java实现同态加密算法的实例代码
什么是同态加密？
同态加密是上世纪七十年代就被提出的一个开放问题，旨在不暴露数据的情况下完成对数据的处理，关注的是数据处理安全。
想象一下这样一个场景，作为一名满怀理想的楼二代，你每天过着枯燥乏味的收租生活，希望摆脱世俗的枷锁、铜臭的苟且去追求诗与远方。
你需要雇一个代理人去承担收租的粗活，但又不希望其窥探你每月躺赚的收入。于是，你请高人打造了一套装备，既能保证代理人顺利完成收租，又不会泄露收入信息。
这套装备包括信封、胶水、皮夹和神奇剪刀，每一样东西都有奇特的功能：
- 信封一旦用胶水密封，只有神奇剪刀才能拆开。
- 不论信封里装了多少钱，信封的大小和重量都不会发生改变。
- 把多个信封放在皮夹里后，信封会在不拆开的情况下两两合并，最后变成一个信封，里面装的钱正好是合并前所有信封金额的总和。
你把信封和胶水分发给所有租客，把皮夹交给代理人。
到了约定交租的日子，租客把租金放到信封里密封后交给代理人；代理人收齐信封，放到皮夹中，最后得到一个装满所有租金的信封，再转交给你；你使用神奇剪刀拆开，拿到租金。
在这个场景中，信封的a、b两个性质其实就是公钥加密的特性，即使用公钥加密得到的密文只有掌握私钥的人能够解密，并且密文不会泄露明文的语义信息；而c则代表加法同态的特性，两个密文可以进行计算，得到的结果解密后正好是两个原始明文的和。
原理：
paillier加密算法步骤：密钥生成、加密、解密
1、密钥生成
1.1 随机选择两个大质数p和q满足gcd(pq,(p-1)(q-1)) =1。这个属性保证两个质数长度相等。
1.2 计算n=pq和λ=lcm(p-1,q-1)
1.3 选择随机整数g(g ∈ Z n 2 ∗ g∈Z_{n^2}^*g∈Zn2∗)，使得满足n整除g的阶。
1.4 公钥为(N,g)
1.5 私钥为λ
g c d ( L ( g λ m o d n 2 ) , n ) = 1 gcd(L(g^λ mod n^2),n)=1gcd(L(gλmodn2),n)=1
2、加密
2.1 选择随机数r ∈ Z n r∈Z_nr∈Zn
2.2 计算密文
c = E ( m , r ) = g m r n m o d n 2 , r ∈ Z n c = E(m,r) = g^m r^n mod n^2 ,r∈Z_nc=E(m,r)=gmrnmodn2,r∈Zn,其中m为加密信息。
3、解密
m = D ( c , λ ) = ( L ( c λ m o d n 2 ) / L ( g λ m o d n 2 ) ) m o d n , 其 中 L ( u ) = u − 1 / N m= D(c,λ)=(L(c^λ mod n^2)/L(g^λ mod n^2)) mod n,其中 L(u)=u-1/Nm=D(c,λ)=(L(cλmodn2)/L(gλmodn2))modn,其中L(u)=u−1/N
java实现：
package com;
/**
* 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 <http://www.gnu.org/licenses/>.
*/
import java.math.*;
import java.util.*;
/**
* Paillier Cryptosystem <br>
* <br>
* References: <br>
* [1] Pascal Paillier,
* "Public-Key Cryptosystems Based on Composite Degree Residuosity Classes,"
* EUROCRYPT'99. URL:
* <a href="http://www.gemplus.com/smart/rd/publications/pdf/Pai99pai.pdf" rel="external nofollow" >http:
* //www.gemplus.com/smart/rd/publications/pdf/Pai99pai.pdf</a><br>
*
* [2] Paillier cryptosystem from Wikipedia. URL:
* <a href="http://en.wikipedia.org/wiki/Paillier_cryptosystem" rel="external nofollow" >http://en.
* wikipedia.org/wiki/Paillier_cryptosystem</a>
*
* @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("--------------------------------");
}
}
参考：https://mp.weixin.qq.com/s?__biz=MzA3MTI5Njg4Mw==&mid=2247486135&idx=1&sn=8c9431012aef19bbdefdcd673a783c34&chksm=9f2ef8aba85971bdfb623e8303b103fd70ac2a5ad802668388233ca930d1b0cd77fb02d4b0f2&scene=21#wechat_redirect
https://www.csee.umbc.edu/~kunliu1/research/Paillier.html
总结
到此这篇关于java实现同态加密算法的文章就介绍到这了,更多相关java同态加密算法内容请搜索我们以前的文章或继续浏览下面的相关文章希望大家以后多多支持我们！
赞 (0)