非对称密码之DH密钥交换算法

1、DH算法的简介

DH，全称为“Diffie-Hellman”，他是一种确保共享KEY安全穿越不安全网络的方法，也就是常说的密钥一致协议。由公开密钥密码体制的奠基人Diffie和Hellman所提出的一种思想。

简单的说就是允许两名用户在公开媒体上交换信息以生成“一致”的、可以共享的密钥。也就是由甲方产出一对密钥（公钥、私钥），乙方依照甲方公钥产生乙方密钥对（公钥、私钥）。

以此为基线，作为数据传输保密基础，同时双方使用同一种对称加密算法构建本地密钥（SecretKey）对数据加密。这样，在互通了本地密钥（SecretKey）算法后，甲乙双方公开自己的公钥，使用对方的公钥和刚才产生的私钥加密数据，同时可以使用对方的公钥和自己的私钥对数据解密。不单单是甲乙双方两方，可以扩展为多方共享数据通讯，这样就完成了网络交互数据的安全通讯！

2、DH算法的通信模型

2.1 甲方将自己的公钥发给乙方

甲方将自己的公钥发给乙方

2.2 乙方根据甲方发来的公钥，生成自己的公钥和私钥

乙方根据甲方发来的公钥，生成自己的公钥和私钥

2.3 乙方将自己的公钥发送给甲方

乙方将自己的公钥发送给甲方

2.4 甲方和乙方，生成一样的秘钥。用于加密数据

甲方和乙方，生成一样的秘钥。用于加密数据

3、DH算法的数学原理

DH算法的数学原理

4、 JDK实现

JDK实现

5、DH算法的实现

import javax.crypto.*;
import javax.crypto.interfaces.DHPrivateKey;
import javax.crypto.interfaces.DHPublicKey;
import javax.crypto.spec.DHParameterSpec;
import java.security.*;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.HashMap;
import java.util.Map;

public class DHUtil {
    /**
     * 定义加密方式
     */
    private static final String KEY_DH = "DH";
    public static final String PUBLIC_KEY = "DHPublicKey";
    public static final String PRIVATE_KEY = "DHPrivateKey";
    // 开始生成本地密钥SecretKey 密钥算法为对称密码算法
    // 可以为 DES DES AES
    public static final String KEY_DH_DES = "DES";

    /**
     * 甲方初始化并返回密钥对
     *
     * @return
     */
    public static Map<String, Object> initKey() {
        try {
            // 实例化密钥对生成器
            KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance(KEY_DH);
            // 初始化密钥对生成器 默认是1024 512-1024 & 64的倍数
            keyPairGenerator.initialize(1024);
            // 生成密钥对
            KeyPair keyPair = keyPairGenerator.generateKeyPair();
            // 得到甲方公钥
            DHPublicKey publicKey = (DHPublicKey) keyPair.getPublic();
            // 得到甲方私钥
            DHPrivateKey privateKey = (DHPrivateKey) keyPair.getPrivate();
            // 将公钥和私钥封装在Map中， 方便之后使用
            Map<String, Object> keyMap = new HashMap<String, Object>();
            keyMap.put(PUBLIC_KEY, publicKey);
            keyMap.put(PRIVATE_KEY, privateKey);
            return keyMap;
        } catch (Exception e) {
            throw new RuntimeException(e);
        }

    }

    /**
     * 乙方根据甲方公钥初始化并返回密钥对
     *
     * @param key 甲方的公钥
     * @return
     */
    public static Map<String, Object> initKey(byte[] key) {
        try {
            // 将甲方公钥从字节数组转换为PublicKey
            X509EncodedKeySpec keySpec = new X509EncodedKeySpec(key);
            // 实例化密钥工厂
            KeyFactory keyFactory = KeyFactory.getInstance(KEY_DH);
            // 产生甲方公钥pubKey
            DHPublicKey dhPublicKey = (DHPublicKey) keyFactory.generatePublic(keySpec);
            // 剖析甲方公钥，得到其参数
            DHParameterSpec dhParameterSpec = dhPublicKey.getParams();
            // 实例化密钥对生成器
            KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance(KEY_DH);
            // 用甲方公钥初始化密钥对生成器
            keyPairGenerator.initialize(dhParameterSpec);
            // 产生密钥对
            KeyPair keyPair = keyPairGenerator.generateKeyPair();
            // 得到乙方公钥
            DHPublicKey publicKey = (DHPublicKey) keyPair.getPublic();
            // 得到乙方私钥
            DHPrivateKey privateKey = (DHPrivateKey) keyPair.getPrivate();
            // 将公钥和私钥封装在Map中， 方便之后使用
            Map<String, Object> keyMap = new HashMap<String, Object>();
            keyMap.put(PUBLIC_KEY, publicKey);
            keyMap.put(PRIVATE_KEY, privateKey);
            return keyMap;
        } catch (Exception e) {
            throw new RuntimeException(e);
        }

    }

    /**
     * 根据对方的公钥和自己的私钥生成 本地密钥,返回的是SecretKey对象的字节数组
     *
     * @param publicKey  公钥
     * @param privateKey 私钥
     * @return
     */
    public static byte[] getSecretKeyBytes(byte[] publicKey, byte[] privateKey) {
        try {
            // 实例化密钥工厂
            KeyFactory keyFactory = KeyFactory.getInstance(KEY_DH);
            // 将公钥从字节数组转换为PublicKey
            X509EncodedKeySpec pubKeySpec = new X509EncodedKeySpec(publicKey);
            PublicKey pubKey = keyFactory.generatePublic(pubKeySpec);
            // 将私钥从字节数组转换为PrivateKey
            PKCS8EncodedKeySpec priKeySpec = new PKCS8EncodedKeySpec(privateKey);
            PrivateKey priKey = keyFactory.generatePrivate(priKeySpec);

            // 准备根据以上公钥和私钥生成本地密钥SecretKey
            // 先实例化KeyAgreement
            KeyAgreement keyAgreement = KeyAgreement.getInstance(KEY_DH);
            // 用自己的私钥初始化keyAgreement
            keyAgreement.init(priKey);
            // 结合对方的公钥进行运算
            keyAgreement.doPhase(pubKey, true);
            // 开始生成本地密钥SecretKey 密钥算法为对称密码算法
            SecretKey secretKey = keyAgreement.generateSecret(KEY_DH_DES);
            return secretKey.getEncoded();
        } catch (Exception e) {
            throw new RuntimeException(e);
        }

    }

    /**
     * 根据对方的公钥和自己的私钥生成 本地密钥,返回的是SecretKey对象
     *
     * @param publicKey  公钥
     * @param privateKey 私钥
     * @return
     */
    public static SecretKey getSecretKey(byte[] publicKey, byte[] privateKey) {
        try {
            // 实例化密钥工厂
            KeyFactory keyFactory = KeyFactory.getInstance(KEY_DH);
            // 将公钥从字节数组转换为PublicKey
            X509EncodedKeySpec pubKeySpec = new X509EncodedKeySpec(publicKey);
            PublicKey pubKey = keyFactory.generatePublic(pubKeySpec);
            // 将私钥从字节数组转换为PrivateKey
            PKCS8EncodedKeySpec priKeySpec = new PKCS8EncodedKeySpec(privateKey);
            PrivateKey priKey = keyFactory.generatePrivate(priKeySpec);

            // 准备根据以上公钥和私钥生成本地密钥SecretKey
            // 先实例化KeyAgreement
            KeyAgreement keyAgreement = KeyAgreement.getInstance(KEY_DH);
            // 用自己的私钥初始化keyAgreement
            keyAgreement.init(priKey);
            // 结合对方的公钥进行运算
            keyAgreement.doPhase(pubKey, true);
            // 开始生成本地密钥SecretKey 密钥算法为对称密码算法
            SecretKey secretKey = keyAgreement.generateSecret(KEY_DH_DES);
            return secretKey;
        } catch (Exception e) {
            throw new RuntimeException(e);
        }

    }

    /**
     * 从 Map 中取得公钥
     *
     * @param keyMap
     * @return
     */
    public static byte[] getPublicKey(Map<String, Object> keyMap) {
        DHPublicKey key = (DHPublicKey) keyMap.get(PUBLIC_KEY);
        return key.getEncoded();
    }

    /**
     * 从 Map 中取得私钥
     *
     * @param keyMap
     * @return
     */
    public static byte[] getPrivateKey(Map<String, Object> keyMap) {
        DHPrivateKey key = (DHPrivateKey) keyMap.get(PRIVATE_KEY);
        return key.getEncoded();
    }

    /**
     * DH 加密
     *
     * @param data       带加密数据
     * @param publicKey  甲方公钥
     * @param privateKey 乙方私钥
     * @return
     */
    public static byte[] encryptDH(byte[] data, byte[] publicKey, byte[] privateKey) {
        byte[] bytes = null;
        try {
            //
            SecretKey secretKey = getSecretKey(publicKey, privateKey);
            // 数据加密
            Cipher cipher = Cipher.getInstance(secretKey.getAlgorithm());
            cipher.init(Cipher.ENCRYPT_MODE, secretKey);
            bytes = cipher.doFinal(data);
        } catch (NoSuchAlgorithmException e) {
            e.printStackTrace();
        } catch (NoSuchPaddingException e) {
            e.printStackTrace();
        } catch (InvalidKeyException e) {
            e.printStackTrace();
        } catch (BadPaddingException e) {
            e.printStackTrace();
        } catch (IllegalBlockSizeException e) {
            e.printStackTrace();
        }
        return bytes;
    }

    /**
     * DH 解密
     *
     * @param data       待解密数据
     * @param publicKey  乙方公钥
     * @param privateKey 甲方私钥
     * @return
     */
    public static byte[] decryptDH(byte[] data, byte[] publicKey, byte[] privateKey) {
        byte[] bytes = null;
        try {
            //
            SecretKey secretKey = getSecretKey(publicKey, privateKey);
            // 数据加密
            Cipher cipher = Cipher.getInstance(secretKey.getAlgorithm());
            cipher.init(Cipher.DECRYPT_MODE, secretKey);
            bytes = cipher.doFinal(data);
        } catch (NoSuchAlgorithmException e) {
            e.printStackTrace();
        } catch (NoSuchPaddingException e) {
            e.printStackTrace();
        } catch (InvalidKeyException e) {
            e.printStackTrace();
        } catch (BadPaddingException e) {
            e.printStackTrace();
        } catch (IllegalBlockSizeException e) {
            e.printStackTrace();
        }
        return bytes;
    }

}

测试代码

import org.junit.Test;

import java.util.Map;

public class DHUtilTest {
    // 待加密的明文
    public static final String DATA = "testDH我爱你中国";

    @Test
    public void dhTest() {
        /* Test DH */
        // 甲方公钥
        byte[] publicKey1;
        // 甲方私钥
        byte[] privateKey1;
        // 甲方本地密钥
        byte[] secretKey1;
        // 乙方公钥
        byte[] publicKey2;
        // 乙方私钥
        byte[] privateKey2;
        // 乙方本地密钥
        byte[] secretKey2;

        // 初始化密钥 并生成甲方密钥对
        Map<String, Object> keyMap1 = DHUtil.initKey();
        publicKey1 = DHUtil.getPublicKey(keyMap1);
        privateKey1 = DHUtil.getPrivateKey(keyMap1);
        System.out.println("DH 甲方公钥 : " + fromBytesToHex(publicKey1));
        System.out.println("DH 甲方私钥 : " + fromBytesToHex(privateKey1));

        // 乙方根据甲方公钥产生乙方密钥对
        Map<String, Object> keyMap2 = DHUtil.initKey(publicKey1);
        publicKey2 = DHUtil.getPublicKey(keyMap2);
        privateKey2 = DHUtil.getPrivateKey(keyMap2);
        System.out.println("DH 乙方公钥 : " + fromBytesToHex(publicKey2));
        System.out.println("DH 乙方私钥 : " + fromBytesToHex(privateKey2));

        // 对于甲方， 根据其私钥和乙方发过来的公钥， 生成其本地密钥secretKey1
        secretKey1 = DHUtil.getSecretKeyBytes(publicKey2, privateKey1);
        System.out.println("DH 甲方 本地密钥 : " + fromBytesToHex(secretKey1));

        // 对于乙方， 根据其私钥和甲方发过来的公钥， 生成其本地密钥secretKey2
        secretKey2 = DHUtil.getSecretKeyBytes(publicKey1, privateKey2);
        System.out.println("DH 乙方 本地密钥 : " + fromBytesToHex(secretKey2));
        // ---------------------------
        // 测试数据加密和解密
        System.out.println("加密前的数据" + DATA);

        System.out.println(">>>>>>>>>>>甲向乙发送数据>>>>>>>>>>>");

        //  甲方进行数据的加密,用的是甲方的私钥和乙方的公钥
        byte[] encryptDH = DHUtil.encryptDH(DATA.getBytes(), publicKey2, privateKey1);
        System.out.println("加密后的数据 字节数组转16进制显示:" + fromBytesToHex(encryptDH));
        // 乙方进行数据的解密
        // 用的是乙方的私钥和甲方的公钥
        byte[] decryptDH = DHUtil.decryptDH(encryptDH, publicKey1, privateKey2);
        System.out.println("解密后数据:" + new String(decryptDH));

        System.out.println(">>>>>>>>>>>乙向甲发送数据>>>>>>>>>>>");
        //客户端发送数据
        byte[] clientEncryptDH = DHUtil.encryptDH(DATA.getBytes(), publicKey1, privateKey2);
        System.out.println("加密后的数据 字节数组转16进制显示:" + fromBytesToHex(clientEncryptDH));
        //服务端接收数据
        byte[] serverEncryptDH = DHUtil.decryptDH(clientEncryptDH, publicKey2, privateKey1);
        System.out.println("解密后数据:" + new String(serverEncryptDH));
    }

    private static String fromBytesToHex(byte[] resultBytes) {
        StringBuilder builder = new StringBuilder();
        for (int i = 0; i < resultBytes.length; i++) {
            if (Integer.toHexString(0xFF & resultBytes[i]).length() == 1) {
                builder.append("0").append(Integer.toHexString(0xFF & resultBytes[i]));
            } else {
                builder.append(Integer.toHexString(0xFF & resultBytes[i]));
            }
        }
        return builder.toString();
    }
}

结果验证：

DH 甲方公钥 : 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
DH 甲方私钥 : 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
DH 乙方公钥 : 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
DH 乙方私钥 : 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
DH 甲方 本地密钥 : 9ba867f70eb69464
DH 乙方 本地密钥 : 9ba867f70eb69464
加密前的数据testDH我爱你中国
>>>>>>>>>>>甲向乙发送数据>>>>>>>>>>>
加密后的数据 字节数组转16进制显示:15222436d88b2e36cbeb11aef4d80a7b6312d9d3985b3483
解密后数据:testDH我爱你中国
>>>>>>>>>>>乙向甲发送数据>>>>>>>>>>>
加密后的数据 字节数组转16进制显示:15222436d88b2e36cbeb11aef4d80a7b6312d9d3985b3483
解密后数据:testDH我爱你中国