【1】RSA简介
RSA公钥加密算法是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。
RSA算法是一种非对称密码算法，所谓非对称，就是指该算法需要一对密钥，使用其中一个加密，则需要用另一个才能解密。
非对称算法主要有：RSA、Elgamal、背包算法、Rabin、D-H、ECC（椭圆曲线加密算法）。
使用最广泛的是RSA算法，Elgamal是另一种常用的非对称加密算法。
RSA的算法涉及三个参数，n、e1、e2。其中，n是两个大质数p、q的积，n的二进制表示时所占用的位数，就是所谓的密钥长度。
e1和e2是一对相关的值，e1可以任意取，但要求e1与(p-1)*(q-1)互质；再选择e2，要求(e2×e1)≡1(mod(p-1)×(q-1))；（n，e1),(n，e2)就是密钥对。其中(n，e1)为公钥，(n，e2)为私钥。
RSA加解密的算法完全相同，设A为明文，B为密文，则：A≡B^e2( mod n)；B≡A^e1 (mod n)；（公钥加密体制中，一般用公钥加密，私钥解密）。
e1和e2可以互换使用，即：A≡B^e1 (mod n)；B≡A^e2( mod n);
【2】使用过程
如下图，甲乙之间使用非对称加密的方式传输数据。
① 乙方生成一对密钥（公钥和私钥）并将公钥向其它方公开；
② 得到该公钥的甲方使用该密钥(公钥)对机密信息进行加密后再发送给乙方；
③ 乙方再用自己保存的另一把专用密钥（私钥）对加密后的信息进行解密；
④ 乙方只能用其专用密钥（私钥）解密由对应的公钥加密后的信息；
在传输过程中，即使攻击者截获了传输的密文，并得到了乙的公钥，也无法破解密文，因为只有乙的私钥才能解密密文。
有一种情况是，丙替换掉了甲获取乙的公钥，然后冒充乙给甲发信息，这样就造成了信息泄露。其中一种解决方法是：CA证书。
使用RSA算法做签名示意图如下：
【3】Java实现
RSAUtil如下：
package mon.encrypt;import java.io.ByteArrayOutputStream;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;/*** @author Janus* @version 创建时间：1月25日 下午6:38:10* @ClassName 类名称* @Description 类描述*/public class RSAUtil {/*** <p>* RSA公钥/私钥/签名工具包* </p>* <p>* 罗纳德·李维斯特（Ron [R]ivest）、阿迪·萨莫尔（Adi [S]hamir）和伦纳德·阿德曼（Leonard [A]dleman）* </p>* <p>* 字符串格式的密钥在未在特殊说明情况下都为BASE64编码格式<br/>* 由于非对称加密速度极其缓慢，一般文件不使用它来加密而是使用对称加密，<br/>* 非对称加密算法可以用来对对称加密的密钥加密，这样保证密钥的安全也就保证了数据的安全* </p>*注意：RSA加密明文最大长度117字节，解密要求密文最大长度为128字节，所以在加密和解密的过程中需要分块进行。*//*** 定义加密方式*/private final static String KEY_RSA = "RSA";/*** 定义签名算法*/private final static String KEY_RSA_SIGNATURE = "MD5withRSA";/*** 定义公钥算法*/private final static String KEY_RSA_PUBLICKEY = "RSAPublicKey";/*** 定义私钥算法*/private final static String KEY_RSA_PRIVATEKEY = "RSAPrivateKey";/*** RSA最大加密明文大小*/private static final int MAX_ENCRYPT_BLOCK = 117;/*** RSA最大解密密文大小*/private static final int MAX_DECRYPT_BLOCK = 128;/*** 初始化密钥:生成密钥对(公钥和私钥)* @return*/public static Map<String, Object> init() {Map<String, Object> map = null;try {KeyPairGenerator generator = KeyPairGenerator.getInstance(KEY_RSA);generator.initialize(1024);KeyPair keyPair = generator.generateKeyPair();// 公钥RSAPublicKey publicKey = (RSAPublicKey) keyPair.getPublic();// 私钥RSAPrivateKey privateKey = (RSAPrivateKey) keyPair.getPrivate();// 将密钥封装为mapmap = new HashMap<String,Object>();map.put(KEY_RSA_PUBLICKEY, publicKey);map.put(KEY_RSA_PRIVATEKEY, privateKey);} catch (Exception e) {e.printStackTrace();}return map;}/*** 用私钥对信息生成数字签名* @param data 加密数据* @param privateKey 私钥(BASE64编码)* @return*/public static String sign(byte[] data, String privateKey) {String str = "";try {// 解密由base64编码的私钥byte[] bytes = Base64Util.decode(privateKey);// 构造PKCS8EncodedKeySpec对象PKCS8EncodedKeySpec pkcs = new PKCS8EncodedKeySpec(bytes);// 指定的加密算法KeyFactory factory = KeyFactory.getInstance(KEY_RSA);// 取私钥对象PrivateKey key = factory.generatePrivate(pkcs);// 用私钥对信息生成数字签名Signature signature = Signature.getInstance(KEY_RSA_SIGNATURE);signature.initSign(key);signature.update(data);byte[] sign= signature.sign();//对数字签名进行Base64编码str = Base64Util.encode(sign);} catch (Exception e) {e.printStackTrace();}return str;}/*** 校验数字签名* @param data 加密数据* @param publicKey 公钥(BASE64编码)* @param sign 数字签名* @return 校验成功返回true，失败返回false*/public static boolean verify(byte[] data, String publicKey, String sign) {boolean flag = false;try {// 解密由base64编码的公钥byte[] bytes = Base64Util.decode(publicKey);// 构造X509EncodedKeySpec对象X509EncodedKeySpec keySpec = new X509EncodedKeySpec(bytes);// 指定的加密算法KeyFactory factory = KeyFactory.getInstance(KEY_RSA);// 取公钥对象PublicKey publicK = factory.generatePublic(keySpec);// 用公钥验证数字签名Signature signature = Signature.getInstance(KEY_RSA_SIGNATURE);signature.initVerify(publicK);signature.update(data);flag = signature.verify(Base64Util.decode(sign));} catch (Exception e) {e.printStackTrace();}return flag;}/*** 私钥解密* @param data 已加密数据* @param key 私钥* @return*/public static byte[] decryptByPrivateKey(byte[] data, String privateKey) {byte[] result = null;try {// 对私钥解密byte[] bytes = Base64Util.decode(privateKey);// 取得私钥PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(bytes);KeyFactory factory = KeyFactory.getInstance(KEY_RSA);PrivateKey privateK = factory.generatePrivate(keySpec);// 对数据解密Cipher cipher = Cipher.getInstance(factory.getAlgorithm());cipher.init(Cipher.DECRYPT_MODE, privateK);result = cipher.doFinal(data);} catch (Exception e) {e.printStackTrace();}return result;}/*** 私钥解密* @param data 已加密数据* @param key 私钥* @return*/public static byte[] decryptByPrivateKey2(byte[] encryptedData, String privateKey) {byte[] result = null;try {// 对私钥解密byte[] bytes = Base64Util.decode(privateKey);// 取得私钥PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(bytes);KeyFactory factory = KeyFactory.getInstance(KEY_RSA);PrivateKey privateK = factory.generatePrivate(keySpec);// 对数据解密Cipher cipher = Cipher.getInstance(factory.getAlgorithm());cipher.init(Cipher.DECRYPT_MODE, privateK);int inputLen = encryptedData.length;ByteArrayOutputStream out = new ByteArrayOutputStream();int offSet = 0;byte[] cache;int i = 0;// 对数据分段解密while (inputLen - offSet > 0) {if (inputLen - offSet > MAX_DECRYPT_BLOCK) {cache = cipher.doFinal(encryptedData, offSet, MAX_DECRYPT_BLOCK);} else {cache = cipher.doFinal(encryptedData, offSet, inputLen - offSet);}out.write(cache, 0, cache.length);i++;offSet = i * MAX_DECRYPT_BLOCK;}result = out.toByteArray();out.close();return result;} catch (Exception e) {e.printStackTrace();}return null;}/*** 公钥解密* @param data 加密数据* @param key 公钥(BASE64编码)* @return*/public static byte[] decryptByPublicKey(byte[] data, String key) {byte[] result = null;try {// 对公钥解密byte[] bytes = Base64Util.decode(key);// 取得公钥X509EncodedKeySpec keySpec = new X509EncodedKeySpec(bytes);KeyFactory factory = KeyFactory.getInstance(KEY_RSA);PublicKey publicKey = factory.generatePublic(keySpec);// 对数据解密Cipher cipher = Cipher.getInstance(factory.getAlgorithm());cipher.init(Cipher.DECRYPT_MODE, publicKey);result = cipher.doFinal(data);} catch (Exception e) {e.printStackTrace();}return result;}/*** <p>* 公钥解密* </p>* * @param encryptedData 已加密数据* @param publicKey 公钥(BASE64编码)* @return* @throws Exception*/public static byte[] decryptByPublicKey2(byte[] encryptedData, String publicKey)throws Exception {byte[] keyBytes = Base64Util.decode(publicKey);X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);KeyFactory keyFactory = KeyFactory.getInstance(KEY_RSA);Key publicK = keyFactory.generatePublic(x509KeySpec);Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());cipher.init(Cipher.DECRYPT_MODE, publicK);int inputLen = encryptedData.length;ByteArrayOutputStream out = new ByteArrayOutputStream();int offSet = 0;byte[] cache;int i = 0;// 对数据分段解密while (inputLen - offSet > 0) {if (inputLen - offSet > MAX_DECRYPT_BLOCK) {cache = cipher.doFinal(encryptedData, offSet, MAX_DECRYPT_BLOCK);} else {cache = cipher.doFinal(encryptedData, offSet, inputLen - offSet);}out.write(cache, 0, cache.length);i++;offSet = i * MAX_DECRYPT_BLOCK;}byte[] decryptedData = out.toByteArray();out.close();return decryptedData;}/*** 公钥加密* @param data 待加密数据* @param key 公钥(BASE64编码)* @return*/public static byte[] encryptByPublicKey(byte[] data, String key) {byte[] result = null;try {byte[] bytes = Base64Util.decode(key);// 取得公钥X509EncodedKeySpec keySpec = new X509EncodedKeySpec(bytes);KeyFactory factory = KeyFactory.getInstance(KEY_RSA);PublicKey publicKey = factory.generatePublic(keySpec);// 对数据加密Cipher cipher = Cipher.getInstance(factory.getAlgorithm());cipher.init(Cipher.ENCRYPT_MODE, publicKey);result = cipher.doFinal(data);} catch (Exception e) {e.printStackTrace();}return result;}/*** <p>* 公钥加密* </p>* @param data 源数据* @param publicKey 公钥(BASE64编码)* @throws Exception*/public static byte[] encryptByPublicKey2(byte[] data, String publicKey)throws Exception {byte[] keyBytes = Base64Util.decode(publicKey);X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);KeyFactory keyFactory = KeyFactory.getInstance(KEY_RSA);Key publicK = keyFactory.generatePublic(x509KeySpec);// 对数据加密Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());cipher.init(Cipher.ENCRYPT_MODE, publicK);int inputLen = data.length;ByteArrayOutputStream out = new ByteArrayOutputStream();int offSet = 0;byte[] cache;int i = 0;// 对数据分段加密while (inputLen - offSet > 0) {if (inputLen - offSet > MAX_ENCRYPT_BLOCK) {cache = cipher.doFinal(data, offSet, MAX_ENCRYPT_BLOCK);} else {cache = cipher.doFinal(data, offSet, inputLen - offSet);}out.write(cache, 0, cache.length);i++;offSet = i * MAX_ENCRYPT_BLOCK;}byte[] encryptedData = out.toByteArray();out.close();return encryptedData;}/*** 私钥加密* @param data 待加密数据* @param key 私钥* @return*/public static byte[] encryptByPrivateKey(byte[] data, String key) {byte[] result = null;try {byte[] bytes = Base64Util.decode(key);// 取得私钥PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(bytes);KeyFactory factory = KeyFactory.getInstance(KEY_RSA);PrivateKey privateKey = factory.generatePrivate(keySpec);// 对数据加密Cipher cipher = Cipher.getInstance(factory.getAlgorithm());cipher.init(Cipher.ENCRYPT_MODE, privateKey);result = cipher.doFinal(data);} catch (Exception e) {e.printStackTrace();}return result;}/*** <p>* 私钥加密* </p>* * @param data 源数据* @param privateKey 私钥(BASE64编码)* @return* @throws Exception*/public static byte[] encryptByPrivateKey2(byte[] data, String privateKey)throws Exception {byte[] keyBytes = Base64Util.decode(privateKey);PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);KeyFactory keyFactory = KeyFactory.getInstance(KEY_RSA);Key privateK = keyFactory.generatePrivate(pkcs8KeySpec);Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());cipher.init(Cipher.ENCRYPT_MODE, privateK);int inputLen = data.length;ByteArrayOutputStream out = new ByteArrayOutputStream();int offSet = 0;byte[] cache;int i = 0;// 对数据分段加密while (inputLen - offSet > 0) {if (inputLen - offSet > MAX_ENCRYPT_BLOCK) {cache = cipher.doFinal(data, offSet, MAX_ENCRYPT_BLOCK);} else {cache = cipher.doFinal(data, offSet, inputLen - offSet);}out.write(cache, 0, cache.length);i++;offSet = i * MAX_ENCRYPT_BLOCK;}byte[] encryptedData = out.toByteArray();out.close();return encryptedData;}/*** 获取公钥* @param map* @return*/public static String getPublicKey(Map<String, Object> map) {String str = "";try {Key key = (Key) map.get(KEY_RSA_PUBLICKEY);str = Base64Util.encode(key.getEncoded());} catch (Exception e) {e.printStackTrace();}return str;}/*** 获取私钥* @param map* @return*/public static String getPrivateKey(Map<String, Object> map) {String str = "";try {Key key = (Key) map.get(KEY_RSA_PRIVATEKEY);str = Base64Util.encode(key.getEncoded());} catch (Exception e) {e.printStackTrace();}return str;}}
测试方法如下：
/*** 测试方法* @param args*/public static void main(String[] args) {String privateKey = "";String publicKey = "";// 生成公钥私钥Map<String, Object> map = init();publicKey = getPublicKey(map);privateKey = getPrivateKey(map);System.out.println("公钥: \n\r" + publicKey);System.out.println("私钥： \n\r" + privateKey);System.out.println("公钥加密--------私钥解密");String word = "今天阳光明媚！";byte[] encWord = encryptByPublicKey(word.getBytes(), publicKey);String decWord = new String(decryptByPrivateKey(encWord, privateKey));System.out.println("加密前: " + word + "\n\r" + "解密后: " + decWord);System.out.println("私钥加密--------公钥解密");String english = "Hello, World!";byte[] encEnglish = encryptByPrivateKey(english.getBytes(), privateKey);String decEnglish = new String(decryptByPublicKey(encEnglish, publicKey));System.out.println("加密前: " + english + "\n\r" + "解密后: " + decEnglish);System.out.println("私钥签名——公钥验证签名");// 产生签名String sign = sign(encEnglish, privateKey);System.out.println("签名:\r" + sign);// 验证签名boolean status = verify(encEnglish, publicKey, sign);System.out.println("状态:\r" + status);}
结果输出如下：
公钥: MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCl2IboMytnscgAl/hT0hlGL+/SOPC7vNKst/Hiu0PcZttxjUmY/y5wBWuHb++ZS5Hg7yKZ/fB8DnhZOxKzDkKWxwW3xguNE8/b4QyAhSv6nSKKV+4pa777cragsyImvRx3vTBMtfskhV0lXYJqhuH6CF0RzsFKZKad1Cx0+KYrQQIDAQAB私钥： 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公钥加密--------私钥解密加密前: 今天阳光明媚！解密后: 今天阳光明媚！私钥加密--------公钥解密加密前: Hello, World!解密后: Hello, World!私钥签名——公钥验证签名签名:Id4hZvEUhWJq5fTSZqn/pKNv18V+yqnxtGqRXEyjSoCWsvylUtCwJ7Bo4wwdpSOrue+7I8NnEDNE5YQQXVHadaKdAiThvJ+7rMZBADWf3LSS9LCzTvt3KOoidixx08UfjR70KCM3AlFpB5AvL82gQn9tt9Qa7U72u5XRi6xSNBA=状态:true
【Tips】
需要注意的是，加密的明文不能超过117字节。如，需要加密的明文如下：
String word = "今天阳光明媚！今天阳光明媚！今天阳光明媚！今天阳光明媚！今天阳光明媚！今天阳光明媚！";
测试结果输出如下：
javax.crypto.IllegalBlockSizeException: Data must not be longer than 117 bytesat com.sun.crypto.provider.RSACipher.doFinal(RSACipher.java:344)at com.sun.crypto.provider.RSACipher.engineDoFinal(RSACipher.java:389)at javax.crypto.Cipher.doFinal(Cipher.java:2165)at mon.encrypt.RSAUtil.encryptByPublicKey(RSAUtil.java:299)at mon.encrypt.RSAUtil.main(RSAUtil.java:453)java.lang.IllegalArgumentException: Null input bufferat javax.crypto.Cipher.doFinal(Cipher.java:2161)at mon.encrypt.RSAUtil.decryptByPrivateKey(RSAUtil.java:169)at mon.encrypt.RSAUtil.main(RSAUtil.java:454)Exception in thread "main" java.lang.NullPointerExceptionat java.lang.String.<init>(String.java:566)at mon.encrypt.RSAUtil.main(RSAUtil.java:454)
