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RSA算法原理如下：

1.随机选择两个大质数p和q，p不等于q，计算N=pq； 
2.选择一个大于1小于N的自然数e，e必须与(p-1)(q-1)互素。 
3.用公式计算出d：d×e = 1 (mod (p-1)(q-1)) 。
4.销毁p和q。

最终得到的N和e就是“公钥”，d就是“私钥”，发送方使用N去加密数据，接收方只有使用d才能解开数据内容。

RSAUtils工具类：

package com.example.xiaobai.aes;import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.NoSuchAlgorithmException;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.ArrayList;
import java.util.List;import javax.crypto.Cipher;/*** Created by xiaobai on 2017/12/7/007.*/public class RSAUtils {public static final String RSA = "RSA";// 非对称加密密钥算法public static final String ECB_PKCS1_PADDING = "RSA/ECB/PKCS1Padding";//加密填充方式public static final int DEFAULT_KEY_SIZE = 2048;//秘钥默认长度public static final byte[] DEFAULT_SPLIT = "#PART#".getBytes();    // 当要加密的内容超过bufferSize，则采用partSplit进行分块加密public static final int DEFAULT_BUFFERSIZE = (DEFAULT_KEY_SIZE / 8) - 11;// 当前秘钥支持加密的最大字节数/*** 随机生成RSA密钥对** @param keyLength 密钥长度，范围：512～2048*                  一般1024* @return*/public static KeyPair generateRSAKeyPair(int keyLength) {try {KeyPairGenerator kpg = KeyPairGenerator.getInstance(RSA);kpg.initialize(keyLength);return kpg.genKeyPair();} catch (NoSuchAlgorithmException e) {e.printStackTrace();return null;}}/*** 用公钥对字符串进行加密** @param data 原文*/public static byte[] encryptByPublicKey(byte[] data, byte[] publicKey) throws Exception {// 得到公钥X509EncodedKeySpec keySpec = new X509EncodedKeySpec(publicKey);KeyFactory kf = KeyFactory.getInstance(RSA);PublicKey keyPublic = kf.generatePublic(keySpec);// 加密数据Cipher cp = Cipher.getInstance(ECB_PKCS1_PADDING);cp.init(Cipher.ENCRYPT_MODE, keyPublic);return cp.doFinal(data);}/*** 私钥加密** @param data       待加密数据* @param privateKey 密钥* @return byte[] 加密数据*/public static byte[] encryptByPrivateKey(byte[] data, byte[] privateKey) throws Exception {// 得到私钥PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(privateKey);KeyFactory kf = KeyFactory.getInstance(RSA);PrivateKey keyPrivate = kf.generatePrivate(keySpec);// 数据加密Cipher cipher = Cipher.getInstance(ECB_PKCS1_PADDING);cipher.init(Cipher.ENCRYPT_MODE, keyPrivate);return cipher.doFinal(data);}/*** 公钥解密** @param data      待解密数据* @param publicKey 密钥* @return byte[] 解密数据*/public static byte[] decryptByPublicKey(byte[] data, byte[] publicKey) throws Exception {// 得到公钥X509EncodedKeySpec keySpec = new X509EncodedKeySpec(publicKey);KeyFactory kf = KeyFactory.getInstance(RSA);PublicKey keyPublic = kf.generatePublic(keySpec);// 数据解密Cipher cipher = Cipher.getInstance(ECB_PKCS1_PADDING);cipher.init(Cipher.DECRYPT_MODE, keyPublic);return cipher.doFinal(data);}/*** 使用私钥进行解密*/public static byte[] decryptByPrivateKey(byte[] encrypted, byte[] privateKey) throws Exception {// 得到私钥PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(privateKey);KeyFactory kf = KeyFactory.getInstance(RSA);PrivateKey keyPrivate = kf.generatePrivate(keySpec);// 解密数据Cipher cp = Cipher.getInstance(ECB_PKCS1_PADDING);cp.init(Cipher.DECRYPT_MODE, keyPrivate);byte[] arr = cp.doFinal(encrypted);return arr;}/*** 用公钥对字符串进行分段加密**/public static byte[] encryptByPublicKeyForSpilt(byte[] data, byte[] publicKey) throws Exception {int dataLen = data.length;if (dataLen <= DEFAULT_BUFFERSIZE) {return encryptByPublicKey(data, publicKey);}List<Byte> allBytes = new ArrayList<Byte>(2048);int bufIndex = 0;int subDataLoop = 0;byte[] buf = new byte[DEFAULT_BUFFERSIZE];for (int i = 0; i < dataLen; i++) {buf[bufIndex] = data[i];if (++bufIndex == DEFAULT_BUFFERSIZE || i == dataLen - 1) {subDataLoop++;if (subDataLoop != 1) {for (byte b : DEFAULT_SPLIT) {allBytes.add(b);}}byte[] encryptBytes = encryptByPublicKey(buf, publicKey);for (byte b : encryptBytes) {allBytes.add(b);}bufIndex = 0;if (i == dataLen - 1) {buf = null;} else {buf = new byte[Math.min(DEFAULT_BUFFERSIZE, dataLen - i - 1)];}}}byte[] bytes = new byte[allBytes.size()];{int i = 0;for (Byte b : allBytes) {bytes[i++] = b.byteValue();}}return bytes;}/*** 分段加密** @param data       要加密的原始数据* @param privateKey 秘钥*/public static byte[] encryptByPrivateKeyForSpilt(byte[] data, byte[] privateKey) throws Exception {int dataLen = data.length;if (dataLen <= DEFAULT_BUFFERSIZE) {return encryptByPrivateKey(data, privateKey);}List<Byte> allBytes = new ArrayList<Byte>(2048);int bufIndex = 0;int subDataLoop = 0;byte[] buf = new byte[DEFAULT_BUFFERSIZE];for (int i = 0; i < dataLen; i++) {buf[bufIndex] = data[i];if (++bufIndex == DEFAULT_BUFFERSIZE || i == dataLen - 1) {subDataLoop++;if (subDataLoop != 1) {for (byte b : DEFAULT_SPLIT) {allBytes.add(b);}}byte[] encryptBytes = encryptByPrivateKey(buf, privateKey);for (byte b : encryptBytes) {allBytes.add(b);}bufIndex = 0;if (i == dataLen - 1) {buf = null;} else {buf = new byte[Math.min(DEFAULT_BUFFERSIZE, dataLen - i - 1)];}}}byte[] bytes = new byte[allBytes.size()];{int i = 0;for (Byte b : allBytes) {bytes[i++] = b.byteValue();}}return bytes;}/*** 公钥分段解密** @param encrypted 待解密数据* @param publicKey 密钥*/public static byte[] decryptByPublicKeyForSpilt(byte[] encrypted, byte[] publicKey) throws Exception {int splitLen = DEFAULT_SPLIT.length;if (splitLen <= 0) {return decryptByPublicKey(encrypted, publicKey);}int dataLen = encrypted.length;List<Byte> allBytes = new ArrayList<Byte>(1024);int latestStartIndex = 0;for (int i = 0; i < dataLen; i++) {byte bt = encrypted[i];boolean isMatchSplit = false;if (i == dataLen - 1) {// 到data的最后了byte[] part = new byte[dataLen - latestStartIndex];System.arraycopy(encrypted, latestStartIndex, part, 0, part.length);byte[] decryptPart = decryptByPublicKey(part, publicKey);for (byte b : decryptPart) {allBytes.add(b);}latestStartIndex = i + splitLen;i = latestStartIndex - 1;} else if (bt == DEFAULT_SPLIT[0]) {// 这个是以split[0]开头if (splitLen > 1) {if (i + splitLen < dataLen) {// 没有超出data的范围for (int j = 1; j < splitLen; j++) {if (DEFAULT_SPLIT[j] != encrypted[i + j]) {break;}if (j == splitLen - 1) {// 验证到split的最后一位，都没有break，则表明已经确认是split段isMatchSplit = true;}}}} else {// split只有一位，则已经匹配了isMatchSplit = true;}}if (isMatchSplit) {byte[] part = new byte[i - latestStartIndex];System.arraycopy(encrypted, latestStartIndex, part, 0, part.length);byte[] decryptPart = decryptByPublicKey(part, publicKey);for (byte b : decryptPart) {allBytes.add(b);}latestStartIndex = i + splitLen;i = latestStartIndex - 1;}}byte[] bytes = new byte[allBytes.size()];{int i = 0;for (Byte b : allBytes) {bytes[i++] = b.byteValue();}}return bytes;}/*** 使用私钥分段解密**/public static byte[] decryptByPrivateKeyForSpilt(byte[] encrypted, byte[] privateKey) throws Exception {int splitLen = DEFAULT_SPLIT.length;if (splitLen <= 0) {return decryptByPrivateKey(encrypted, privateKey);}int dataLen = encrypted.length;List<Byte> allBytes = new ArrayList<Byte>(1024);int latestStartIndex = 0;for (int i = 0; i < dataLen; i++) {byte bt = encrypted[i];boolean isMatchSplit = false;if (i == dataLen - 1) {// 到data的最后了byte[] part = new byte[dataLen - latestStartIndex];System.arraycopy(encrypted, latestStartIndex, part, 0, part.length);byte[] decryptPart = decryptByPrivateKey(part, privateKey);for (byte b : decryptPart) {allBytes.add(b);}latestStartIndex = i + splitLen;i = latestStartIndex - 1;} else if (bt == DEFAULT_SPLIT[0]) {// 这个是以split[0]开头if (splitLen > 1) {if (i + splitLen < dataLen) {// 没有超出data的范围for (int j = 1; j < splitLen; j++) {if (DEFAULT_SPLIT[j] != encrypted[i + j]) {break;}if (j == splitLen - 1) {// 验证到split的最后一位，都没有break，则表明已经确认是split段isMatchSplit = true;}}}} else {// split只有一位，则已经匹配了isMatchSplit = true;}}if (isMatchSplit) {byte[] part = new byte[i - latestStartIndex];System.arraycopy(encrypted, latestStartIndex, part, 0, part.length);byte[] decryptPart = decryptByPrivateKey(part, privateKey);for (byte b : decryptPart) {allBytes.add(b);}latestStartIndex = i + splitLen;i = latestStartIndex - 1;}}byte[] bytes = new byte[allBytes.size()];{int i = 0;for (Byte b : allBytes) {bytes[i++] = b.byteValue();}}return bytes;}
}

Base64：

package com.example.xiaobai.aes;/*** Created by xiaobai on 2017/12/7/007.*/import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.OutputStream;public class Base64 {private static final char[] legalChars = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/".toCharArray();public static String encode(byte[] data) {int start = 0;int len = data.length;StringBuffer buf = new StringBuffer(data.length * 3 / 2);int end = len - 3;int i = start;int n = 0;while (i <= end) {int d = ((((int) data[i]) & 0x0ff) << 16)| ((((int) data[i + 1]) & 0x0ff) << 8)| (((int) data[i + 2]) & 0x0ff);buf.append(legalChars[(d >> 18) & 63]);buf.append(legalChars[(d >> 12) & 63]);buf.append(legalChars[(d >> 6) & 63]);buf.append(legalChars[d & 63]);i += 3;if (n++ >= 14) {n = 0;buf.append(" ");}}if (i == start + len - 2) {int d = ((((int) data[i]) & 0x0ff) << 16)| ((((int) data[i + 1]) & 255) << 8);buf.append(legalChars[(d >> 18) & 63]);buf.append(legalChars[(d >> 12) & 63]);buf.append(legalChars[(d >> 6) & 63]);buf.append("=");} else if (i == start + len - 1) {int d = (((int) data[i]) & 0x0ff) << 16;buf.append(legalChars[(d >> 18) & 63]);buf.append(legalChars[(d >> 12) & 63]);buf.append("==");}return buf.toString();}private static int decode(char c) {if (c >= 'A' && c <= 'Z')return ((int) c) - 65;else if (c >= 'a' && c <= 'z')return ((int) c) - 97 + 26;else if (c >= '0' && c <= '9')return ((int) c) - 48 + 26 + 26;elseswitch (c) {case '+':return 62;case '/':return 63;case '=':return 0;default:throw new RuntimeException("unexpected code: " + c);}}/*** Decodes the given Base64 encoded String to a new byte array. The byte* array holding the decoded data is returned.*/public static byte[] decode(String s) {ByteArrayOutputStream bos = new ByteArrayOutputStream();try {decode(s, bos);} catch (IOException e) {throw new RuntimeException();}byte[] decodedBytes = bos.toByteArray();try {bos.close();bos = null;} catch (IOException ex) {System.err.println("Error while decoding BASE64: " + ex.toString());}return decodedBytes;}private static void decode(String s, OutputStream os) throws IOException {int i = 0;int len = s.length();while (true) {while (i < len && s.charAt(i) <= ' ')i++;if (i == len)break;int tri = (decode(s.charAt(i)) << 18)+ (decode(s.charAt(i + 1)) << 12)+ (decode(s.charAt(i + 2)) << 6)+ (decode(s.charAt(i + 3)));os.write((tri >> 16) & 255);if (s.charAt(i + 2) == '=')break;os.write((tri >> 8) & 255);if (s.charAt(i + 3) == '=')break;os.write(tri & 255);i += 4;}}
}

主函数：

package com.example.xiaobai.aes;import android.app.Activity;
import android.os.Bundle;
import android.util.Log;import java.security.KeyPair;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;public class MainActivity extends Activity {@Overrideprotected void onCreate(Bundle savedInstanceState) {super.onCreate(savedInstanceState);setContentView(R.layout.activity_main);String text = "hello RSA!";KeyPair keyPair= RSAUtils.generateRSAKeyPair(RSAUtils.DEFAULT_KEY_SIZE);// 公钥RSAPublicKey publicKey = (RSAPublicKey) keyPair.getPublic();// 私钥RSAPrivateKey privateKey = (RSAPrivateKey) keyPair.getPrivate();//公钥加密byte[] encryptBytes= new byte[0];try {encryptBytes = RSAUtils.encryptByPublicKeyForSpilt(text.getBytes(),publicKey.getEncoded());} catch (Exception e) {e.printStackTrace();}String encryStr=Base64.encode(encryptBytes);Log.e("RSA","加密后的数据："+encryStr);//私钥解密byte[] decryptBytes= new byte[0];try {decryptBytes = RSAUtils.decryptByPrivateKeyForSpilt(Base64.decode(encryStr),privateKey.getEncoded());} catch (Exception e) {e.printStackTrace();}String decryStr=new String(decryptBytes);Log.e("RSA","解密后的数据："+decryStr);//私钥加密try {encryptBytes= RSAUtils.encryptByPrivateKeyForSpilt(text.getBytes(),privateKey.getEncoded());} catch (Exception e) {e.printStackTrace();}encryStr=Base64.encode(encryptBytes);Log.e("RSA","加密后的数据："+encryStr);//公钥解密try {decryptBytes= RSAUtils.decryptByPublicKeyForSpilt(Base64.decode(encryStr),publicKey.getEncoded());} catch (Exception e) {e.printStackTrace();}decryStr=new String(decryptBytes);Log.e("RSA","解密后的数据："+decryStr);}}

打印结果：

12-07 18:59:55.909 7040-7040/? E/RSA: 加密后的数据：WXDat4zGP9ugHju+F5LP7av6SPxFYGfew/Y/k09HTmPOsxAMzr7lbnrWYziR 7Gno6933rmHMxkhV4KR3ykS7qW0i6tqw8GD8kirAGC04R2ndb698olJZEGKr ZNnf08u7P0P5r5wyqDjSkdcPFfwcdtSiMBnbGjP9csgsbTMctN9RA5zCdlQZ He6p9Kg7qoPb0gKJ7fMj92/qVrlD2UnYgsTRXvVoMf8JS2v8NCor4ySphEsI GVYKqNTfkQ+h79AF+QzFUxijhHB/qQ827p6H5Vy3XWKAejRPrYO/1T96yJDk ZF1OOulPt7Va8QyRqb5BfkPOb0++pCa0KHkt41BZug==
12-07 18:59:55.922 7040-7040/? E/RSA: 解密后的数据：hello RSA!
12-07 18:59:55.933 7040-7040/? E/RSA: 加密后的数据：OTGdrYaKyiSJXZ3xscyv1UKNcVU2nsAmkJaG+evdKbkDhx0o003ZwPyLdMAR j85R8aSGZIu0PHZ4uc9TsVFyYbKsBO507cG2x2IEaLvSwpgm7vZy40r6bDn2 XcGpqNZSTdBvv1NjABZ4htV7ZgAPMOPI6FkmkulDFGZ1UL2xTCQy+9yZv1kS dZr09EvwyW3G07HwibirBOfP7+mNeP7ULsiJWW0GFGaG/RxdoxEXFsmQ1aJa vlTUM4i6FEO8oWFxW1VGrjmJBRphurbqsFC7x9KgKnE1wXP4YwzBmXr4igoC /E4b/2yDDCUUd1e15KNFguO1iPPll6gRGe3R4298tw==
12-07 18:59:55.935 7040-7040/? E/RSA: 解密后的数据：hello RSA!

附加：

通过OpenSSl工具生成密钥对

OpenSSl工具下载：OpenSSI下载，使用OpenSSl工具生成密钥对的过程如下：

首先双击打开bin文件夹下的openssl.exe，打开之后是一个命令行窗口：

然后通过如下命令生成私钥：

这条命令是让openssl随机生成了一份私钥，加密长度是1024位， 密钥长度，范围：512～2048。执行完命令后就可在bin文件夹下看到rsa_private_key.pem文件了。

用文本类工具打开可看到里面的内容：

这里面的内容是标准的ASCII字符，中间的一大串字符就是私钥数据了。

然后通过如下命令生成公钥：

打开文件看下里面的内容:

可以看到是跟私钥的文件类似的。

这样密钥就基本生成了，不过这样密钥对的私钥是无法在代码中直接使用的，要想使用它需要借助RSAPrivateKeyStructure这个类，java是不自带的。所以为了方便使用，我们需要对私钥进行PKCS#8编码，命令如下：

这条命令的结果依然是在bin文件夹生成了pkcs8_rsa_private_key.pem文件，打开内容如下：

可以看到中间的私钥内容有所变化了，这样的私钥我们在代码里就方便使用了。

以上的密钥文件使用时需要注意吧头和尾的字符串去掉，我们只取中间的内容。