Java加密与解密笔记非对称加密

Posted 2020-10-11 业精于勤，行成于思

tags:

篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了Java加密与解密笔记非对称加密相关的知识，希望对你有一定的参考价值。

非对称的特点是加密和解密时使用的是不同的钥匙。密钥分为公钥和私钥，用公钥加密的数据只能用私钥进行解密，反之亦然。

另外，密钥还可以用于数字签名。数字签名跟上文说的消息摘要是一个道理，通过一定方法对数据内容进行处理得到一个签名，查看这个签名是否与对方传递的签名一致。

在非对称加密中用密钥来指公钥和私钥。

RSA

RAS是最早的非对称签名，是1977年由罗纳德·李维斯特（Ron Rivest）、阿迪·萨莫尔（Adi Shamir）和伦纳德·阿德曼（Leonard Adleman）一起提出的。1987年7月首次在美国公布，当时他们三人都在麻省理工学院工作实习。RSA就是他们三人姓氏开头字母拼在一起组成的。

对于非对称加密，在Java中可以用KeyPairGenerator工具类来负责生成密钥对：

public class RSAUtil {
    
    public final static String ALGORITHM = "RSA";

    public static KeyPair getKey() throws Exception{
        KeyPairGenerator generator = KeyPairGenerator.getInstance(ALGORITHM);
        return generator.generateKeyPair();
    }
    
    public static void main(String[] args) throws Exception{
        KeyPair keyPair = getKey();
        RSAPrivateKey privateKey = (RSAPrivateKey)keyPair.getPrivate();
        RSAPublicKey  publicKey = (RSAPublicKey)keyPair.getPublic();
        
        String privateKeyStr = Base64.encode(privateKey.getEncoded());
        String publicKeyStr = Base64.encode(publicKey.getEncoded());
        
        System.out.println("私钥：" + privateKeyStr);
        System.out.println("公钥：" + publicKeyStr);
    }
    
}

使用公钥加密：

    public static String encryptByPublicKey(String data,String key)throws Exception{
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        
        Key k = keyFactory.generatePublic(keySpec);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.ENCRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(data.getBytes("UTF-8"));
        
        return Base64Util.encode(bytes);
    }

加密的时候用X509EncodedKeySpec来获取公钥，不要害怕X509，其实没有别的X508或者X609，就这么一个X509。X.509是一种非常通用的证书格式。所有的证书都符合ITU-T X.509国际标准。

和之前的DES类似，使用私钥解密的代码如下：

    public static String decryptByPrivateKey(String data,String key)throws Exception{
        
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        
        Key k = keyFactory.generatePrivate(keySpec);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.DECRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(Base64Util.decode(data));
        
        return new String(bytes,"UTF-8");
    }

还用X509去读私钥就不行了，会报下面这个错误：

Exception in thread "main" java.security.spec.InvalidKeySpecException: Only RSAPrivate(Crt)KeySpec and PKCS8EncodedKeySpec supported for RSA private keys

意思是只能用RSAPrivate(Crt)KeySpec 或者 PKCS8EncodedKeySpec去读私钥，改成下面这样就好了：

    public static String decryptByPrivateKey(String data,String key)throws Exception{
        
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        
        Key k = keyFactory.generatePrivate(keySpec);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.DECRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(Base64Util.decode(data));
        
        return new String(bytes,"UTF-8");
    }

使用私钥加密和公钥解密的方法就不用多说了，只需要在加密和解密时换成另外一个钥匙就行了。

签名和签名验证

/**
     * 使用私钥进行签名
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String sign(String data,String key)throws Exception{
        PrivateKey k = (PrivateKey)getPrivateKey(key);
        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);  
        signature.initSign(k);  
        signature.update(data.getBytes("UTF-8"));  
        return Base64.encode(signature.sign());
    }
    
    /**
     * 使用公钥进行签名验证
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static boolean signVerify(String data,String key,String sign)throws Exception{
        PublicKey k = (PublicKey)getPublicKey(key);
        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);  
        signature.initVerify(k);  
        signature.update(data.getBytes("UTF-8"));
        return signature.verify(Base64.decode(sign));  
    }

JDK中有专门用于签名的工具类Signature，可用的签名算法如下：

完整代码重构如下：

public class RSAUtil {
    
    public final static String ALGORITHM = "RSA";
    public final static String SIGNATURE_ALGORITHM = "MD5withRSA";

    /**
     * 获取公钥密钥对
     * @return
     * @throws Exception
     */
    public static KeyPair getKey() throws Exception{
        KeyPairGenerator generator = KeyPairGenerator.getInstance(ALGORITHM);
        return generator.generateKeyPair();
    }
    
    private static Key getPublicKey(String key)throws Exception{
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        Key k = keyFactory.generatePublic(keySpec);
        return k;
    }
    
    private static Key getPrivateKey(String key)throws Exception{
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        Key k = keyFactory.generatePrivate(keySpec);
        return k;
    }
    
    /**
     * 使用公钥进行加密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String encryptByPublicKey(String data,String key)throws Exception{
        
        Key k = getPublicKey(key);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.ENCRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(data.getBytes("UTF-8"));
        
        return Base64Util.encode(bytes);
    }
    
    /**
     * 使用私钥进行加密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String encryptByPrivateKey(String data,String key)throws Exception{
        
        Key k = getPrivateKey(key);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.ENCRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(data.getBytes("UTF-8"));
        
        return Base64Util.encode(bytes);
    }
    
    /**
     * 使用密钥进行解密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String decryptByPrivateKey(String data,String key)throws Exception{
        Key k = getPrivateKey(key);
        
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.DECRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(Base64Util.decode(data));
        
        return new String(bytes,"UTF-8");
    }
    
    /**
     * 使用公钥进行解密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String decryptByPublicKey(String data,String key)throws Exception{
        Key k = getPublicKey(key);
        Cipher cipher = Cipher.getInstance(ALGORITHM);
        cipher.init(Cipher.DECRYPT_MODE, k);
        
        byte[] bytes = cipher.doFinal(Base64Util.decode(data));
        
        return new String(bytes,"UTF-8");
    }
    
    /**
     * 使用私钥进行签名
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String sign(String data,String key)throws Exception{
        PrivateKey k = (PrivateKey)getPrivateKey(key);
        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);  
        signature.initSign(k);  
        signature.update(data.getBytes("UTF-8"));  
        return Base64.encode(signature.sign());
    }
    
    /**
     * 使用公钥进行签名验证
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static boolean signVerify(String data,String key,String sign)throws Exception{
        PublicKey k = (PublicKey)getPublicKey(key);
        Signature signature = Signature.getInstance(SIGNATURE_ALGORITHM);  
        signature.initVerify(k);  
        signature.update(data.getBytes("UTF-8"));
        return signature.verify(Base64.decode(sign));  
    }
    
    public static void main(String[] args) throws Exception{
        KeyPair keyPair = getKey();
        RSAPrivateKey privateKey = (RSAPrivateKey)keyPair.getPrivate();
        RSAPublicKey  publicKey = (RSAPublicKey)keyPair.getPublic();
        
        String privateKeyStr = Base64.encode(privateKey.getEncoded());
        String publicKeyStr = Base64.encode(publicKey.getEncoded());
        
        System.out.println("私钥：" + privateKeyStr);
        System.out.println("公钥：" + publicKeyStr);
        
        String data = "Hello,RSA,Hello,RSAHello,RSAHello,RSAHello,RSAHello,RSAHello,RSA";
        System.out.println("---------------公钥加密，私钥解密-----------------");
        String encryptedData = encryptByPublicKey(data,publicKeyStr);
        System.out.println("加密后：" + encryptedData);
        
        String decryptedData = decryptByPrivateKey(encryptedData, privateKeyStr);
        System.out.println("解密后：" + decryptedData);
        System.out.println("---------------私钥加密，公钥解密-----------------");
        
        encryptedData = encryptByPrivateKey(data,privateKeyStr);
        System.out.println("加密后：" + encryptedData);
        decryptedData = decryptByPublicKey(encryptedData, publicKeyStr);
        System.out.println("解密后：" + decryptedData);
        
        String sign = sign(data,privateKeyStr);
        System.out.println("签名：" + sign);
        System.out.println("签名验证：" + signVerify(data,publicKeyStr,sign));
        
        
    }
    
}

DH（Diffie-Hellman）

非对称加密的算法比较耗时，所以不能用它来传输大数据。通常情况下会是这样：

因为对称加密算法中没法安全传递密钥，所以用非对称加密算法来传递对称加密的密钥；
等对称加密的秘钥传递成功之后，正式的数据就用对称加密算法来传递了。

DH算法就是为了实现这个目的而产生的。DH能实现甲乙双方的密钥沟通。

假设客户端要发送数据到服务端，在Java中DH加密的完整步骤：

服务端先生成自己的密钥对：

/**
 * 数据处理服务端*/
public class Server {

    private String publicKey;
    private String privateKey;
    private SecretKey key;
    
    public Server(){
        try {
            String[] keyPair = DHUtil.getStringKeyPair();
            publicKey = keyPair[0];
            privateKey = keyPair[1];
        } catch (Exception e) {
            e.printStackTrace();
        }
        
    }
   ...

服务端的私钥自己保持，公布公钥，客户端则需要根据服务端的公钥生成自己的密钥对：

/**
 * 数据传输客户端*/
public class Client {
    
    private String publicKey;
    private String privateKey;private Server server;
    
    public Client(Server server){
        this.server = server;
        String serverPublicKey = server.getPublicKey();//明文获取到公钥
        try{
            String[] keyPair = DHUtil.getStringKeyPair(serverPublicKey);
            publicKey = keyPair[0];
            privateKey = keyPair[1]；
        }catch(Exception e){
            e.printStackTrace();
        }
    }
    ...

客户端在和服务端通信时，使用的加密算法是对称加密。对称加密的密钥是根据服务端的公钥和客户端的私钥生成的。

public class Client {
    
    private String publicKey;
    private String privateKey;
    private SecretKey key;
    
    private Server server;
    
    public Client(Server server){
        this.server = server;
        String serverPublicKey = server.getPublicKey();
        try{
            String[] keyPair = DHUtil.getStringKeyPair(serverPublicKey);
            publicKey = keyPair[0];
            privateKey = keyPair[1];
            key = DHUtil.getAgreementSecretKey(serverPublicKey, privateKey);
        }catch(Exception e){
            e.printStackTrace();
        }
    }
...

好了，现在可以往服务端发送数据了，比如有一个登录操作：

public class Client {
    ...
    public boolean login(String user,String pwd){
        String data = "user=" + user + "&pwd=" + pwd;
        try {
            data = DHUtil.encrypt(data, key);
        } catch (Exception e) {
            e.printStackTrace();
        }
        String response = server.service(data,publicKey);
        System.out.println("Login Response:" + response);
        return response.equals("OK");
    }
}

可见，公钥是通过明文的形式发送给服务端的。服务端对数据进行处理：

/**
 * 数据处理服务端
 * @author huqiao
 */
public class Server {

    ...

    public String service(String data,String clientPublicKey){try {
            key = DHUtil.getAgreementSecretKey(clientPublicKey, privateKey);//根据客户端的publicKey生成本地密钥
            String decryptedData = DHUtil.decrypt(data, key);
            System.out.println("Data decryped:" + decryptedData);
            if(verfiy(decryptedData)){
                return "OK";
            }else{
                return "Error";
                
            }
        } catch (Exception e) {
            e.printStackTrace();
            return e.getMessage();
        }
    }
    ...

服务器拿到客户端的公钥之后生成本地的密钥，然后对数据进行解密。为了简单起见，这里服务器往客户度返回数据时没有做加密。

非常重要的DHUtil.java完整代码：

public class DHUtil {
    
    public final static String ALGORITHM = "DH";
    public final static String SYMMETRIC_SECRET_ALGORITHM = "AES";//对称加密算法名称

    /**
     * 产生密钥对
     * @return
     * @throws Exception
     */
    public static KeyPair getKeyPair()throws Exception{
        KeyPairGenerator generator = KeyPairGenerator.getInstance(ALGORITHM);
        generator.initialize(1024);
        return generator.generateKeyPair();
    }
    
    /**
     * 获取字符串类型的密钥对
     * @return
     * @throws Exception
     */
    public static String[] getStringKeyPair()throws Exception{
        KeyPair keyPair = getKeyPair();
        return keyPairToStringArray(keyPair);
    }
    
    public static String[] getStringKeyPair(String publicKey)throws Exception{
        KeyPair keyPair = getKeyPairByPublicKey(publicKey);
        return keyPairToStringArray(keyPair);
    }
    
    private static String[] keyPairToStringArray(KeyPair keyPair){
        String[] res = new String[2];
        PublicKey pubKey = keyPair.getPublic(); 
        PrivateKey priKey = keyPair.getPrivate();
        
        res[0] = Base64Util.encode(pubKey.getEncoded());
        res[1] = Base64Util.encode(priKey.getEncoded());
        
        return res;
    }
    
    
    /**
     * 由一个公钥产生密钥对
     * @param publicKey
     * @return
     * @throws Exception
     */
    public static KeyPair getKeyPairByPublicKey(String publicKey)throws Exception{
        
        PublicKey pKey = getPublicKey(publicKey);
        
        KeyPairGenerator generator = KeyPairGenerator.getInstance(pKey.getAlgorithm());
        
        DHParameterSpec dhGenParam = ((DHPublicKey) pKey).getParams();
        generator.initialize(dhGenParam);
        
        return generator.generateKeyPair();
    }
    
    private static PublicKey getPublicKey(String key)throws Exception{
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        PublicKey k = keyFactory.generatePublic(keySpec);
        return k;
    }
    
    private static PrivateKey getPrivateKey(String key)throws Exception{
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        PrivateKey k = keyFactory.generatePrivate(keySpec);
        return k;
    }
    
    /**
     * 根据一方公钥和另外一方私钥构建本地密钥
     * @param publicKey
     * @param privateKey
     * @return
     * @throws Exception
     */
    public static SecretKey getAgreementSecretKey(String publicKey,String privateKey)throws Exception{
        PublicKey pubKey = getPublicKey(publicKey);
        PrivateKey priKey = getPrivateKey(privateKey);
        
        return getAgreementSecretKey(pubKey,priKey);
        
    }
    
    public static SecretKey getAgreementSecretKey(PublicKey pubKey,PrivateKey priKey)throws Exception{
        KeyAgreement argeement = KeyAgreement.getInstance(pubKey.getAlgorithm());
        argeement.init(priKey);
        argeement.doPhase(pubKey, true);
        
        SecretKey secretKey = argeement.generateSecret(SYMMETRIC_SECRET_ALGORITHM);
        return secretKey;
    }
    
    /**
     * 加密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String encrypt(String data,SecretKey key)throws Exception{
        Cipher cipher = Cipher.getInstance(key.getAlgorithm());
        cipher.init(Cipher.ENCRYPT_MODE, key);
        byte[] encryptedData = cipher.doFinal(data.getBytes("UTF-8"));
        return Base64Util.encode(encryptedData);
    }
    
    /**
     * 解密
     * @param data
     * @param key
     * @return
     * @throws Exception
     */
    public static String decrypt(String data,SecretKey key)throws Exception{
        byte[] encryptedData = Base64Util.decode(data);
        Cipher cipher = Cipher.getInstance(key.getAlgorithm());
        cipher.init(Cipher.DECRYPT_MODE, key);
        byte[] decryptedData = cipher.doFinal(encryptedData);
        return new String(decryptedData,"UTF-8");
    }
}

不要被它的长度吓到，它做的事情其实很简单，就是生成密钥对和加密解密。生成密钥对，加密和解密在之前都见过，这里最重要的方法是使用来自两方的公钥和私钥生成一个本地密钥：

    /**
     * 根据一方公钥和另外一方私钥构建本地密钥
     * @param publicKey
     * @param privateKey
     * @return
     * @throws Exception
     */
    public static SecretKey getAgreementSecretKey(String publicKey,String privateKey)throws Exception{
        PublicKey pubKey = getPublicKey(publicKey);
        PrivateKey priKey = getPrivateKey(privateKey);
        
        return getAgreementSecretKey(pubKey,priKey);
        
    }
    
    public static SecretKey getAgreementSecretKey(PublicKey pubKey,PrivateKey priKey)throws Exception{
        KeyAgreement argeement = KeyAgreement.getInstance(pubKey.getAlgorithm());
        argeement.init(priKey);
        argeement.doPhase(pubKey, true);
        
        SecretKey secretKey = argeement.generateSecret(SYMMETRIC_SECRET_ALGORITHM);
        return secretKey;
    }

完整客户端和服务端代码如下：

/**
 * 数据传输客户端
 * @author huqiao
 */
public class Client {
    
    private String publicKey;
    private String privateKey;
    private SecretKey key;
    
    private Server server;
    
    public Client(Server server){
        this.server = server;
        String serverPublicKey = server.getPublicKey();
        try{
            String[] keyPair = DHUtil.getStringKeyPair(serverPublicKey);
            publicKey = keyPair[0];
            privateKey = keyPair[1];
            key = DHUtil.getAgreementSecretKey(serverPublicKey, privateKey);
        }catch(Exception e){
            e.printStackTrace();
        }
    }
    
    public boolean login(String user,String pwd){
        String data = "user=" + user + "&pwd=" + pwd;
        try {
            data = DHUtil.encrypt(data, key);
        } catch (Exception e) {
            e.printStackTrace();
        }
        String response = server.service(data,publicKey);
        System.out.println("Login Response:" + response);
        return response.equals("OK");
    }
}

/**
 * 数据处理服务端
 * @author huqiao
 */
public class Server {

    private String publicKey;
    private String privateKey;
    private SecretKey key;
    
    public Server(){
        try {
            String[] keyPair = DHUtil.getStringKeyPair();
            publicKey = keyPair[0];
            privateKey = keyPair[1];
        } catch (Exception e) {
            e.printStackTrace();
        }
        
    }
    
    public String service(String data,String clientPublicKey){
        System.out.println("----------------Data received at Server:----------------\\r\\n"+ data);
        System.out.println("----------------Client PublicKey received at Server:----------------\\r\\n"+clientPublicKey);
        try {
            key = DHUtil.getAgreementSecretKey(clientPublicKey, privateKey);
            String decryptedData = DHUtil.decrypt(data, key);
            System.out.println("Data decryped:" + decryptedData);
            if(verfiy(decryptedData)){
                return "OK";
            }else{
                return "Error";
                
            }
        } catch (Exception e) {
            e.printStackTrace();
            return e.getMessage();
        }
    }
    
    private boolean verfiy(String decryptedData) {
        //解析用户名和密码，进行验证
        return true;
    }

    /**
     * 明文拿到服务端公钥
     * @return
     */
    public String getPublicKey(){
        return publicKey;
    }
}

测试：

public class DHTest {
    
    public static void main(String[] args) {
        Server server = new Server();
        
        Client client = new Client(server);
        boolean loginSuccess = client.login("admin", "123456");
        
        System.out.println("login success:" + loginSuccess);
    }
}

测试结果：

----------------Data received at Server:----------------
pVWbVMP57wkLftZN3bXx1mf4631yTMlxJ+hnMm4Dwmg=
----------------Client PublicKey received at Server:----------------
MIIBpzCCARsGCSqGSIb3DQEDATCCAQwCgYEA/X9TgR11EilS30qcLuzk5/YRt1I870QAwx4/gLZR
JmlFXUAiUftZPY1Y+r/F9bow9subVWzXgTuAHTRv8mZgt2uZUKWkn5/oBHsQIsJPu6nX/rfGG/g7
V+fGqKYVDwT7g/bTxR7DAjVUE1oWkTL2dfOuK2HXKu/yIgMZndFIAccCgYEA9+GghdabPd7LvKtc
NrhXuXmUr7v6OuqC+VdMCz0HgmdRWVeOutRZT+ZxBxCBgLRJFnEj6EwoFhO3zwkyjMim4TwWeotU
fI0o4KOuHiuzpnWRbqN/C/ohNWLx+2J6ASQ7zKTxvqhRkImog9/hWuWfBpKLZl6Ae1UlZAFMO/7P
SSoCAgIAA4GFAAKBgQC+WT4qNq/Yay1WFA89n5IOy+hJa8JQh4R0uyy5Yfo2ckgQ4cjh/u5GPKev
Ua2B3vQVFEifKSn7tfP5bmYMQ5IZLPJ3JrP2m/QAjQ1T7swG/Kbtfc4eTgq+wpnb2LbDoznKGN28
Mcrbf4HkwZ8QK0M26CySSEQCFliWydd6u/vl0A==
Data decryped:user=admin&pwd=123456
Login Response:OK
login success:true

DSA

DSA的全称为数字签名算法（Digital Signature Algorithm），它与RSA的区别在于它只用于签名，并且它的速度比RSA要快。在安全性上两者差不多。

因为在RSA中已经说到过签名以及验证的过程，DSA和它完全类似：

public class DSAUtil {

    static final String ALGORITHM = "DSA";
    
    private static KeyPair getKeyPair()throws Exception{
        KeyPairGenerator generator = KeyPairGenerator.getInstance(ALGORITHM);
        generator.initialize(1024);
        return generator.genKeyPair();
    }
    

    
    /**
     * 用私钥签名
     * @param data
     * @param privateKey
     * @return
     */
    public static String sign(String data,String privateKey)throws Exception{
        PrivateKey priKey = getPrivateKey(privateKey);
        Signature sign = Signature.getInstance(ALGORITHM);
        sign.initSign(priKey);
        sign.update(data.getBytes("UTF-8"));
        byte[] signBytes = sign.sign();
        return Base64Util.encode(signBytes);
    }
    
    /**
     * 用公钥进行签名验证
     * @param data
     * @param publicKey
     * @param signData
     * @return
     * @throws Exception
     */
    public static boolean verify(String data,String publicKey,String signData)throws Exception{
        PublicKey pubKey = getPublicKey(publicKey);
        Signature sign = Signature.getInstance(ALGORITHM);
        sign.initVerify(pubKey);
        sign.update(data.getBytes("UTF-8"));
        return sign.verify(Base64Util.decode(signData));
    }
    
    
    private static PublicKey getPublicKey(String key)throws Exception{
        X509EncodedKeySpec keySpec = new X509EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        PublicKey k = keyFactory.generatePublic(keySpec);
        return k;
    }
    
    private static PrivateKey getPrivateKey(String key)throws Exception{
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(Base64Util.decode(key));
        KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM);
        PrivateKey k = keyFactory.generatePrivate(keySpec);
        return k;
    }
    
    /**
     * 获取字符串类型的密钥对
     * @returnJava对称与非对称加密解密,AES与RSA
 Java加密与解密笔记 对称加密
 java编写非对称加密,解密,公钥加密，私钥解密，RSA，rsa
 Java加密与安全11-非对称加密算法
 非对称加密和对称加密
 C 语言文件操作 ( 文件加密解密 | 加密解密原理 | 对称加密 | 非对称加密 | 散列函数 )

Java加密与解密笔记 非对称加密

RSA

DH（Diffie-Hellman）

DSA

Java加密与解密笔记非对称加密