可认证的DH密钥交换协议

一、实验目的

通过使用密码学库实现可认证的DH密钥交换协议（简化STS协议），能够编写简单的实验代码进行正确的协议实现和验证。

二、实验要求

1. 熟悉DH密钥交换算法基本原理；
2. 理解原始DH密钥交换算法存在的中间人攻击；
3. 理解简化STS协议抗中间人攻击的原理。
4. 掌握使用java编写实验代码进行正确的简化STS协议实现和验证。

三、 开发环境

JDK 1.7，Java开发环境（本实验采用Windows+eclipse作为实验环境），要求参与实验的同学按照对称加密提供的方法，提前安装好JDK。

四、实验原理

通过使用密码学库实现可认证的DH密钥交换协议（简化STS协议），能够编写简单的实验代码进行正确的协议实现和验证。

代码段：
AuthDHKeyAgree

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

public class AuthDHKeyAgree {
	private static final int securityParam = 1023;
	public static BigInteger p;
	public static BigInteger q;
	public static BigInteger g;
	
	//生成安全素数p,p=2q+1,q为一个1023 bits的大素数
	public static void safePGen() {
		BigInteger one = new BigInteger("1",10);
		BigInteger two = new BigInteger("2",10);
		do {
			p = new BigInteger("0",10);
			q = new BigInteger(securityParam, 100, new Random());
			p = p.add(q.multiply(two).add(one));
		}while( p.isProbablePrime(100) == false );
	}
	
	//选取随机生成元g,通过随机选择[2,p-2]之间的数g,然后判断g^q mod p是否等于1,如果不等于1,则g为生成元
	public static void generatorGGen() {
		BigInteger one = new BigInteger("1",10);
		BigInteger two = new BigInteger("2",10);
		BigInteger result;
		do {
			g = new BigInteger(securityParam, new Random());
			g = g.mod(p.subtract(one));
			result = g.modPow(q, p);
		}while( g.compareTo(two) < 0 || result.compareTo(one) == 0 );
	}
	
	public static void main(String[] args) {
		System.out.println("系统初始化,生成安全素数p,选取随机生成元g...");
		safePGen();
		System.out.println("p: "+p.toString(16));
		System.out.println("q: "+q.toString(16));
		generatorGGen();
		System.out.println("g: "+g.toString(16));
		
		//Alice选择随机秘密值 0<=r1<=p-1
		BigInteger r1 = new BigInteger(securityParam, new Random());
		BigInteger A;
		r1 = r1.mod(p);
		//Alice计算g^r1 mod p
		A = g.modPow(r1, p);
		//Bob选择随机秘密值0<=r2<=p-1
		BigInteger r2 = new BigInteger(securityParam, new Random());
		BigInteger B;
		//Bob计算g^r2 mod p
		B = g.modPow(r2, p);
		//Bob初始化一个RSA签名算法对象
		RSASignatureAlgorithm BobRSA = new RSASignatureAlgorithm();
		BobRSA.initKeys();
		byte[] BobM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
		//Bob生成签名
		BigInteger BobSig = BobRSA.signature(BobM);
		//Alice验证签名
		BobM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
		boolean result = BobRSA.verify(BobM, BobSig);
		if( result == true ) System.out.println("Alice验证签名通过。");
		else System.out.println("Alice验证签名不通过。");
		//Alice计算会话密钥
		BigInteger sessionKey = (A.multiply(B)).mod(p);
		System.out.println("Alice计算得到的会话密钥为:"+sessionKey.toString(16));
		//Alice初始化一个RSA签名算法对象
		RSASignatureAlgorithm AliceRSA = new RSASignatureAlgorithm();
		AliceRSA.initKeys();
		byte[] AliceM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
		//Alice生成签名
		BigInteger AliceSig = AliceRSA.signature(AliceM);
		//Bob验证签名
		AliceM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
		result = AliceRSA.verify(AliceM, AliceSig);
		if ( result == true ) System.out.println("Bob验证签名通过。");
		else System.out.println("Bob验证签名不通过");
		//Bob计算会话密钥
		sessionKey = (B.multiply(A)).mod(p);
		System.out.println("Bob计算得到的会话密钥为:"+sessionKey.toString(16));
	}

}

RSASignatureAlgorithm

import java.math.BigInteger;
import java.math.BigInteger;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.Random;

public class RSASignatureAlgorithm {
	BigInteger n;
	BigInteger e;
	BigInteger d;
	public BigInteger __hash(byte m[]) {
		MessageDigest md;
		try {
			md = MessageDigest.getInstance("SHA-256");
			md.update(m);
		byte b[] = new byte[33];
		System.arraycopy(md.digest(), 0, b, 1, 32);
		return new BigInteger(b);
		} catch (NoSuchAlgorithmException e) {
			System.out.println("this cannot happen.");
		}
	return null;
	}
	public void initKeys() {
		BigInteger p = new BigInteger(1024, 500, new Random());
		BigInteger q = new BigInteger(1024, 500, new Random());
		assert(p.compareTo(q) != 0);
		n = p.multiply(q);
		BigInteger fi_n = p.subtract(BigInteger.ONE)
			.multiply(q.subtract(BigInteger.ONE));
		e = new BigInteger(512, 100, new Random());
		d = e.modInverse(fi_n);
		
		System.out.println("n : " + n.toString(16));
		System.out.println("e : " + e.toString(16));
		System.out.println("d : " + d.toString(16));
	}
	public BigInteger signature(byte m[]) {
		BigInteger s = __hash(m).modPow(d, n);
		System.out.println("s : " + s);
		return s;
	}
	public boolean verify(byte m[], BigInteger s) {
		BigInteger left  = __hash(m).mod(n);
		BigInteger right = s.modPow(e, n);
		return left.compareTo(right) == 0;
	}
}