[密码学]ElGamal算法大整数版本的JAVA实现

[注：本文为本人本科期间实验成果，仅供参考，拷贝以及转载引起的后果自负！]

ElGamal算法大整数版本的JAVA实现

ElGamal加密体制是基于有限域上离散对数问题的公钥密码体制。

算法实现过程中，唯一的难点是如何寻找生成元。后来在网上找到求生成元的办法（根据欧拉定理和拉格朗日定理，主要是利用安全素数的概念）。

算法执行结果：

JAVA代码如下：

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Random;
import java.util.Scanner;

public class ElGamal {
	static BigInteger p, g; // 大素数和本原元
	static BigInteger C, C1;// 密文

	public static double entropy(String mess) {
		ArrayList jieguo = new ArrayList();
		jieguo.clear();
		double num = mess.length();
		for (int i = 0; i < num; i++) {
			boolean flag_exit = true;
			for (int j = 0; j < jieguo.size(); j++) {
				if (jieguo.get(j).getalpha() == mess.charAt(i)) {
					flag_exit = false;
					jieguo.get(j).setp(jieguo.get(j).getp() + 1 / num);
				}
			}
			if (flag_exit)
				jieguo.add(new Node(1 / num, mess.charAt(i)));
		}
		/** 计算熵 */
		double entropy = 0;
		for (int i = 0; i < jieguo.size(); i++) {
			double p1 = jieguo.get(i).getp();
			entropy += (-p1 * (Math.log(p1) / Math.log(2)));
		}
		return entropy;
	}

	/** 取一个大的随机素数P,和P的生成元a */
	public static void getRandomP(int alpha) {
		Random r = new Random();
		BigInteger q = null;
		while (true) {
			q = BigInteger.probablePrime(alpha, r);
			if (q.bitLength() != alpha)
				continue;
			if (q.isProbablePrime(10)) // 如果q为素数则再进一步计算生成元
			{
				p = q.multiply(new BigInteger("2")).add(BigInteger.ONE);
				if (p.isProbablePrime(10)) // 如果P为素数则OK~，否则继续
					break;
			}
		}
		while (true) {
			g = BigInteger.probablePrime(p.bitLength() - 1, r);
			if (!g.modPow(BigInteger.ONE, p).equals(BigInteger.ONE)
					&& !g.modPow(q, p).equals(BigInteger.ONE)) {
				break;
			}
		}
	}

	/** 取随机数a */
	public static BigInteger getRandoma(BigInteger p) {
		BigInteger a;
		Random r = new Random();
		a = new BigInteger(p.bitLength() - 1, r);
		return a;
	}

	/** 计算密钥的值 */
	public static BigInteger calculatey(BigInteger x, BigInteger g, BigInteger p) {
		BigInteger y;
		y = g.modPow(x, p);
		return y;
	}

	/** 加密 */
	public static void encrypt(String m, BigInteger y, BigInteger p,
			BigInteger g) {
		BigInteger message = new BigInteger(m.getBytes());// 把字串转成一个BigInteger对象
		Random r = new Random();
		BigInteger k;
		while (true) {
			k = new BigInteger(p.bitLength() - 1, r);// 产生一0<=k，私钥 0为: (" + x + "," + g + "," + p + ")");
			System.out.println("公钥为:" + "(" + y + "," + g + "," + p
					+ ")");
			x = ElGamal.getRandoma(p);
			y = ElGamal.calculatey(x, g, p);
			ElGamal.encrypt(str, y, p, g);
			System.out
					.println("计算得到的明文熵：" + entropy(str.getBytes().toString()));
			System.out.println("加密后的密文为:" + C + "," + C1);
			System.out.println("计算得到的密文熵："
					+ entropy(C.toString().concat(C1.toString())));
			String designm = ElGamal.decrypt(C, C1, x, p);
			System.out.println("解密得到明文为:" + designm);
		}
	}
}

2.Node.java

public class Node {
	private double p;// 记录概率
	private char alpha;// 记录对应的字母

	public Node(double p, char alpha) {
		this.p = p;
		this.alpha = alpha;
	}

	public void setp(double p) {
		this.p = p;
	}

	public void setalpha(char a) {
		this.alpha = a;
	}

	public double getp() {
		return p;
	}

	public char getalpha() {
		return alpha;
	}
}