非对称加密的特点是有两把钥匙，公钥和私钥。公钥加密只能私钥解密；私钥加密只能公钥解密。
在公开密钥密码体制中，加密密钥(即公开密钥)PK是公开信息，而解密密钥(即秘密密钥)SK是需要保密的。加密算法E和解密算法D也都是公开的。虽然解密密钥SK是由公开密钥PK决定的，但却不能根据PK计算出SK。
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年首次公布，当时他们三人都在麻省理工学院工作。RSA就是他们三人姓氏开头字母拼在一起组成的。
这种加密算法的特点主要是密钥的变化。DES只有一个密钥，相当于只有一把钥匙，如果这把钥匙丢了，数据也就不安全了。RSA同时有两把钥匙，公钥与私钥。同时支持数字签名。数字签名的意义在于，对传输过来的数据进行校验，确保数据在传输过程中不被修改。
Java示例
package com.zzj.encryption;
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 javax.crypto.Cipher;
import org.apache.commons.codec.binary.Base64;
public class RSATest {
static final String ALGORITHM_RSA = "RSA";
static final String ALGORITHM_SIGN = "MD5withRSA";
static String publicKey = null;
static String privateKey = null;
public static void main(String[] args) throws Exception {
// 生成公钥和私钥
generatorKeyPair();
String source = "我是程序猿！";
System.out.println("加密前的数据：\r\n" + source);
System.out.println("--------------------------公钥加密，私钥解密------------------------------");
// 公钥加密
String target = encryptionByPublicKey(source);
// 私钥解密
decryptionByPrivateKey(target);
System.out.println("--------------------------私钥加密并且签名，公钥验证签名并且解密------------------------------");
// 私钥加密
target = encryptionByPrivateKey(source);
// 签名
String sign = signByPrivateKey(target);
// 验证签名
verifyByPublicKey(target, sign);
// 公钥解密
decryptionByPublicKey(target);
}
static void generatorKeyPair() throws Exception {
KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance(ALGORITHM_RSA);
keyPairGen.initialize(1024);
KeyPair keyPair = keyPairGen.generateKeyPair();
RSAPublicKey rsaPublicKey = (RSAPublicKey) keyPair.getPublic();
byte[] keyBs = rsaPublicKey.getEncoded();
publicKey = encodeBase64(keyBs);
System.out.println("生成的公钥：\r\n" + publicKey);
RSAPrivateKey rsaPrivateKey = (RSAPrivateKey) keyPair.getPrivate();
keyBs = rsaPrivateKey.getEncoded();
privateKey = encodeBase64(keyBs);
System.out.println("生成的私钥：\r\n" + privateKey);
}
static PublicKey getPublicKey() throws Exception {
X509EncodedKeySpec publicKeySpec = new X509EncodedKeySpec(decodeBase64(publicKey));
KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM_RSA);
return keyFactory.generatePublic(publicKeySpec);
}
static PrivateKey getPrivateKey() throws Exception {
PKCS8EncodedKeySpec privateKeySpec = new PKCS8EncodedKeySpec(decodeBase64(privateKey));
KeyFactory keyFactory = KeyFactory.getInstance(ALGORITHM_RSA);
return keyFactory.generatePrivate(privateKeySpec);
}
static String encryptionByPublicKey(String source) throws Exception{
PublicKey publicKey = getPublicKey();
Cipher cipher = Cipher.getInstance(publicKey.getAlgorithm());
cipher.init(Cipher.ENCRYPT_MODE, publicKey);
cipher.update(source.getBytes("UTF-8"));
String target = encodeBase64(cipher.doFinal());
System.out.println("公钥加密后的数据：\r\n" + target);
return target;
}
static void decryptionByPublicKey(String target) throws Exception{
PublicKey publicKey = getPublicKey();
Cipher cipher = Cipher.getInstance(publicKey.getAlgorithm());
cipher.init(Cipher.DECRYPT_MODE, publicKey);
cipher.update(decodeBase64(target));
String source = new String(cipher.doFinal(), "UTF-8");
System.out.println("公钥解密后的数据：\r\n" + source);
}
static void verifyByPublicKey(String target, String sign) throws Exception{
PublicKey publicKey = getPublicKey();
Signature signature = Signature.getInstance(ALGORITHM_SIGN);
signature.initVerify(publicKey);
signature.update(target.getBytes("UTF-8"));
if (signature.verify(decodeBase64(sign))) {
System.out.println("签名正确！");
} else {
System.out.println("签名错误！");
}
}
static String encryptionByPrivateKey(String source) throws Exception {
PrivateKey privateKey = getPrivateKey();
Cipher cipher = Cipher.getInstance(privateKey.getAlgorithm());
cipher.init(Cipher.ENCRYPT_MODE, privateKey);
cipher.update(source.getBytes("UTF-8"));
String target = encodeBase64(cipher.doFinal());
System.out.println("私钥加密后的数据：\r\n" + target);
return target;
}
static void decryptionByPrivateKey(String target) throws Exception {
PrivateKey privateKey = getPrivateKey();
Cipher cipher = Cipher.getInstance(privateKey.getAlgorithm());
cipher.init(Cipher.DECRYPT_MODE, privateKey);
cipher.update(decodeBase64(target));
String source = new String(cipher.doFinal(), "UTF-8");
System.out.println("私钥解密后的数据：\r\n" + source);
}
static String signByPrivateKey(String target) throws Exception{
PrivateKey privateKey = getPrivateKey();
Signature signature = Signature.getInstance(ALGORITHM_SIGN);
signature.initSign(privateKey);
signature.update(target.getBytes("UTF-8"));
String sign = encodeBase64(signature.sign());
System.out.println("生成的签名：\r\n" + sign);
return sign;
}
static String encodeBase64(byte[] source) throws Exception{
return new String(Base64.encodeBase64(source), "UTF-8");
}
static byte[] decodeBase64(String target) throws Exception{
return Base64.decodeBase64(target.getBytes("UTF-8"));
}
}结果：
生成的公钥：
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCcQiaArjqiJeDPT8RCmkwrKi1Bh4Y16wH49u1jmX3RQdf0B2tRD42bItY1oqZtqj/2xqDdXLSOWOr3aldwr6ucofMPEUm2l4sJnTrM96IVNOl8jIqw2d8m7P/PhyOfTgvtOemm725y4TJm3F0q0c1WfjO55orNUTolAmoOW57SQQIDAQAB
生成的私钥：
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
加密前的数据：
我是程序猿！
--------------------------公钥加密，私钥解密------------------------------
公钥加密后的数据：
TJZlueYjat5gFTWtGXzafN2TNAsG4D6HiSOjX9h/mm/WMtaUWOXVvySD5iHBhQmEL+Hqa6TG8sSm6aVESQFqhKgHuni4GhD/ctC5vCD6aL0K9oLlpo4oV5RZJIQfIfYB28ZJW59fE6E4GYMxyQca/hulK/jaZJFmU5esxvkZaSg=
私钥解密后的数据：
我是程序猿！
--------------------------私钥加密并且签名，公钥验证签名并且解密------------------------------
私钥加密后的数据：
iAu34RZPt0LH4+5EyATXYDIJ5dCcTHpapXjsO2riRiEBdh1lhMNmOmTbAGhBUC7FyneHhQY3nwOWwS99w7e06y95YegRrotvoN3ss6xo8G3/cX1eTdzaXTadOkJR++Npj8SsodAZ675gHcUkTENkRmcBA4wuozUCzCJc7Pg3AMk=
生成的签名：
SzUGGICDv1JOen09qeYSH+UHB2B2XBCI4zPkDo8JVkRr3YVKSj465nmQWNxoXqAZFcUyxjlWVAbEfE+KnrGP56lv01vwL84J2j5v5hhmwShclgbMDUi6OQt+4ACXBn1Er8zF/DJfK6USP2jJPaUL4U1vZUzEOE2AXOChcpYMHDw=
签名正确！
公钥解密后的数据：
我是程序猿！