def factorize(number):
arr = []
gen = generate_primes()
prime = next(gen)
while number >= prime:
if number % prime == 0:
arr.append(prime)
number /= prime
continue
else:
prime = next(gen)
return arr
def factorize(number):
arr = []
gen = generate_primes()
prime = next(gen)
while number >= prime:
if number % prime == 0:
arr.append(prime)
number /= prime
continue
else:
prime = next(gen)
return arr
def RSA_keygen(n=512):
"""
Perform steps 1. to 5. in the RSA Key Generation process.
"""
# step 1
import generate_primes
p = generate_primes.generate_primes(n=n, k=1)[0]
q = generate_primes.generate_primes(n=n, k=1)[0]
# step 2
n = p * q
# step 3
phi_n = (p - 1) * (q - 1)
# step 4 and step 5
while True:
e = random.randrange(1, phi_n - 1)
if math.gcd(e, phi_n) == 1:
# step 5
gcd, s, t = eea.EEA(phi_n, e)
if gcd == (s * phi_n + t * e):
d = t % phi_n
break
return (e, n, d)
def rsa(bits=512, e=pow(2, 16) + 1):
r"""
>>> e, d, n = rsa()
>>> message = 109
>>> encrypted_message = encrypt(e, n, message)
>>> decrypted_message = decrypt(d, n, encrypted_message)
>>> message == decrypted_message
True
"""
gcd = None
while gcd != 1:
p, q = generate_primes(bits=bits, n_primes=2)
n = p * q
phi = (p - 1) * (q - 1)
d, k, gcd = extended_gcd(phi, e)
while d < 0 and gcd == 1:
d += phi
return e % n, d % n, n
def is_prime(n):
"""Calculate if n is prime or not"""
if n < 2:
return False
if n < 4:
return True
try:
return manager.get(n)
except KeyError:
pass # Continue on to the rest of the function
value = True
for i in gp.generate_primes(end=int(sqrt(n))):
if n % i == 0:
value = False
break
manager.add(n, value)
return value
def is_prime(n):
"""Calculate if n is prime or not"""
if n < 2:
return False
if n < 4:
return True
try:
return manager.get(n)
except KeyError:
pass # Continue on to the rest of the function
value = True
for i in gp.generate_primes(end=int(sqrt(n))):
if n % i == 0:
value = False
break
manager.add(n, value)
return value