Example of a Paillier Cryptosystem voting scheme where voters simply vote yes (1) or no (0) and the votes are tallied up using the homomorphic properties of the Paillier PKC.

Paillier Cryptovoting

#Paillier Cryptovoting System
import math
from Crypto import Random
from Crypto.Random import random





# Modular exponentiation
def exp(base, exponent, modulus):
	result = base;
	for i in range (exponent-1):
		result = (result*base)%modulus
	return result

# Paillier encryption using PyCrypto's PRNG
def encrypt(m):
# Private key information (carmicheal function(n))
	p = 293
	q = 433
# Public key pair
	n = p*q # 126869
	g = 6497955158
# Random number from PRNG
	randint = Random.new()
	r = randint.read(n).encode('hex')
	r = int(r, 16)%n
	print "Random Number: " + str(r)
# Begin Encryption
	print "Ballot Cast: " + str(int(m, 10))
	c = (pow(g, int (m, 10) )*pow(r,n))%(n*n)
	return c

# L function defined by Paillier PKC
def L(u):
	n = 126869
	l = (u - 1)/n
	return l

#http://www.programiz.com/python-programming/examples/lcm
# Used for the Carmicheal Function
def lcm(x, y):
   """This function takes two
   integers and returns the L.C.M."""

   # choose the greater number
   if x > y:
       greater = x
   else:
       greater = y

   while(True):
       if((greater % x == 0) and (greater % y == 0)):
           lcm = greater
           break
       greater += 1

   return lcm

# Decrypts the Paillier encryption using the given u = 53022
def decrypt(c):
	p = 293
	q = 433
	n = p*q # 126869
	g = 6497955158
	u = pow(L(pow(g, lcm(p-1,q-1))%(n*n)), -1)%n
	m = ((L((pow(c, lcm(p-1,q-1)))%(n*n)))*u)%n
	return m

# Tallys the votes by adding up the ciphertexts
def tally(ctxt):
	tally = 1
	for i in range (0, len(ctxt)):
		tally = tally*ctxt[i]%(126869*126869)
	return tally

# Loops through the first 4 and prints their encryptions and decryptions
def main():
	ctxts = []
# Begin Random Voting
	for i in range (0, 5):
		print "Iteration: m = " + str(i)
		c = encrypt(random.choice(['0', '1']))
		print "Ciphertext: " + str(c)
		print ""
		ctxts.append(c)
# Tally Votes without decrypting them
	print "The Cryptographic Tally of Votes: " + str(tally(ctxts))
	print "The Decryption of the Tally: " +  str(decrypt(tally(ctxts))%126869)

main()