def isComposite(a, k, m, n):
if ModularExponentiation.modExp(a, m, n) == 1: # test to see if a^m mod n == 1, if so n is probably prime
return False
for i in range(k):
# test to see if a^(m*(2^i)) mod n is -1, where 0 <= i < k
# This covers the a^m mod n == -1 as well as all future increments by the power of 2
# because a^(m*(2*i)) mod n = (a^m)^(2*i) mod n, where 0 <= i < k
if ModularExponentiation.modExp(a, 2**i * m, n) == n-1: # if this result is -1 then it is probably prime
return False
return True # if the result was never -1 after k iterations, this number is composite
def Encrypt(message):
PublicKeyFile = open("K1", "r")
prime = int(PublicKeyFile.readline()) # the prime number
PrimitiveRoot = int(PublicKeyFile.readline()) # the primitve root of the prime
h = int(PublicKeyFile.readline()) # PrimitiveRoot^x mod prime Where x is the random number in the private key
PublicKeyFile.close()
CiphertextFile = open("Cipher", "w")
for character in message: # for every ascii character that is in the string message
k = random.randint(0, prime - 1) # Find a random number, k, where 0 <= k <= p-1
r = ModularExponentiation.modExp(PrimitiveRoot, k, prime) # Compute r, where r = PrimitiveRoot^k mod prime
t = (
ModularExponentiation.modExp(h, k, prime) * ord(character) % prime
) # Compute t, where t = (h^k mod prime) * [ascii value of character] mod prime
CiphertextFile.write(str(r) + " " + str(t) + "\n") # writes these values to the file named 'Cipher'
CiphertextFile.close()
def primitiveRoot(p):
while True: # until a primitive root is found
g = random.randint(2, p-1) # take a random integer value 2 <= g <= p-1
if ModularExponentiation.modExp(g, p-1, p) == 1: # Test to see if g is a primitive root
return g # if it is a primitive root, return g
__author__ = 'David'
import ModularExponentiation as ME
import random
"""
This module is used to ensure the correctness of the Modular Exponentiation module.
Python has a built in modular exponentiation function so this test is very simple.
The current setting has this testing 10000 random values x, y, n where x^y mod n is calculated
by both the pow function and my modular exponentiation function. If they differ increment the error
counter and alert the tester
"""
if __name__ == '__main__':
ErrorCount = 0
for i in range(10000):
x = random.randint(2, 10000)
y = random.randint(2, 10000)
n = random.randint(1000, 20000)
powVale = pow(x, y, n)
ModExpVal = ME.modExp(x, y, n)
if(ModExpVal != powVale):
print('Error! PowVal = ', powVale, 'ModExpVal = ', ModExpVal)
ErrorCount += 1
print(ErrorCount)
