Merge pull request TheAlgorithms#53 from prateekiiest/master

Upadated RSA Algorithm under Cryptography Section

Cryptography/RSA.py

@@ -0,0 +1,113 @@
+import random
+
+
+'''
+Euclid's algorithm for determining the greatest common divisor
+Use iteration to make it faster for larger integers
+'''
+def 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 multiplicative_inverse(e, phi):
+    d = 0
+    x1 = 0
+    x2 = 1
+    y1 = 1
+    temp_phi = phi
+
+    while e > 0:
+        temp1 = temp_phi/e
+        temp2 = temp_phi - temp1 * e
+        temp_phi = e
+        e = temp2
+
+        x = x2- temp1* x1
+        y = d - temp1 * y1
+
+        x2 = x1
+        x1 = x
+        d = y1
+        y1 = y
+
+    if temp_phi == 1:
+        return d + phi
+
+'''
+Tests to see if a number is prime.
+'''
+def is_prime(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 (is_prime(p) and is_prime(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 = gcd(e, phi)
+    while g != 1:
+        e = random.randrange(1, phi)
+        g = gcd(e, phi)
+
+    #Use Extended Euclid's Algorithm to generate the private key
+    d = multiplicative_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 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 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(raw_input("Enter a prime number (17, 19, 23, etc): "))
+    q = int(raw_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 = raw_input("Enter a message to encrypt with your private key: ")
+    encrypted_msg = 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 decrypt(public, encrypted_msg)