首先RSA是一个非对称的加密算法，所以在使用该算法加密解密之前，必须先行生成密钥对，包括公钥和私钥

JDK中提供了生成密钥对的类KeyPairGenerator，实例如下：

public static Map<String, Object> genKeyPair() throws Exception {		// 获取公钥私钥密钥对的生成器		KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");		// 初始化确定密钥大小的密钥生成器		kpg.initialize(1024);		// 生成密钥对		KeyPair kp = kpg.generateKeyPair();		RSAPublicKey publicKey = (RSAPublicKey) kp.getPublic();		RSAPrivateKey privateKey = (RSAPrivateKey) kp.getPrivate();		Map<String, Object> keyMap = new HashMap<String, Object>();		keyMap.put(PUBLIC_KEY, publicKey);		keyMap.put(PRIVATE_KEY, privateKey);		return keyMap;	}

当你完成了密钥对的生成之后，你就可以将公钥公开出去了，让相关的加密程序通过该公钥对实施RSA加密

public static byte[] encryptByPublicKey(byte[] data, String publicKey)            throws Exception {        //data即是待加密的数据String.getBytes即可        byte[] keyBytes = Base64Utils.decode(publicKey);        //根据指定的编码密钥创建一个新的X509EncodedKeySpec        X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);        KeyFactory keyFactory = KeyFactory.getInstance(ENCRYPT_ALGORITHM);        //根据提供的密钥规范生成公钥对象        Key publicK = keyFactory.generatePublic(x509KeySpec);        // 对数据加密        Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());        //用密钥初始化加密模式的cipher，所有后面的doFinal方法做的是加密        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) {//一次加密的字节长度                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 = http://www.mamicode.com/out.toByteArray();>
加密完成之后通过自己的私钥对密文进行解密
public static byte[] decryptByPrivateKey(byte[] data, String privateKey)			throws Exception {		byte[] keyBytes = Base64Utils.decode(privateKey);		PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);		KeyFactory keyFactory = KeyFactory.getInstance(ENCRYPT_ALGORITHM);		Key privateK = keyFactory.generatePrivate(pkcs8KeySpec);		Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());		cipher.init(Cipher.DECRYPT_MODE, privateK);		int inputLen = data.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(data, offSet, MAX_DECRYPT_BLOCK);			} else {				cache = cipher.doFinal(data, offSet, inputLen - offSet);			}			out.write(cache, 0, cache.length);			i++;			offSet = i * MAX_DECRYPT_BLOCK;		}		byte[] decryptedData = http://www.mamicode.com/out.toByteArray();>生成密钥对：
try {			Map<String, Object> keyMap = RSAUtils.genKeyPair();			publicKey = RSAUtils.getPublicKey(keyMap);			privateKey = RSAUtils.getPrivateKey(keyMap);			System.out.println("公钥-->" + publicKey);			System.out.println("私钥-->" + privateKey);		} catch (Exception e) {			e.printStackTrace();		}

运行结果展示：
公钥-->MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCjJOdVRlDN/5nWHmpFtc9XffgmT2SAj7b+yBk55HSr1iQQt5k8/4O5qdnk3qxhgIgWuSyDpxR2FK5dzfXsomjc0L2CZGaStAkbbvw1wbOSYo11cxNpkphn3PIVbuBxrpEuCJ4HrMKTuBk662aA0ysxy2/BrK4NXxtRlMxI+/BYsQIDAQAB
私钥-->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
利用公钥加密，私钥解密：
System.out.println("公钥加密——私钥解密");		System.out.println("加密前数据的内容是-->" + sourceStr);		byte[] data = http://www.mamicode.com/sourceStr.getBytes();>
公钥加密——私钥解密
加密前数据的内容是-->这是一段待加密的数据
加密后的数据内容是-->(???%5    [??W??uA- ??m?u?&w?2??gQ???-5?Q???`7:Й?C,?8t?qM?gJ??e2"?)y????????    ?Y??@?y*_?M?????x*;?f1???v??@?h?}P?X?2
解密后的数据内容是-->这是一段待加密的数据