpicker % i)
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curpicker >>= 10
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known[i] = pow(x, w, P)
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known[i] = pow(x, w, p)
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else:
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for j in range(hk):
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x ^= calc(curpicker % t)
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curpicker >>= 10
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known[i] = pow(x, hw, p)
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return known[i]
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o = calc(pos)
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print 'Calculated index %d in %d lookups' % (pos, len(known))
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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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# 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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# 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_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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# 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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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, lookups, header, nonce):
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def hashimoto(params, daggerset, 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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@ -178,41 +142,48 @@ def hashimoto(daggerset, lookups, header, nonce):
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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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rand = sha3(header + encode_int(nonce)) % params.p
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mix = rand
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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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for i in range(params.lookups):
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v = mix if params.is_serial else rand >> i
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dag = daggerset[v % params.num_dags] # modulo
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pos = v % params.dag_size # modulo
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mix ^= dag[pos] # xor
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# print v % params.num_dags, pos, dag[pos]
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print header, nonce, mix
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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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rand = sha3(header + encode_int(nonce)) % params.p
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mix = rand
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for i in range(params.lookups):
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v = mix if params.is_serial else rand >> i
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seed = seedset[v % len(seedset)]
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pos = v % params.dag_size
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qc = quick_calc(params, seed, pos)
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# print v % params.num_dags, pos, qc
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mix ^= qc
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print 'Calculated %d lookups' % \
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(params.lookups)
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print header, nonce, mix
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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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h = light_hashimoto(params, seedset, header, nonce)
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return h <= 256**params.wordsz / params.diff
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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.lookups, header, nonce)
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if h <= 2**512 / params.diff:
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h = hashimoto(params, daggerset, header, nonce)
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if h <= 256**params.wordsz / 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 %.2f seconds (%d per sec)' % \
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@ -228,44 +199,55 @@ class params(object):
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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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num_dags: 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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p = (2 ** 256 - 4294968273)**2 # prime modulus
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wordsz = 64 # word size
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memory = 10 * 1024**2 # memory usage
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num_dags = 2 # number of dags
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dag_size = memory/num_dags/wordsz # num 64byte values per dag
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lookups = 40 # 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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hk = 8 # dependencies for final nodes
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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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w = 2 # work factor on node generation
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hw = 8 # work factor on final node generation
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h_threshold = dag_size*2/5 # cutoff between final and nonfinal nodes
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is_serial = False # hashimoto is serial
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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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print dict((k, v) for k, v in params.__dict__.items()
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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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print 'P success per hash with %d%% mem missing: %d%%' % \
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(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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# which actually only results in a slower mining,
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# 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' % \
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(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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seedset = [str(i) for i in range(params.num_dags)]
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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 'daggerset with %d dags' % len(daggerset), 'size:', \
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64*params.dag_size*params.num_dags / 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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update_daggerset(params, daggerset, seedset, seed='qwe')
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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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for i in range(1):
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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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@ -273,7 +255,3 @@ if __name__ == '__main__':
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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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