def generate_h(p_s, p, q_s, q):
"""Compute a generator of a subgroup of Z^*_n that has order
p_s mod p and order q_s mod q"""
rs = PRNG()
while True:
hp = gmpy2.powmod(rs.random_Zsp(p), mpz((p-1)/p_s), p)
if hp != 1:
break
while True:
hq = gmpy2.powmod(rs.random_Zsp(q), mpz((q-1)/q_s), q)
if hq != 1:
break
return crt([p, q], [hp, hq])
def generate_g(b, d, p, q):
"""Compute a generator of a subgroup of Z^*_n that has order
b**d mod p and order b**d mod q"""
rs = PRNG()
b_to_the_d = b ** d
while True:
x = rs.random_Zsp(p)
if gmpy2.powmod(x, mpz((p-1)/b), p) != 1:
gp = gmpy2.powmod(x, mpz((p-1)/b_to_the_d), p)
break
while True:
x = rs.random_Zsp(q)
if gmpy2.powmod(x, mpz((q-1)/b), q) != 1:
gq = gmpy2.powmod(x, mpz((q-1)/b_to_the_d), q)
break
return crt([p, q], [gp, gq])
def pohlig(curve, g, f, n, limit=0):
subgroups = n
if isinstance(n, int):
subgroups = factorint(n)
factors = [i**j for i, j in subgroups.items()]
prod = 1
for i in factors:
prod *= i
exponents = [prod // i for i in factors]
remainders = []
for factor, power in zip(factors, exponents):
if limit != 0 and factor > limit:
continue
g_power_k = curve.mult(power, g)
assert curve.check(g_power_k)
r_power_k = curve.mult(power, f)
remainders.append(bsgs(curve, g_power_k, r_power_k, factor))
return crt(remainders, factors)
def pohlig_hellman_attack(h, g, p): primes = get_factor_counts_dict(p - 1) crt_dict = dict() for prime, power in primes.items(): x_list = [] h_sub = h for j in range(1, power + 1): i = 0 q = (p - 1) // pow(prime, j) h_pow = pow(h_sub, q, p) g_pow = pow(g, (p - 1) // prime, p) while True: if pow(g_pow, i, p) == h_pow: x_list += [i] break i += 1 h_sub = (h_sub * pow(ext_euc(g, p)[1], i * pow(prime, j - 1))) % p res_mod_prime = 0 for j in range(power): res_mod_prime += pow(prime, j) * x_list[j] crt_dict[res_mod_prime % pow(prime, power)] = pow(prime, power) return crt(crt_dict)
nums = parse_nums(line)
data = parse_line(r'', line)
for x, c in enumerate(line):
board[Point(x, y)] = c
if y == 0:
timestamp = int(line)
else:
for x in line.split(','):
if x == 'x':
buses.append(None)
else:
buses.append(int(x))
m = []
x = []
for i, b in enumerate(buses):
if b:
m.append(b)
x.append(i)
print crt(x, m)
num = 1777307553937916
l1 = 2265213528143033
num2 = num - l1
print abs(num2) < abs(num)