$ ./fullyhomo.py SaaS Example: Alice wants to use Bob's calculation service to calculate 5 + 10 She encrypts 5 ...and the encrypted value is 408231311223330758911876050904... She then encrypts 10 ...and the encypted value is 6811593647043826157618544194678... Alice also wants to to multiply 6 with the constant 3 She encrypts 6 ...and the encrypted value is 275872367736262799842862895600.. Then Alice sends the encrypted values to Bob along with her public key Bob adds the two encrypted values without knowing what they are the encrypted result is 3509690235178988491246734744677382694... Bob multiplies the third encrypted value with the constant the encrypted result is 8919545079897387397953169089569936011... Bob sends the encrypted results back to Alice Alice uses her private key to view the plain text results: Addition: 15 Multiplication: 18

#!/usr/bin/env python3

import random

# Alice's Private/Public key pair, hard coded for simplicity
class PrivateKey():
        lambdA = 73842165240981452554905699590449542088961757004289873177979834078905122488912
        mu = 14623866067924162049758185900912462985982902037214491087468255488155427133263

class PublicKey():
        n = 73842165240981452554905699590449542089513117936657660262085094366199671389241
        n2 = 5452665367476409421070096932669081750981552257584472365472731868555542659457163641469759175897028833132670904633495629764635203858875472896093430930556081
        g = 73842165240981452554905699590449542089513117936657660262085094366199671389242

# Alice's Implementation of a fully homomorphic Paillier cipher
class FullyHomoCipher():
        def __init__(self, a1, b1):
                self.a = a1
                self.b = b1
        def expCalc(self, base,exponent,modulus):
                result = 1
                while exponent > 0:
                        if exponent & 1 == 1:
                                result = (result * base) % modulus
                        exponent = exponent >> 1
                        base = (base * base) % modulus
                return result

        def encrypt(self, pub, plain):
                while True:
                        r = random.getrandbits(128)
                        if r > 0 and r < pub.n:
                                break
                x = self.expCalc(r, pub.n, pub.n2)
                cipher = (self.expCalc(pub.g, plain, pub.n2) * x) % pub.n2
                return cipher

        def decrypt(self, priv, pub, cipher):
                x = self.expCalc(cipher, priv.lambdA, pub.n2) - 1
                plain = ((x // pub.n) * priv.mu) % pub.n
                return plain

        def encrypt_message(self, pub, m):
                r = random.randrange(256, pub.n)
                b = self.encrypt(pub, r)
                a = (m-r) % pub.n
                self.a = a
                self.b = b

        def decrypt_message(self, priv, pub):
                val = (self.a + self.decrypt(priv, pub, self.b)) % pub.n
                return val

# Bob's encrypted calculation service
class BobsCalculationService():
        # Add two encrypted numbers
        def encrypted_add(self, pub, a, b):
                return a * b % pub.n2
        def sum (self, c1, c2, pub):
                a = (c1.a + c2.a) % pub.n
                b = self.encrypted_add(pub, c1.b, c2.b)
                c = FullyHomoCipher(a, b)
                return c
        # Multiply two encrypted numbers with a constant (Bob)
        def encrypted_mult(self, pub, a, n):
                return FullyHomoCipher(-1, -1).expCalc(a, n, pub.n2)
        def product(self, const, c1, pub):
                a = (c1.a * const) % pub.n
                b = self.encrypted_mult(pub, c1.b, const)
                c = FullyHomoCipher(a, b)
                return c

# THE SAAS EXAMPLE BEGINS HERE
if __name__ == '__main__':
         # Alice's Key Pair
         pub = PublicKey
         priv = PrivateKey
         # The top secret numbers Alice wants to use
         secretNumber1 = 5
         secretNumber2 = 10
         secretNumber3 = 6
         const = 3
         # The Cipher objects Alice uses for encryption
         alice1 = FullyHomoCipher(-1,-1)
         alice2 = FullyHomoCipher(-1,-1)
         alice3 = FullyHomoCipher(-1,-1)
         # Alice performs encryption
         print ("SaaS Example:")
         print ("Alice wants to use Bob's calculation service to calculate ", secretNumber1, "+", secretNumber2)
         print ("She encrypts ", secretNumber1)
         alice1.encrypt_message(pub, secretNumber1)
         print ("...and the encrypted value is ", alice1.a, alice1.b)
         print ("She then encrypts ", secretNumber2)
         alice2.encrypt_message(pub, secretNumber2)
         print ("...and the encypted value is ", alice2.a, alice2.b)
         print ("")
         print ("Alice also wants to to multiply ", secretNumber3," with the constant ", const)
         print ("She encrypts ", secretNumber3)
         alice3.encrypt_message(pub, secretNumber3)
         print ("...and the encrypted value is ", alice3.a, alice3.b)
         print ("")
         print ("Then Alice sends the encrypted values to Bob along with her public key")
         print ("")
         # These are the encrypted values Alice sends to Bob
         encr1_a=alice1.a
         encr1_b=alice1.b
         encr2_a=alice2.a
         encr2_b=alice2.b
         encr3_a=alice3.a
         encr3_b=alice3.b
         # Bob's Cipher objects, initialized with Alice's encrypted numbers
         # Since Bob doesn't have the private key he can't decrypt the numbers
         bob1 = FullyHomoCipher(encr1_a, encr1_b)
         bob2 = FullyHomoCipher(encr2_a, encr2_b)
         bob3 = FullyHomoCipher(encr3_a, encr3_b)
         # Addition
         print ("Bob adds the two encrypted values without knowing what they are")
         result1=BobsCalculationService().sum(bob1, bob2, pub)
         print ("the encrypted result is ", result1.a, result1.b)
         # Multiplication with a constant
         print ("Bob multiplies the third encrypted value with the constant")
         result2=BobsCalculationService().product(const, bob3, pub)
         print ("the encrypted result is ", result2.a, result2.b)
         print ("")
         print ("Bob sends the encrypted results back to Alice")
         print ("Alice uses her private key to view the plain text results:")
         print ("Addition: ", result1.decrypt_message(priv, pub))
         print ("Multiplication: ", result2.decrypt_message(priv, pub))