java 同态加密代码

以下是使用 Paillier 同态加密算法实现的 Java 代码示例：

import java.math.BigInteger;
import java.security.SecureRandom;

public class Paillier {

    private final int CERTAINTY = 64;
    private final SecureRandom random = new SecureRandom();

    private BigInteger p;
    private BigInteger q;
    private BigInteger lambda;
    private BigInteger n;
    private BigInteger nsquare;
    private BigInteger g;

    public Paillier(int numBits) {
        generateKeys(numBits);
    }

    public Paillier(BigInteger p, BigInteger q) {
        setKeys(p, q);
    }

    public void generateKeys(int numBits) {
        p = BigInteger.probablePrime(numBits / 2, random);
        q = BigInteger.probablePrime(numBits / 2, random);
        n = p.multiply(q);
        nsquare = n.multiply(n);
        g = n.add(BigInteger.ONE);
        lambda = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE)).divide(
                p.subtract(BigInteger.ONE).gcd(q.subtract(BigInteger.ONE)));
    }

    public void setKeys(BigInteger p, BigInteger q) {
        this.p = p;
        this.q = q;
        n = p.multiply(q);
        nsquare = n.multiply(n);
        g = n.add(BigInteger.ONE);
        lambda = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE)).divide(
                p.subtract(BigInteger.ONE).gcd(q.subtract(BigInteger.ONE)));
    }

    public BigInteger encrypt(BigInteger m) {
        BigInteger r = new BigInteger(n.bitLength(), random);
        return g.modPow(m, nsquare).multiply(r.modPow(n, nsquare)).mod(nsquare);
    }

    public BigInteger add(BigInteger em1, BigInteger em2) {
        return em1.multiply(em2).mod(nsquare);
    }

    public BigInteger multiply(BigInteger em, int k) {
        return em.modPow(BigInteger.valueOf(k), nsquare);
    }

    public BigInteger decrypt(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);
    }
}

使用示例：

Paillier paillier = new Paillier(1024);
BigInteger m1 = BigInteger.valueOf(42);
BigInteger m2 = BigInteger.valueOf(123);
BigInteger em1 = paillier.encrypt(m1);
BigInteger em2 = paillier.encrypt(m2);
BigInteger em3 = paillier.add(em1, em2);
BigInteger em4 = paillier.multiply(em1,5);
BigInteger dm3 = paillier.decrypt(em3);
BigInteger dm4 = paillier.decrypt(em4);
System.out.println(dm3); // output: 165
System.out.println(dm4); // output: 210