gentry同态加密算法_同态加密算法简述

/** * This program is free software: you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the Free * Software Foundation, either version 3 of the License, or (at your option) * any later version. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. * * You should have received a copy of the GNU General Public License along with * this program. If not, see . */

import java.math.*;

import java.util.*;

/** * Paillier Cryptosystem
*
* References:
* [1] Pascal Paillier, * "Public-Key Cryptosystems Based on Composite Degree Residuosity Classes," * EUROCRYPT'99. URL: * http: * //www.gemplus.com/smart/rd/publications/pdf/Pai99pai.pdf
* * [2] Paillier cryptosystem from Wikipedia. URL: * http://en. * wikipedia.org/wiki/Paillier_cryptosystem * *@author Kun Liu (kunliu1@cs.umbc.edu) *@version 1.0 */

public class Paillier {

/** * p and q are two large primes. lambda = lcm(p-1, q-1) = * (p-1)*(q-1)/gcd(p-1, q-1). */

private BigInteger p, q, lambda;

/** * n = p*q, where p and q are two large primes. */

public BigInteger n;

/** * nsquare = n*n */

public BigInteger nsquare;

/** * a random integer in Z*_{n^2} where gcd (L(g^lambda mod n^2), n) = 1. */

private BigInteger g;

/** * number of bits of modulus */

private int bitLength;

/** * Constructs an instance of the Paillier cryptosystem. * *@param bitLengthVal * number of bits of modulus *@param certainty * The probability that the new BigInteger represents a prime * number will exceed (1 - 2^(-certainty)). The execution time of * this constructor is proportional to the value of this * parameter. */

public Paillier(int bitLengthVal, int certainty) {

KeyGeneration(bitLengthVal, certainty);

}

/** * Constructs an instance of the Paillier cryptosystem with 512 bits of * modulus and at least 1-2^(-64) certainty of primes generation. */

public Paillier() {

KeyGeneration(512, 64);

}

/** * Sets up the public key and private key. * *@param bitLengthVal * number of bits of modulus. *@param certainty * The probability that the new BigInteger represents a prime * number will exceed (1 - 2^(-certainty)). The execution time of * this constructor is proportional to the value of this * parameter. */

public void KeyGeneration(int bitLengthVal, int certainty) {

bitLength = bitLengthVal;

/* * Constructs two randomly generated positive BigIntegers that are * probably prime, with the specified bitLength and certainty. */

p = new BigInteger(bitLength / 2, certainty, new Random());

q = new BigInteger(bitLength / 2, certainty, new Random());

n = p.multiply(q);

nsquare = n.multiply(n);

g = new BigInteger("2");

lambda = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE))

.divide(p.subtract(BigInteger.ONE).gcd(q.subtract(BigInteger.ONE)));

/* check whether g is good. */

if (g.modPow(lambda, nsquare).subtract(BigInteger.ONE).divide(n).gcd(n).intValue() != 1) {

System.out.println("g is not good. Choose g again.");

System.exit(1);

}

}

/** * Encrypts plaintext m. ciphertext c = g^m * r^n mod n^2. This function * explicitly requires random input r to help with encryption. * *@param m * plaintext as a BigInteger *@param r * random plaintext to help with encryption *@return ciphertext as a BigInteger */

public BigInteger Encryption(BigInteger m, BigInteger r) {

return g.modPow(m, nsquare).multiply(r.modPow(n, nsquare)).mod(nsquare);

}

/** * Encrypts plaintext m. ciphertext c = g^m * r^n mod n^2. This function * automatically generates random input r (to help with encryption). * *@param m * plaintext as a BigInteger *@return ciphertext as a BigInteger */

public BigInteger Encryption(BigInteger m) {

BigInteger r = new BigInteger(bitLength, new Random());

return g.modPow(m, nsquare).multiply(r.modPow(n, nsquare)).mod(nsquare);

}

/** * Decrypts ciphertext c. plaintext m = L(c^lambda mod n^2) * u mod n, where * u = (L(g^lambda mod n^2))^(-1) mod n. * *@param c * ciphertext as a BigInteger *@return plaintext as a BigInteger */

public BigInteger Decryption(BigInteger c) {

BigInteger u = g.modPow(lambda, nsquare).subtract(BigInteger.ONE).divide(n).modInverse(n);

return c.modPow(lambda, nsquare).subtract(BigInteger.ONE).divide(n).multiply(u).mod(n);

}

/** * sum of (cipher) em1 and em2 * *@param em1 *@param em2 *@return */

public BigInteger cipher_add(BigInteger em1, BigInteger em2) {

return em1.multiply(em2).mod(nsquare);

}

/** * main function * *@param str * intput string */

public static void main(String[] str) {

/* instantiating an object of Paillier cryptosystem */

Paillier paillier = new Paillier();

/* instantiating two plaintext msgs */

BigInteger m1 = new BigInteger("20");

BigInteger m2 = new BigInteger("60");

/* encryption */

BigInteger em1 = paillier.Encryption(m1);

BigInteger em2 = paillier.Encryption(m2);

/* printout encrypted text */

System.out.println(em1);

System.out.println(em2);

/* printout decrypted text */

System.out.println(paillier.Decryption(em1).toString());

System.out.println(paillier.Decryption(em2).toString());

/* * test homomorphic properties -> D(E(m1)*E(m2) mod n^2) = (m1 + m2) mod * n */

// m1+m2,求明文数值的和

BigInteger sum_m1m2 = m1.add(m2).mod(paillier.n);

System.out.println("original sum: " + sum_m1m2.toString());

// em1+em2，求密文数值的乘

BigInteger product_em1em2 = em1.multiply(em2).mod(paillier.nsquare);

System.out.println("encrypted sum: " + product_em1em2.toString());

System.out.println("decrypted sum: " + paillier.Decryption(product_em1em2).toString());

/* test homomorphic properties -> D(E(m1)^m2 mod n^2) = (m1*m2) mod n */

// m1*m2,求明文数值的乘

BigInteger prod_m1m2 = m1.multiply(m2).mod(paillier.n);

System.out.println("original product: " + prod_m1m2.toString());

// em1的m2次方，再mod paillier.nsquare

BigInteger expo_em1m2 = em1.modPow(m2, paillier.nsquare);

System.out.println("encrypted product: " + expo_em1m2.toString());

System.out.println("decrypted product: " + paillier.Decryption(expo_em1m2).toString());

//sum test

System.out.println("--------------------------------");

Paillier p = new Paillier();

BigInteger t1 = new BigInteger("21");System.out.println(t1.toString());

BigInteger t2 = new BigInteger("50");System.out.println(t2.toString());

BigInteger t3 = new BigInteger("50");System.out.println(t3.toString());

BigInteger et1 = p.Encryption(t1);System.out.println(et1.toString());

BigInteger et2 = p.Encryption(t2);System.out.println(et2.toString());

BigInteger et3 = p.Encryption(t3);System.out.println(et3.toString());

BigInteger sum = new BigInteger("1");

sum = p.cipher_add(sum, et1);

sum = p.cipher_add(sum, et2);

sum = p.cipher_add(sum, et3);

System.out.println("sum: "+sum.toString());

System.out.println("decrypted sum: "+p.Decryption(sum).toString());

System.out.println("--------------------------------");

}

}