RSA算法

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package com.security.rsa;    import java.security.KeyFactory;  import java.security.KeyPair;  import java.security.KeyPairGenerator;  import java.security.PrivateKey;  import java.security.PublicKey;  import java.security.interfaces.RSAPrivateKey;  import java.security.interfaces.RSAPublicKey;  import java.security.spec.PKCS8EncodedKeySpec;  import java.security.spec.X509EncodedKeySpec;    import javax.crypto.Cipher;  public class RSAsecurity {    public static String src="RSA 加密字符串";          public void priENpubDE() {        try {        //1.初始化秘钥       KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA");       //秘钥长度       keyPairGenerator.initialize(512);       //初始化秘钥对       KeyPair keyPair = keyPairGenerator.generateKeyPair();       //公钥       RSAPublicKey rsaPublicKey = (RSAPublicKey) keyPair.getPublic();       //私钥       RSAPrivateKey rsaPrivateKey = (RSAPrivateKey) keyPair.getPrivate();        //2.私钥加密，公钥解密----加密       //生成私钥       PKCS8EncodedKeySpec pkcs8EncodedKeySpec = new PKCS8EncodedKeySpec(rsaPrivateKey.getEncoded());       KeyFactory keyFactory =KeyFactory.getInstance("RSA");       PrivateKey privateKey = keyFactory.generatePrivate(pkcs8EncodedKeySpec);       //Cipher类为加密和解密提供密码功能，通过getinstance实例化对象       Cipher cipher =Cipher.getInstance("RSA");       //初始化加密       cipher.init(Cipher.ENCRYPT_MODE,privateKey);       byte[] result = cipher.doFinal(src.getBytes());       System.out.println("私钥加密，公钥解密----加密:"+Base64.encode(result));                     //3.私钥加密，公钥解密----解密       //生成公钥       X509EncodedKeySpec x509EncodedKeySpec = new X509EncodedKeySpec(rsaPublicKey.getEncoded());       keyFactory=KeyFactory.getInstance("RSA");       PublicKey publicKey= keyFactory.generatePublic(x509EncodedKeySpec);       cipher = Cipher.getInstance("RSA");       //初始化解密       cipher.init(Cipher.DECRYPT_MODE,publicKey);       result = cipher.doFinal(result);       System.out.println("私钥加密，公钥解密----解密:"+new String(result));      } catch (Exception e) {       // TODO Auto-generated catch block       e.printStackTrace();   }                   }                   public void pubENpriDE() {           try {           //1.初始化秘钥          KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA");          //秘钥长度          keyPairGenerator.initialize(512);          //初始化秘钥对          KeyPair keyPair = keyPairGenerator.generateKeyPair();          //公钥          RSAPublicKey rsaPublicKey = (RSAPublicKey) keyPair.getPublic();          //私钥          RSAPrivateKey rsaPrivateKey = (RSAPrivateKey) keyPair.getPrivate();                                         //2.公钥加密，私钥解密----加密         X509EncodedKeySpec x509EncodedKeySpec=new X509EncodedKeySpec(rsaPublicKey.getEncoded());      KeyFactory keyFactory = KeyFactory.getInstance("RSA");      PublicKey publicKey = keyFactory.generatePublic(x509EncodedKeySpec);       //初始化加密      //Cipher类为加密和解密提供密码功能，通过getinstance实例化对象      Cipher cipher =Cipher.getInstance("RSA");      cipher.init(Cipher.ENCRYPT_MODE,publicKey);       //加密字符串      byte[] result = cipher.doFinal(src.getBytes());       System.out.println("公钥加密，私钥解密----加密:"+Base64.encode(result));              //3.公钥加密，私钥解密-----解密     PKCS8EncodedKeySpec pkcs8EncodedKeySpec = new PKCS8EncodedKeySpec(rsaPrivateKey.getEncoded());            keyFactory=KeyFactory.getInstance("RSA");     PrivateKey  privateKey = keyFactory.generatePrivate(pkcs8EncodedKeySpec);       //初始化解密       cipher.init(Cipher.DECRYPT_MODE, privateKey);       //解密字符串       result = cipher.doFinal(result);       System.out.println("公钥加密，私钥解密-----解密:"+new String(result));                } catch (Exception e) {          // TODO Auto-generated catch block          e.printStackTrace();      }                         }  }

RSA 工具类。提供加密，解密，生成密钥对等方法。

RSA加密原理概述：
RSA的安全性依赖于大数的分解，公钥和私钥都是两个大素数（大于100的十进制位）的函数。
据猜测，从一个密钥和密文推断出明文的难度等同于分解两个大素数的积
密钥的产生：
1.选择两个大素数 p,q ,计算 n=p*q;
2.随机选择加密密钥 e ,要求 e 和 (p-1)*(q-1)互质
3.利用 Euclid 算法计算解密密钥 d , 使其满足 e*d = 1(mod(p-1)*(q-1)) (其中 n,d 也要互质)
4:至此得出公钥为 (n,e) 私钥为 (n,d)
RSA速度
由于进行的都是大数计算，使得RSA最快的情况也比DES慢上100倍，无论是软件还是硬件实现。
速度一直是RSA的缺陷。一般来说只用于少量数据加密。

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