#
# implementing RSA algorithm(Python Version)
#
#
#
def gcd (a, b):
"Compute GCD of two numbers"
if b == 0: return a
else: return gcd(b, a % b)
def multiplicative_inverse(a, b):
""" Find multiplicative inverse of a modulo b (a > b)
using Extended Euclidean Algorithm """
origA = a
X = 0
prevX = 1
Y = 1
prevY = 0
while b != 0:
temp = b
quotient = a/b
b = a % b
a = temp
temp = X
a = prevX - quotient * X
prevX = temp
temp = Y
Y = prevY - quotient * Y
prevY = temp
return origA + prevY
def generateRSAKeys(p, q):
"Generate RSA Public and Private Keys from prime numbers p & q"
n = p * q
m = (p - 1) * (q - 1)
# Generate a number e so that gcd(n, e) = 1, start with e = 3
e = 3
while 1:
if gcd(m, e) == 1: break
else: e = e + 2
# start with a number d = m/e will be atleast 1
d = multiplicative_inverse(m, e)
# Return a tuple of public and private keys
return ((n,e), (n,d))
if __name__ == "__main__":
print "RSA Encryption algorithm...."
p = long(raw_input("Enter the value of p (prime number):"))
q = long(raw_input("Enter the value of q (prime number):"))
print "Generating public and private keys...."
(publickey, privatekey) = generateRSAKeys(p, q)
print "Public Key (n, e) =", publickey
print "Private Key (n, d) =", privatekey
n, e = publickey
n, d = privatekey
input_num = long(raw_input("Enter a number to be encrypted:"))
encrypted_num = (input_num ** e) % n
print "Encrypted number using public key =", encrypted_num
decrypted_num = encrypted_num ** d % n
print "Decrypted (Original) number using private key =", decrypted_num
