Some updates
This commit is contained in:
Vitalik Buterin
parent
d4a36a28c4
commit
e41f3f15dd
|
|
@ -36,15 +36,10 @@ than multiple memory lookups would - even for GPUs/FPGAs/ASICs.
|
|||
"""
|
||||
|
||||
|
||||
try:
|
||||
shathree = __import__('sha3')
|
||||
except:
|
||||
shathree = __import__('python_sha3')
|
||||
import time
|
||||
|
||||
from pyethereum import utils
|
||||
|
||||
def sha3(x):
|
||||
return decode_int(shathree.sha3_256(x).digest()) #
|
||||
|
||||
def decode_int(s):
|
||||
o = 0
|
||||
|
|
@ -61,107 +56,76 @@ def encode_int(x):
|
|||
return o
|
||||
|
||||
|
||||
def sha3(x):
|
||||
return decode_int(utils.sha3(x))
|
||||
|
||||
|
||||
def cantor_pair(x, y, p):
|
||||
return ((x+y) * (x+y+1) / 2 + y) % p
|
||||
|
||||
|
||||
def get_daggerset(params, seedset):
|
||||
return [produce_dag(params, i) for i in seedset]
|
||||
|
||||
|
||||
def update_daggerset(params, daggerset, seedset, seed):
|
||||
idx = decode_int(seed) % len(daggerset)
|
||||
seedset[idx] = seed
|
||||
daggerset[idx] = produce_dag(params, seed)
|
||||
|
||||
|
||||
P = (2**256 - 4294968273)**2
|
||||
|
||||
|
||||
def produce_dag(params, seed):
|
||||
k, w, d = params.k, params.w, params.d
|
||||
o = [sha3(seed)**2]
|
||||
k, hk, w, hw, n, p, t = params.k, params.hk, params.w, \
|
||||
params.hw, params.dag_size, params.p, params.h_threshold
|
||||
print 'Producing dag of size %d (%d memory)' % (n, n * params.wordsz)
|
||||
o = [sha3(seed)]
|
||||
init = o[0]
|
||||
picker = 1
|
||||
for i in range(1, params.dag_size):
|
||||
for i in range(1, n):
|
||||
x = 0
|
||||
picker = (picker * init) % P
|
||||
#assert picker == pow(init, i, P)
|
||||
picker = (picker * init) % p
|
||||
curpicker = picker
|
||||
for j in range(k): # can be flattend if params are known
|
||||
pos = curpicker % i
|
||||
x |= o[pos]
|
||||
curpicker >>= 10
|
||||
o.append(pow(x, w, P)) # use any "hash function" here
|
||||
return o
|
||||
|
||||
def quick_calc(params, seed, pos, known={}):
|
||||
init = sha3(seed)**2
|
||||
k, w, d = params.k, params.w, params.d
|
||||
known[0] = init
|
||||
def calc(i):
|
||||
if i not in known:
|
||||
curpicker = pow(init, i, P)
|
||||
x = 0
|
||||
for j in range(k):
|
||||
pos = curpicker % i
|
||||
x |= calc(pos)
|
||||
if i < t:
|
||||
for j in range(k): # can be flattend if params are known
|
||||
x ^= o[curpicker % i]
|
||||
curpicker >>= 10
|
||||
known[i] = pow(x, w, P)
|
||||
return known[i]
|
||||
o = calc(pos)
|
||||
else:
|
||||
for j in range(hk):
|
||||
x ^= o[curpicker % t]
|
||||
curpicker >>= 10
|
||||
o.append(pow(x, w if i < t else hw, p)) # use any "hash function" here
|
||||
return o
|
||||
|
||||
|
||||
def produce_dag_k2dr(params, seed):
|
||||
"""
|
||||
# k=2 and dependency ranges d [:i/d], [-i/d:]
|
||||
Idea is to prevent partitial memory availability in
|
||||
which a significant part of the higher mem acesses
|
||||
can be substituted by two low mem accesses, plus some calc.
|
||||
"""
|
||||
w, d = params.w, params.d
|
||||
o = [sha3(seed)**2]
|
||||
init = o[0]
|
||||
picker = 1
|
||||
for i in range(1, params.dag_size):
|
||||
x = 0
|
||||
picker = (picker * init) % P
|
||||
curpicker = picker
|
||||
# higher end
|
||||
f = i/d + 1
|
||||
pos = i - f + curpicker % f
|
||||
x |= o[pos]
|
||||
curpicker >>= 10
|
||||
# lower end
|
||||
pos = f - curpicker % f - 1
|
||||
x |= o[pos]
|
||||
o.append(pow(x, w, P)) # use any "hash function" here
|
||||
return o
|
||||
|
||||
|
||||
def quick_calc_k2dr(params, seed, pos, known={}):
|
||||
# k=2 and dependency ranges d [:i/d], [-i/d:]
|
||||
init = sha3(seed) ** 2
|
||||
k, w, d = params.k, params.w, params.d
|
||||
def quick_calc(params, seed, pos, known=None):
|
||||
k, hk, w, hw, p, t = params.k, params.hk, params.w, \
|
||||
params.hw, params.p, params.h_threshold
|
||||
init = sha3(seed) % p
|
||||
if known is None:
|
||||
known = {}
|
||||
known[0] = init
|
||||
|
||||
def calc(i):
|
||||
if i not in known:
|
||||
curpicker = pow(init, i, P)
|
||||
curpicker = pow(init, i, p)
|
||||
x = 0
|
||||
# higher end
|
||||
f = i/d + 1
|
||||
pos = i - f + curpicker % f
|
||||
x |= calc(pos)
|
||||
curpicker >>= 10
|
||||
# lower end
|
||||
pos = f - curpicker % f - 1
|
||||
x |= calc(pos)
|
||||
known[i] = pow(x, w, P)
|
||||
if i < t:
|
||||
for j in range(k):
|
||||
x ^= calc(curpicker % i)
|
||||
curpicker >>= 10
|
||||
known[i] = pow(x, w, p)
|
||||
else:
|
||||
for j in range(hk):
|
||||
x ^= calc(curpicker % t)
|
||||
curpicker >>= 10
|
||||
known[i] = pow(x, hw, p)
|
||||
return known[i]
|
||||
o = calc(pos)
|
||||
print 'Calculated index %d in %d lookups' % (pos, len(known))
|
||||
return o
|
||||
|
||||
produce_dag = produce_dag_k2dr
|
||||
quick_calc = quick_calc_k2dr
|
||||
|
||||
def hashimoto(daggerset, lookups, header, nonce):
|
||||
def hashimoto(params, daggerset, header, nonce):
|
||||
"""
|
||||
Requirements:
|
||||
- I/O bound: cycles spent on I/O ≫ cycles spent in cpu
|
||||
|
|
@ -178,41 +142,48 @@ def hashimoto(daggerset, lookups, header, nonce):
|
|||
lookups depend on previous lookup results
|
||||
impossible to route computation/lookups based on the initial sha3
|
||||
"""
|
||||
num_dags = len(daggerset)
|
||||
dag_size = len(daggerset[0])
|
||||
mix = sha3(header + encode_int(nonce)) ** 2
|
||||
rand = sha3(header + encode_int(nonce)) % params.p
|
||||
mix = rand
|
||||
# loop, that can not be unrolled
|
||||
# dag and dag[pos] depended on previous lookup
|
||||
for i in range(lookups):
|
||||
dag = daggerset[mix % num_dags] # modulo
|
||||
pos = mix % dag_size # modulo
|
||||
for i in range(params.lookups):
|
||||
v = mix if params.is_serial else rand >> i
|
||||
dag = daggerset[v % params.num_dags] # modulo
|
||||
pos = v % params.dag_size # modulo
|
||||
mix ^= dag[pos] # xor
|
||||
# print v % params.num_dags, pos, dag[pos]
|
||||
print header, nonce, mix
|
||||
return mix
|
||||
|
||||
|
||||
def light_hashimoto(params, seedset, header, nonce):
|
||||
lookups = params.lookups
|
||||
dag_size = params.dag_size
|
||||
known = dict((s, {}) for s in seedset) # cache results for each dag
|
||||
mix = sha3(header + encode_int(nonce)) ** 2
|
||||
for i in range(lookups):
|
||||
seed = seedset[mix % len(seedset)]
|
||||
pos = mix % dag_size
|
||||
mix ^= quick_calc(params, seed, pos, known[seed])
|
||||
num_accesses = sum(len(known[s]) for s in seedset)
|
||||
print 'Calculated %d lookups with %d accesses' % (lookups, num_accesses)
|
||||
rand = sha3(header + encode_int(nonce)) % params.p
|
||||
mix = rand
|
||||
|
||||
for i in range(params.lookups):
|
||||
v = mix if params.is_serial else rand >> i
|
||||
seed = seedset[v % len(seedset)]
|
||||
pos = v % params.dag_size
|
||||
qc = quick_calc(params, seed, pos)
|
||||
# print v % params.num_dags, pos, qc
|
||||
mix ^= qc
|
||||
print 'Calculated %d lookups' % \
|
||||
(params.lookups)
|
||||
print header, nonce, mix
|
||||
return mix
|
||||
|
||||
|
||||
def light_verify(params, seedset, header, nonce):
|
||||
return light_hashimoto(params, seedset, header, nonce) \
|
||||
<= 2**512 / params.diff
|
||||
h = light_hashimoto(params, seedset, header, nonce)
|
||||
return h <= 256**params.wordsz / params.diff
|
||||
|
||||
|
||||
def mine(daggerset, params, header, nonce=0):
|
||||
orignonce = nonce
|
||||
origtime = time.time()
|
||||
while 1:
|
||||
h = hashimoto(daggerset, params.lookups, header, nonce)
|
||||
if h <= 2**512 / params.diff:
|
||||
h = hashimoto(params, daggerset, header, nonce)
|
||||
if h <= 256**params.wordsz / params.diff:
|
||||
noncediff = nonce - orignonce
|
||||
timediff = time.time() - origtime
|
||||
print 'Found nonce: %d, tested %d nonces in %.2f seconds (%d per sec)' % \
|
||||
|
|
@ -228,44 +199,55 @@ class params(object):
|
|||
lookups: hashes_per_sec(lookups=0) ≫ hashes_per_sec(lookups_mem_hard)
|
||||
k: ?
|
||||
d: higher values enfore memory availability but require more quick_calcs
|
||||
numdags: so that a dag can be updated in reasonable time
|
||||
num_dags: so that a dag can be updated in reasonable time
|
||||
"""
|
||||
memory = 512 * 1024**2 # memory usage
|
||||
numdags = 128 # number of dags
|
||||
dag_size = memory /numdags / 64 # num 64byte values per dag
|
||||
lookups = 512 # memory lookups per hash
|
||||
diff = 2**14 # higher is harder
|
||||
k = 2 # num dependecies of each dag value
|
||||
d = 8 # max distance of first dependency (1/d=fraction of size)
|
||||
w = 2
|
||||
p = (2 ** 256 - 4294968273)**2 # prime modulus
|
||||
wordsz = 64 # word size
|
||||
memory = 10 * 1024**2 # memory usage
|
||||
num_dags = 2 # number of dags
|
||||
dag_size = memory/num_dags/wordsz # num 64byte values per dag
|
||||
lookups = 40 # memory lookups per hash
|
||||
diff = 2**14 # higher is harder
|
||||
k = 2 # num dependecies of each dag value
|
||||
hk = 8 # dependencies for final nodes
|
||||
d = 8 # max distance of first dependency (1/d=fraction of size)
|
||||
w = 2 # work factor on node generation
|
||||
hw = 8 # work factor on final node generation
|
||||
h_threshold = dag_size*2/5 # cutoff between final and nonfinal nodes
|
||||
is_serial = False # hashimoto is serial
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
print dict((k,v) for k,v in params.__dict__.items() if isinstance(v,int))
|
||||
print dict((k, v) for k, v in params.__dict__.items()
|
||||
if isinstance(v, int))
|
||||
|
||||
# odds of a partitial storage attack
|
||||
missing_mem = 0.01
|
||||
P_partitial_mem_success = (1-missing_mem) ** params.lookups
|
||||
print 'P success per hash with %d%% mem missing: %d%%' %(missing_mem*100, P_partitial_mem_success*100)
|
||||
print 'P success per hash with %d%% mem missing: %d%%' % \
|
||||
(missing_mem*100, P_partitial_mem_success*100)
|
||||
|
||||
# which actually only results in a slower mining, as more hashes must be tried
|
||||
slowdown = 1/ P_partitial_mem_success
|
||||
print 'x%.1f speedup required to offset %d%% missing mem' % (slowdown, missing_mem*100)
|
||||
# which actually only results in a slower mining,
|
||||
# as more hashes must be tried
|
||||
slowdown = 1 / P_partitial_mem_success
|
||||
print 'x%.1f speedup required to offset %d%% missing mem' % \
|
||||
(slowdown, missing_mem*100)
|
||||
|
||||
# create set of DAGs
|
||||
st = time.time()
|
||||
seedset = [str(i) for i in range(params.numdags)]
|
||||
seedset = [str(i) for i in range(params.num_dags)]
|
||||
daggerset = get_daggerset(params, seedset)
|
||||
print 'daggerset with %d dags' % len(daggerset), 'size:', 64*params.dag_size*params.numdags / 1024**2 , 'MB'
|
||||
print 'daggerset with %d dags' % len(daggerset), 'size:', \
|
||||
64*params.dag_size*params.num_dags / 1024**2, 'MB'
|
||||
print 'creation took %.2fs' % (time.time() - st)
|
||||
|
||||
# update DAG
|
||||
st = time.time()
|
||||
update_daggerset(params, daggerset, seedset, seed='new')
|
||||
update_daggerset(params, daggerset, seedset, seed='qwe')
|
||||
print 'updating 1 dag took %.2fs' % (time.time() - st)
|
||||
|
||||
# Mine
|
||||
for i in range(10):
|
||||
for i in range(1):
|
||||
header = 'test%d' % i
|
||||
print '\nmining', header
|
||||
nonce = mine(daggerset, params, header)
|
||||
|
|
@ -273,7 +255,3 @@ if __name__ == '__main__':
|
|||
st = time.time()
|
||||
assert light_verify(params, seedset, header, nonce)
|
||||
print 'verification took %.2fs' % (time.time() - st)
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue