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client.py
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# EXAMPLE IMPLEMENTATION on ETHEREUM: https://kovan.etherscan.io/address/0x23cacafb1f32c62b805b14fac3417f1e1e3fec98
# pk = (13671745300223455622296976647036122779409479348541974397577710233068369091353, 13911240)
# sk = 13671745300223455622296976647036122779053175926061888065608023302499601004900
import random
from timeit import timeit
from gmpy2 import invert as gmpy2invert
modinv = lambda x,y: int(gmpy2invert(x,y))
from Crypto.Hash.keccak import Keccak_Hash
keccak256 = lambda preimage: Keccak_Hash(preimage, digest_bytes=32, update_after_digest=False) # the REAL keccak256
eth_pack = lambda x: x.to_bytes(32, 'big')
class VDF: # y = x^(2^Time) mod RSA-N
# Time constants to help
Time_1s = 2**16 + 2**15 + 2**14 + 2**10 + 2**7 + 2**6 + 2**4 + 7
Time_10s = 10*Time_1s
Time_1m = 6*Time_10s
# SETUP
def TrapSetup(Lambda, Time):
sk, pk = RSA.Setup(Lambda)
(Totient, d), (N, e) = sk, pk
PublicParameters, Trap = (N, Time), Totient
return PublicParameters, Trap
def Setup_Wes18(Lambda, Time): # this is the unknown group order setup
return
return PublicParameters
# GENERATE input
def Gen(PublicParameters, Time): # potential plug into blockchain, to hash/randomize the input
return
return x, Time
# EVAL
def Eval(PublicParameters, x):
N, Time = PublicParameters
y = x
for _ in range(Time):
y = pow(y,2,N)
return y
def TrapEval(PublicParameters, Trap, x):
(N, Time), Totient = PublicParameters, Trap
exponent = pow(2, Time, Totient)
y = pow(x, exponent, N)
return y
def Eval_Wes18(PublicParameters, x):
y = VDF.Eval(PublicParameters, x)
(N, Time) = PublicParameters
# long-division algorithm
pi, residue = 1, 1
Challenge = VDF.HPrime(N,Time,x,y)
for _ in range(Time):
bit = 2*residue // Challenge
residue = 2*residue % Challenge
pi = (pi**2 * x**bit) % N
return y, pi
def TrapEval_Wes18(PublicParameters, Trap, x):
y = VDF.TrapEval(PublicParameters, Trap, x)
(N, Time), Totient = PublicParameters, Trap
Challenge = VDF.HPrime(N,Time,x,y)
residue = pow(2, Time, Challenge)
exponent = ((pow(2, Time, Totient) - residue) * modinv(Challenge, Totient)) % Totient
pi = pow(x, exponent, N)
return y,pi
# VERIFY
def Verify_Wes18(PublicParameters,x,y,pi):
(N, Time) = PublicParameters
Challenge = VDF.HPrime(N,Time,x,y)
residue = pow(2, Time, Challenge)
return y == (pow(pi, Challenge, N) * pow(x, residue, N)) % N
# FiatShamir Challenge 256bits
def HPrime(_N, _Time, _x, _y):
# due to solidity limitations i had to limit primes to 256 bits
# due to performance issues i reduced it to 256-3
p = int(keccak256(eth_pack(_N)+eth_pack(_Time)+eth_pack(_x)+eth_pack(_y)).hexdigest(), 16)>>3
if p%2 == 0:
p = p+1
while True:
if Primes.CheckProbablePrime(p):
RandomProbablePrime = p
return RandomProbablePrime
p = p+2
class RSA:
def Setup(Lambda):
p, q = Primes.GetProbablePrime(Lambda//2), Primes.GetProbablePrime(Lambda//2)
while p==q:
q = Primes.GetProbablePrime(Lambda//2)
N = p*q
Totient = (p-1)*(q-1) # group order
e = 65537
d = modinv(e, Totient)
SecretKey, PublicKey = (Totient, d), (N, e)
return SecretKey, PublicKey
class Primes:
FIRST_256_PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619]
def Check_MillerRabin(p, tests): # error=1/4^tests
assert(p>0)
if p in {1,2,3}:
return True
if p%2==0:
return False
# factorize n-1 = 2^s * r, r is odd
even, s, r = p-1, 0, 1
while even%2 == 0:
even = even//2
s = s+1
r=even
# do the tests
for _ in range(tests):
a = random.randint(2, p-2)
y = pow(a,r,p)
if y != 1 and y != p-1:
j = 1
while j <= s-1 and y != p-1:
y = pow(y,2,p)
if y == 1:
return False
j = j+1
if y != p-1:
return False
return True
def CheckProbablePrime(p):
# trial division is faster than Miller-Rabin
for x in Primes.FIRST_256_PRIMES:
if p%x == 0:
if p == x:
return True
else:
return False
else:
# final check with Miller-Rabin
return Primes.Check_MillerRabin(p, 20) # switch to 256 for increased accuracy
def GetProbablePrime(Lambda):
while True:
# generate a candidate
p = random.getrandbits(Lambda)
if p%2 == 0:
continue
# check candidate
if Primes.CheckProbablePrime(p):
return p
def performance(TestTime, PrecisionRounds):
pk, sk = VDF.TrapSetup(1024, TestTime)
x = 1337
y, pi = VDF.TrapEval_Wes18(pk, sk, x)
precisionrounds = PrecisionRounds
tot = timeit(lambda: VDF.Verify_Wes18(pk, x, y, pi), number = precisionrounds)
print(f'avg {tot/precisionrounds:.4f} seconds (total {tot:.4f}s)')
#pk, sk = VDF.TrapSetup(256, VDF.Time_1s*120)
#x = 1337
#y, pi = VDF.Eval_Wes18(pk,x)
#print(VDF.Verify_Wes18(pk, x, y, pi))