前言
RSA是一种非对称加密算法，也是目前最常用的加密算法之一。它由三位发明家（Rivest、Shamir、Adleman）于1977年提出，并以他们的姓氏命名。RSA算法使用了两个密钥：公钥和私钥。公钥可用于对数据进行加密，而私钥则用于解密加密数据。
RSA算法的安全性基于两个大素数的乘积难以分解的数学问题。具体地说，RSA算法的核心是数论中的欧拉函数和模反元素。首先，选择两个不同的大素数p和q，计算它们的乘积n=pq，然后计算欧拉函数φ(n)=(p-1)(q-1)。接下来，选择一个整数e，使得1<e<φ(n)且e与φ(n)互质。公钥是一个对(e, n)，私钥是一个对(d, n)，其中d是e关于φ(n)的模反元素，即(e*d) mod φ(n)=1。
使用RSA算法对数据进行加密和解密的过程如下：
- 加密：将明文数据m使用公钥(e, n)进行加密得到密文数据c，计算公式为c=m^e mod n。
- 解密：将密文数据c使用私钥(d, n)进行解密得到明文数据m，计算公式为m=c^d mod n。
由于RSA算法的安全性依赖于大素数的难分解性问题，因此选择足够大的素数对是至关重要的。此外，RSA算法还可以用于数字签名、密钥交换和身份认证等安全应用。
RSA加密工具类
依赖
<!-- https://mvnrepository.com/artifact/commons-codec/commons-codec --><dependency><groupId>commons-codec</groupId><artifactId>commons-codec</artifactId><version>1.15</version></dependency>
RSAUtil.java
import org.apache.commons.codec.binary.Base64;import javax.crypto.Cipher;
import java.io.ByteArrayOutputStream;
import java.security.*;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;/*** RSA非对称加密*/
public class RSAUtil {/*** 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;/*** 获取密钥对** @return 密钥对*/public static KeyPair getKeyPair() throws Exception {KeyPairGenerator generator = KeyPairGenerator.getInstance("RSA");generator.initialize(1024);return generator.generateKeyPair();}/*** 获取私钥** @param privateKey 私钥字符串* @return*/public static PrivateKey getPrivateKey(String privateKey) throws Exception {KeyFactory keyFactory = KeyFactory.getInstance("RSA");byte[] decodedKey = Base64.decodeBase64(privateKey.getBytes());PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(decodedKey);return keyFactory.generatePrivate(keySpec);}/*** 获取公钥** @param publicKey 公钥字符串* @return*/public static PublicKey getPublicKey(String publicKey) throws Exception {KeyFactory keyFactory = KeyFactory.getInstance("RSA");byte[] decodedKey = Base64.decodeBase64(publicKey.getBytes());X509EncodedKeySpec keySpec = new X509EncodedKeySpec(decodedKey);return keyFactory.generatePublic(keySpec);}/*** RSA加密** @param data 待加密数据* @param publicKey 公钥* @return*/public static String encrypt(String data, PublicKey publicKey) throws Exception {Cipher cipher = Cipher.getInstance("RSA");cipher.init(Cipher.ENCRYPT_MODE, publicKey);int inputLen = data.getBytes().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.getBytes(), offset, MAX_ENCRYPT_BLOCK);} else {cache = cipher.doFinal(data.getBytes(), offset, inputLen - offset);}out.write(cache, 0, cache.length);i++;offset = i * MAX_ENCRYPT_BLOCK;}byte[] encryptedData = out.toByteArray();out.close();// 获取加密内容使用base64进行编码,并以UTF-8为标准转化成字符串// 加密后的字符串return new String(Base64.encodeBase64String(encryptedData));}/*** RSA解密** @param data 待解密数据* @param privateKey 私钥* @return*/public static String decrypt(String data, PrivateKey privateKey) throws Exception {Cipher cipher = Cipher.getInstance("RSA");cipher.init(Cipher.DECRYPT_MODE, privateKey);byte[] dataBytes = Base64.decodeBase64(data);int inputLen = dataBytes.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(dataBytes, offset, MAX_DECRYPT_BLOCK);} else {cache = cipher.doFinal(dataBytes, offset, inputLen - offset);}out.write(cache, 0, cache.length);i++;offset = i * MAX_DECRYPT_BLOCK;}byte[] decryptedData = out.toByteArray();out.close();// 解密后的内容return new String(decryptedData, "UTF-8");}/*** 签名** @param data 待签名数据* @param privateKey 私钥* @return 签名*/public static String sign(String data, PrivateKey privateKey) throws Exception {byte[] keyBytes = privateKey.getEncoded();PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(keyBytes);KeyFactory keyFactory = KeyFactory.getInstance("RSA");PrivateKey key = keyFactory.generatePrivate(keySpec);Signature signature = Signature.getInstance("MD5withRSA");signature.initSign(key);signature.update(data.getBytes());return new String(Base64.encodeBase64(signature.sign()));}/*** 验签** @param srcData 原始字符串* @param publicKey 公钥* @param sign 签名* @return 是否验签通过*/public static boolean verify(String srcData, PublicKey publicKey, String sign) throws Exception {byte[] keyBytes = publicKey.getEncoded();X509EncodedKeySpec keySpec = new X509EncodedKeySpec(keyBytes);KeyFactory keyFactory = KeyFactory.getInstance("RSA");PublicKey key = keyFactory.generatePublic(keySpec);Signature signature = Signature.getInstance("MD5withRSA");signature.initVerify(key);signature.update(srcData.getBytes());return signature.verify(Base64.decodeBase64(sign.getBytes()));}public static void main(String[] args) {try {// 生成密钥对KeyPair keyPair = getKeyPair();String privateKey = new String(Base64.encodeBase64(keyPair.getPrivate().getEncoded()));String publicKey = new String(Base64.encodeBase64(keyPair.getPublic().getEncoded()));System.out.println("私钥:" + privateKey);System.out.println("公钥:" + publicKey);// RSA加密String data = "hello world";String encryptData = encrypt(data, getPublicKey(publicKey));System.out.println("加密后内容:" + encryptData);// RSA解密String decryptData = decrypt(encryptData, getPrivateKey(privateKey));System.out.println("解密后内容:" + decryptData);// RSA签名String sign = sign(data, getPrivateKey(privateKey));// RSA验签boolean result = verify(data, getPublicKey(publicKey), sign);System.out.print("验签结果:" + result);} catch (Exception e) {e.printStackTrace();System.out.print("加解密异常");}}}运行结果
