This is a demo of the multiplicative homomorphic qualities of unpadded RSA encryption.

homomorphic_rsa_demo.py

#!/usr/bin/env python3
from Cryptodome.PublicKey import RSA


# A proof of concept demo showing the multiplicative limited
# homomorphic qualities of unpadded RSA
# (Unpadded RSA is not secure by modern standards)

def gen_key(size):
    key = RSA.generate(size)
    return key


def encrypt_integer(integer, key):
    return pow(integer, key.e, key.n)


def decrypt_integer(integer, key):
    return pow(integer, key.d, key.n)


def homomorphise(x1, x2, key):
    return (x1*x2) % key.n


if __name__ == '__main__':
    print("Generating key...")
    key = gen_key(4096)
    print("Done!")

    x1_plain = int(input("Enter first integer: "))
    x2_plain = int(input("Enter second integer: "))

    x1 = encrypt_integer(x1_plain, key)     # Ex: 2
    x2 = encrypt_integer(x2_plain, key)     # Ex: 4
    hom_c = homomorphise(x1, x2, key)       # Ex: 109238740192837409162348...

    p = decrypt_integer(hom_c, key)         # Ex: 8

    print("\nCiphertext 1:\n{}\n\nCiphertext 2:\n{}\n\nHomomorphised Ciphertext:\n{}\n\nPlaintext:\n{}".format(
        x1, x2, hom_c, p))