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+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)