RSA算法 非对称加密算法/数字签名算法

转自 http://security.group.iteye.com/group/wiki/2280-Non-symmetric-encryption-Digital-Signature

接下来我们介绍典型的非对称加密算法/数字签名算法——RSA 

RSA 
    这种算法1978年就出现了，它是第一个既能用于数据加密也能用于数字签名的算法。它易于理解和操作，也很流行。算法的名字以发明者的名字命名：Ron Rivest, AdiShamir 和Leonard Adleman。 
    这种加密算法的特点主要是密钥的变化，上文我们看到DES只有一个密钥。相当于只有一把钥匙，如果这把钥匙丢了，数据也就不安全了。RSA同时有两把钥匙，公钥与私钥。同时支持数字签名。数字签名的意义在于，对传输过来的数据进行校验。确保数据在传输工程中不被修改。 

流程分析： 

1. 甲方构建密钥对儿，将公钥公布给乙方，将私钥保留。
2. 甲方使用私钥加密数据，然后用私钥对加密后的数据签名，发送给乙方签名以及加密后的数据；乙方使用公钥、签名来验证待解密数据是否有效，如果有效使用公钥对数据解密。
3. 乙方使用公钥加密数据，向甲方发送经过加密后的数据；甲方获得加密数据，通过私钥解密。

按如上步骤给出序列图，如下： 

1. 
2. 
3. 

通过java代码实现如下：Coder类见 Java加密技术（一） 

import java.security.Key;
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.Signature;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;

import java.util.HashMap;
import java.util.Map;

import javax.crypto.Cipher;

/**
 * RSA安全编码组件
 *
 * @author 梁栋
 * @version 1.0
 * @since 1.0
 */
public abstract class RSACoder extends Coder {
    public static final String KEY_ALGORITHM = "RSA";
    public static final String SIGNATURE_ALGORITHM = "MD5withRSA";

    private static final String PUBLIC_KEY = "RSAPublicKey";
    private static final String PRIVATE_KEY = "RSAPrivateKey";

    /**
     * 用私钥对信息生成数字签名
     *
     * @param data
     *            加密数据
     * @param privateKey
     *            私钥
     *
     * @return
     * @throws Exception
     */
    public static String sign(byte[] data, String privateKey) throws Exception {
        // 解密由base64编码的私钥
        byte[] keyBytes = decryptBASE64(privateKey);

        // 构造PKCS8EncodedKeySpec对象
        PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);

        // KEY_ALGORITHM 指定的加密算法
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);

        // 取私钥匙对象
        PrivateKey priKey = keyFactory.generatePrivate(pkcs8KeySpec);

        // 用私钥对信息生成数字签名
        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);
        signature.initSign(priKey);
        signature.update(data);

        return encryptBASE64(signature.sign());
    }

    /**
     * 校验数字签名
     *
     * @param data
     *            加密数据
     * @param publicKey
     *            公钥
     * @param sign
     *            数字签名
     *
     * @return 校验成功返回true 失败返回false
     * @throws Exception
     *
     */
    public static boolean verify(byte[] data, String publicKey, String sign)
            throws Exception {

        // 解密由base64编码的公钥
        byte[] keyBytes = decryptBASE64(publicKey);

        // 构造X509EncodedKeySpec对象
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(keyBytes);

        // KEY_ALGORITHM 指定的加密算法
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);

        // 取公钥匙对象
        PublicKey pubKey = keyFactory.generatePublic(keySpec);

        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);
        signature.initVerify(pubKey);
        signature.update(data);

        // 验证签名是否正常
        return signature.verify(decryptBASE64(sign));
    }

    /**
     * 解密<br>
     * 用私钥解密
     *
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static byte[] decryptByPrivateKey(byte[] data, String key)
            throws Exception {
        // 对密钥解密
        byte[] keyBytes = decryptBASE64(key);

        // 取得私钥
        PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
        Key privateKey = keyFactory.generatePrivate(pkcs8KeySpec);

        // 对数据解密
        Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
        cipher.init(Cipher.DECRYPT_MODE, privateKey);

        return cipher.doFinal(data);
    }

    /**
     * 解密<br>
     * 用私钥解密
     *
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static byte[] decryptByPublicKey(byte[] data, String key)
            throws Exception {
        // 对密钥解密
        byte[] keyBytes = decryptBASE64(key);

        // 取得公钥
        X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
        Key publicKey = keyFactory.generatePublic(x509KeySpec);

        // 对数据解密
        Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
        cipher.init(Cipher.DECRYPT_MODE, publicKey);

        return cipher.doFinal(data);
    }

    /**
     * 加密<br>
     * 用公钥加密
     *
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static byte[] encryptByPublicKey(byte[] data, String key)
            throws Exception {
        // 对公钥解密
        byte[] keyBytes = decryptBASE64(key);

        // 取得公钥
        X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
        Key publicKey = keyFactory.generatePublic(x509KeySpec);

        // 对数据加密
        Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
        cipher.init(Cipher.ENCRYPT_MODE, publicKey);

        return cipher.doFinal(data);
    }

    /**
     * 加密<br>
     * 用私钥加密
     *
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static byte[] encryptByPrivateKey(byte[] data, String key)
            throws Exception {
        // 对密钥解密
        byte[] keyBytes = decryptBASE64(key);

        // 取得私钥
        PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);
        KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
        Key privateKey = keyFactory.generatePrivate(pkcs8KeySpec);

        // 对数据加密
        Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
        cipher.init(Cipher.ENCRYPT_MODE, privateKey);

        return cipher.doFinal(data);
    }

    /**
     * 取得私钥
     *
     * @param keyMap
     * @return
     * @throws Exception
     */
    public static String getPrivateKey(Map<String, Object> keyMap)
            throws Exception {
        Key key = (Key) keyMap.get(PRIVATE_KEY);

        return encryptBASE64(key.getEncoded());
    }

    /**
     * 取得公钥
     *
     * @param keyMap
     * @return
     * @throws Exception
     */
    public static String getPublicKey(Map<String, Object> keyMap)
            throws Exception {
        Key key = (Key) keyMap.get(PUBLIC_KEY);

        return encryptBASE64(key.getEncoded());
    }

    /**
     * 初始化密钥
     *
     * @return
     * @throws Exception
     */
    public static Map<String, Object> initKey() throws Exception {
        KeyPairGenerator keyPairGen = KeyPairGenerator
                .getInstance(KEY_ALGORITHM);
        keyPairGen.initialize(1024);

        KeyPair keyPair = keyPairGen.generateKeyPair();

        // 公钥
        RSAPublicKey publicKey = (RSAPublicKey) keyPair.getPublic();

        // 私钥
        RSAPrivateKey privateKey = (RSAPrivateKey) keyPair.getPrivate();

        Map<String, Object> keyMap = new HashMap<String, Object>(2);

        keyMap.put(PUBLIC_KEY, publicKey);
        keyMap.put(PRIVATE_KEY, privateKey);
        return keyMap;
    }
}

再给出一个测试类： 

import static org.junit.Assert.*;

import org.junit.Before;
import org.junit.Test;

import java.util.Map;

/**
 *
 * @author 梁栋
 * @version 1.0
 * @since 1.0
 */
public class RSACoderTest {
    private String publicKey;
    private String privateKey;

    @Before
    public void setUp() throws Exception {
        Map<String, Object> keyMap = RSACoder.initKey();

        publicKey = RSACoder.getPublicKey(keyMap);
        privateKey = RSACoder.getPrivateKey(keyMap);
        System.err.println("公钥: \n\r" + publicKey);
        System.err.println("私钥： \n\r" + privateKey);
    }

    @Test
    public void test() throws Exception {
        System.err.println("公钥加密——私钥解密");
        String inputStr = "abc";
        byte[] data = inputStr.getBytes();

        byte[] encodedData = RSACoder.encryptByPublicKey(data, publicKey);

        byte[] decodedData = RSACoder.decryptByPrivateKey(encodedData,
                privateKey);

        String outputStr = new String(decodedData);
        System.err.println("加密前: " + inputStr + "\n\r" + "解密后: " + outputStr);
        assertEquals(inputStr, outputStr);

    }

    @Test
    public void testSign() throws Exception {
        System.err.println("私钥加密——公钥解密");
        String inputStr = "sign";
        byte[] data = inputStr.getBytes();

        byte[] encodedData = RSACoder.encryptByPrivateKey(data, privateKey);

        byte[] decodedData = RSACoder
                .decryptByPublicKey(encodedData, publicKey);

        String outputStr = new String(decodedData);
        System.err.println("加密前: " + inputStr + "\n\r" + "解密后: " + outputStr);
        assertEquals(inputStr, outputStr);

        System.err.println("私钥签名——公钥验证签名");
        // 产生签名
        String sign = RSACoder.sign(encodedData, privateKey);
        System.err.println("签名:\r" + sign);

        // 验证签名
        boolean status = RSACoder.verify(encodedData, publicKey, sign);
        System.err.println("状态:\r" + status);
        assertTrue(status);

    }

}

控制台输出： 

公钥:

MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCYU/+I0+z1aBl5X6DUUOHQ7FZpmBSDbKTtx89J
EcB64jFCkunELT8qiKly7fzEqD03g8ALlu5XvX+bBqHFy7YPJJP0ekE2X3wjUnh2NxlqpH3/B/xm
1ZdSlCwDIkbijhBVDjA/bu5BObhZqQmDwIxlQInL9oVz+o6FbAZCyHBd7wIDAQAB

私钥：
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公钥加密——私钥解密
加密前: abc

解密后: abc
公钥:

MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDdOj40yEB48XqWxmPILmJAc7UecIN7F32etSHF
9rwbuEh3+iTPOGSxhoSQpOED0vOb0ZIMkBXZSgsxLaBSin2RZ09YKWRjtpCA0kDkiD11gj4tzTiM
l9qq1kwSK7ZkGAgodEn3yIILVmQDuEImHOXFtulvJ71ka07u3LuwUNdB/wIDAQAB

私钥：

MIICdwIBADANBgkqhkiG9w0BAQEFAASCAmEwggJdAgEAAoGBAN06PjTIQHjxepbGY8guYkBztR5w
g3sXfZ61IcX2vBu4SHf6JM84ZLGGhJCk4QPS85vRkgyQFdlKCzEtoFKKfZFnT1gpZGO2kIDSQOSI
PXWCPi3NOIyX2qrWTBIrtmQYCCh0SffIggtWZAO4QiYc5cW26W8nvWRrTu7cu7BQ10H/AgMBAAEC
gYEAz2JWBizjI31bqhP4XiP9PuY5F3vqBW4T+L9cFbQiyumKJc58yzTWUAUGKIIn3enXLG7dNqGr
mbJro4JeFIJ3CiVDpXR9+FluIgI4SXm7ioGKF2NOMA9LR5Fu82W+pLfpTN2y2SaLYWEDZyp53BxY
j9gUxaxi1MQs+C1ZgDF2xmECQQDy70bQntbRfysP+ppCtd56YRnES1Tyekw0wryS2tr+ivQJl7JF
gp5rPAOXpgrq36xHDwUspQ0sJ0vj0O7ywxr1AkEA6SAaLhrJJrYucC0jxwAhUYyaPN+aOsWymaRh
9jA/Wc0wp29SbGTh5CcMuGpXm1g0M+FKW3dGiHgS3rVUKim4owJAbnxgapUzAgiiHxxMeDaavnHW
9C2GrtjsO7qtZOTgYI/1uT8itvZW8lJTF+9OW8/qXE76fXl7ai9dFnl5kzMk2QJBALfHz/vCsArt
mkRiwY6zApE4Z6tPl1V33ymSVovvUzHnOdD1SKQdD5t+UV/crb3QVi8ED0t2B0u0ZSPfDT/D7kMC
QDpwdj9k2F5aokLHBHUNJPFDAp7a5QMaT64gv/d48ITJ68Co+v5WzLMpzJBYXK6PAtqIhxbuPEc2
I2k1Afmrwyw=

私钥加密——公钥解密
加密前: sign

解密后: sign
私钥签名——公钥验证签名
签名:
ud1RsIwmSC1pN22I4IXteg1VD2FbiehKUfNxgVSHzvQNIK+d20FCkHCqh9djP3h94iWnIUY0ifU+
mbJkhAl/i5krExOE0hknOnPMcEP+lZV1RbJI2zG2YooSp2XDleqrQk5e/QF2Mx0Zxt8Xsg7ucVpn
i3wwbYWs9wSzIf0UjlM=

状态:
true

    简要总结一下，使用公钥加密、私钥解密，完成了乙方到甲方的一次数据传递，通过私钥加密、公钥解密，同时通过私钥签名、公钥验证签名，完成了一次甲方到乙方的数据传递与验证，两次数据传递完成一整套的数据交互！ 

类似数字签名，数字信封是这样描述的： 

数字信封 
　　数字信封用加密技术来保证只有特定的收信人才能阅读信的内容。 
流程： 
    信息发送方采用对称密钥来加密信息，然后再用接收方的公钥来加密此对称密钥（这部分称为数字信封），再将它和信息一起发送给接收方；接收方先用相应的私钥打开数字信封，得到对称密钥，然后使用对称密钥再解开信息。