def generate_n(n_size):
# ensures N is exactly the size it is supposed to be
factor_size = n_size / 2
most_significant_bit = 1 << (factor_size * 8)
while True:
p = random_integer(factor_size) | most_significant_bit
if is_prime(p):
break
while True:
q = random_integer(factor_size) | most_significant_bit
if is_prime(q):
break
n = p * q
return n
def generate_n(n_size):
# ensures N is exactly the size it is supposed to be
factor_size = n_size / 2
most_significant_bit = 1 << (factor_size * 8)
while True:
p = random_integer(factor_size) | most_significant_bit
if is_prime(p):
break
while True:
q = random_integer(factor_size) | most_significant_bit
if is_prime(q):
break
n = p * q
return n
def find_p(security_level=SECURITY_LEVEL):
from crypto.utilities import is_prime
p = 2 ** (security_level * 8)
offset = 1
while not is_prime(p + offset):
offset += 2
return p, offset
def find_q(q_size=Q_SIZE):
from crypto.utilities import is_prime
q = 2 ** (q_size * 8)
offset = 1
while not is_prime(q + offset):
offset += 2
return q, offset
def find_p(parameters):
from crypto.utilities import is_prime
p_size = parameters["p_size"]
p = 2 ** ((p_size * 8) + 1)
offset = 1
while not is_prime(p + offset):
offset += 2
return p, offset
def find_q(security_level=SECURITY_LEVEL):
from crypto.utilities import is_prime
q_size = security_level * 3
offset = 1
q = (2 ** (q_size * 8))
while not is_prime(q + offset):
offset += 2
return q, offset
def find_q(q_size):
from crypto.utilities import is_prime
q_size *= 8
q = 2**q_size
offset = 1
while not is_prime(q + offset):
offset += 2
return q, offset
def find_q(q_size):
from crypto.utilities import is_prime
q_size *= 8
q = 2 ** q_size
offset = 1
while not is_prime(q + offset):
offset += 2
return q, offset
def generate_private_key(parameters=PARAMETERS):
ab_size = parameters["ab_size"]
while True:
a = random_integer(ab_size)
b = random_integer(ab_size)
if not is_prime(pow(a, 2) + pow(b, 2)):
break
return a, b
def find_q(security_level=SECURITY_LEVEL):
from crypto.utilities import is_prime
q_size = security_level * 3
offset = 1
q = (2**(q_size * 8))
while not is_prime(q + offset):
offset += 2
return q, offset
def generate_private_key(parameters=PARAMETERS):
ab_size = parameters["ab_size"]
while True:
a = random_integer(ab_size)
b = random_integer(ab_size)
if not is_prime(pow(a, 2) + pow(b, 2)):
break
return a, b
def find_q(parameters=PARAMETERS):
from crypto.utilities import is_prime
q_size = parameters["q_size"]
offset = 1
q_base = (2 ** q_size)
while not is_prime(q_base + offset):
offset += 2
return q_base, offset
def find_q(parameters=PARAMETERS):
from crypto.utilities import is_prime
q_size = parameters["q_size"]
offset = 1
q_base = (2**q_size)
while not is_prime(q_base + offset):
offset += 2
return q_base, offset
def find_p(parameters):
from crypto.utilities import is_prime
p_size = parameters["p_size"]
p = 2**((p_size * 8) + 1)
offset = 1
while not is_prime(p + offset):
offset += 2
return p, offset
def generate_private_key(parameters=PARAMETERS):
ab_size = parameters["ab_size"]
a = random_integer(ab_size)
while True:
b = random_integer(ab_size)
if is_prime(pow(a, 2) + pow(b, 2)):
break
print("Generated a, b")
c = random_integer(ab_size)
while True:
d = random_integer(ab_size)
if is_prime(pow(c, 2) + pow(d, 2)):
break
print("Generated c, d")
x = (a * c) - (b * d)
y = (a * d) + (b * c)
assert (pow(x, 2) + pow(y, 2)) == (pow(a, 2) + pow(b, 2)) * (pow(c, 2) + pow(d, 2))
return x, y
def generate_public_key(p, q_size=32):
q = big_prime(q_size)
N = quicksum(p * q)
#assert not( N % p != 0 or quicksum(N) % p != 0)
while N % p != 0 or quicksum(N) % p != 0:
q = random_integer(q_size)
N = quicksum(p * q)
assert is_prime(q)
assert N % p == 0, (N % p)
assert quicksum(N) % p == 0
return N
def generate_public_key(p, q_size=32):
q = big_prime(q_size)
N = quicksum(p * q)
#assert not( N % p != 0 or quicksum(N) % p != 0)
while N % p != 0 or quicksum(N) % p != 0:
q = random_integer(q_size)
N = quicksum(p * q)
assert is_prime(q)
assert N % p == 0, (N % p)
assert quicksum(N) % p == 0
return N
def test_break():
N = 65537#big_prime(3)
assert is_prime(N)
p_i = 256
p = modular_inverse(p_i, N)
q = random_integer(1)
e = random_integer(1)
c = ((p * q) + e) % N
print q, e, p_i * e < N
_q, _e = break_qtpie(p, c, N)
assert (q, e) == (_q, _e), ((q, e), (_q, _e))
assert _e == e, (e, _e)