def descobrirpg(n):
p = nextprime(
n
) #p já é primo, através do teorema de lucas é possível verificar isso
#print(p)
g = primitive_root(p) #raiz primitiva mais pequena de p
#print(g)
return p, g
def generate_PG(self):
P = randprime(10**26, 10**27)
while not (((P - 1) % 2 == 0) and isprime((P - 1) // 2)):
P = randprime(10**26, 10**27)
G = primitive_root(P)
self.P = P
self.G = G
return P, G
def _generate_root(self) -> int:
"""
Helper function to calculate the smallest primitive root modulo n where n is the prime specified on the instance
"""
print(f"Calculating smallest primitive root modulo n where n = {self._prime}")
return primitive_root(self._prime)
from random import randint
from sympy import isprime
from sympy.ntheory.residue_ntheory import primitive_root
from sympy.ntheory.generate import randprime
from simplecrypt import encrypt, decrypt
message = input("Enter message: ")
P = randprime(10**58, 10**59)
while not (((P - 1) % 2 == 0) and isprime((P - 1) // 2)):
P = randprime(10**58, 10**59)
G = primitive_root(P)
print ("P : ", P, "\nG : ", G)
a_private_number = randint(10**58, 10**59)
print("Private key a: ", a_private_number)
b_private_number = randint(10**58, 10**59)
print("Private key b: ", b_private_number)
a_open_number = pow(G, a_private_number, P)
print("Open key A: ", a_open_number)
b_open_number = pow(G, b_private_number, P)
print("Open key B: ", b_open_number)
a_shared_key = pow(a_open_number, b_private_number, P)
print("Secret key A: ", a_shared_key)
b_shared_key = pow(b_open_number, a_private_number, P)
## return g
def genSecret(prime):
start = randint((prime - 1) / 2, prime - 1)
while coprime2(start, (p - 1)) == False:
start += 1
return start
menu = input("Would you like to generate a new key (G) or accept a key (A)? ")
if menu == "G":
seed = input("Please input a large integer as a seed. ")
p = randprime(int(seed), 2 * int(seed))
g = primitive_root(p)
print("Tell your partner that p = " + str(p) + " and g = " + str(g))
a = genSecret(p)
print("Tell your partner that your unlocked key is " + str(pow(g, a, p)))
B = input("What is your partners unlocked key? ")
pw = pow(int(B), a, p)
print("Password is " + str(pw))
elif menu == "A":
p = input("What is the value of p? ")
g = input("What is the value of g? ")
p = int(p)
g = int(g)
g = primRoots(p)
b = genSecret(p)
print("Tell your partner that your unlocked key is " + str(pow(g, b, p)))
def get_primitive_root(modulo):
# g^phi(m) = 1 mod m
return primitive_root(modulo)