HAVE TO USE PYTHON TO GET IT DONE Asymmetric encryption has been broadly used fo

Question

HAVE TO USE PYTHON TO GET IT DONE

Asymmetric encryption has been broadly used for information security in modern society. Implement and test a prototype for RSA, an asymmetric encryption system. The program should: 1. Generate two large pseudo-prime numbers;

2. Use the two numbers to form a public encryption key and the private decryption key;

3. Create a main program that allows a user to key in a message in plaintext and encrypt it with public key; and decrypt a ciphered-text to plaintext with private key.

Explanation / Answer

import random
'''
Euclid's algorithm for determining the greatest common divisor
Use iteration to make it faster for larger integers
'''
def rsa_gcd(a, b):
while b != 0:
a, b = b, a % b
return a

'''
Euclid's extended algorithm for finding the multiplicative inverse of two numbers
'''
def mul_inverse(e, phi):
d = 0
x1 = 0
x2 = 1
y1 = 1
temps_phi = phi
  
while e > 0:
temps_var1 = temps_phi/e
temps_var2 = temps_phi - temps_var1 * e
temps_phi = e
e = temps_var2
  
x = x2- temp1* x1
y = d - temps_var1 * y1
  
x2 = x1
x1 = x
d = y1
y1 = y
  
if temps_phi == 1:
return d + phi

'''
Tests to see if a number is prime.
'''
def isit_primenum(num):
if num == 2:
return True
if num < 2 or num % 2 == 0:
return False
for n in xrange(3, int(num**0.5)+2, 2):
if num % n == 0:
return False
return True

def generate_keypair(p, q):
if not (isit_primenum(p) and isit_primenum(q)):
raise ValueError('Both numbers must be prime.')
elif p == q:
raise ValueError('p and q cannot be equal')
#n = pq
n = p * q

#Phi is the totient of n
phi = (p-1) * (q-1)

#Choose an integer e such that e and phi(n) are coprime
e = random.randrange(1, phi)

#Use Euclid's Algorithm to verify that e and phi(n) are comprime
g = rsa_gcd(e, phi)
while g != 1:
e = random.randrange(1, phi)
g = rsa_gcd(e, phi)

#Use Extended Euclid's Algorithm to generate the private key
d = mul_inverse(e, phi)
  
#Return public and private keypair
#Public key is (e, n) and private key is (d, n)
return ((e, n), (d, n))

def rsa_encrypt(pk, plaintext):
#Unpack the key into it's components
key, n = pk
#Convert each letter in the plaintext to numbers based on the character using a^b mod m
cipher = [(ord(char) ** key) % n for char in plaintext]
#Return the array of bytes
return cipher

def rsa_decrypt(pk, ciphertext):
#Unpack the key into its components
key, n = pk
#Generate the plaintext based on the ciphertext and key using a^b mod m
plain = [chr((char ** key) % n) for char in ciphertext]
#Return the array of bytes as a string
return ''.join(plain)
  

if __name__ == '__main__':
'''
Detect if the script is being run directly by the user
'''
print ("RSA Encrypter/ Decrypter")
p = int(input("Enter a prime number (17, 19, 23, etc): "))
q = int(input("Enter another prime number (Not one you entered above): "))
print ("Generating your public/private keypairs now . . .")
public, private = generate_keypair(p, q)
print ("Your public key is ", public ," and your private key is ", private)
message = input("Enter a message to rsa_encrypt with your private key: ")
encrypted_msg = rsa_encrypt(private, message)
print ("Your encrypted message is: ")
print (''.join(map(lambda x: str(x), encrypted_msg)))
print ("Decrypting message with public key ", public ," . . .")
print ("Your message is:")
print (rsa_decrypt(public, encrypted_msg))

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