[JAVA加解密]RSA算法、ElGamal算法
一、RSA算法：
1、简介：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。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。RSA是目前最有影响力的公钥加密算法，它能够抵抗到目前为止已知的绝大多数密码攻击，已被ISO推荐为公钥数据加密标准。今天只有短的RSA钥匙才可能被强力方式解破。到2008年为止，世界上还没有任何可靠的攻击RSA算法的方式。只要其钥匙的长度足够长，用RSA加密的信息实际上是不能被解破的。但在分布式计算和量子计算机理论日趋成熟的今天，RSA加密安全性受到了挑战。
RSA算法基于一个十分简单的数论事实：将两个大素数相乘十分容易，但是想要对其乘积进行因式分解却极其困难，因此可以将乘积公开作为加密密钥。
RSA也是目前唯一一个基于因式分解难题的算法。
2、算法描述：RSA的算法涉及三个参数，n、e1、e2。
其中，n是两个大质数p、q的积，n的二进制表示时所占用的位数，就是所谓的密钥长度。
e1和e2是一对相关的值，e1可以任意取，但要求e1与(p-1）*(q-1）互质；再选择e2，要求（e2*e1）mod((p-1）*(q-1））=1。
（n，e1）,(n，e2）就是密钥对。其中(n，e1）为公钥，(n，e2）为私钥。[1]
RSA加解密的算法完全相同，设A为明文，B为密文，则：A=B^e2 mod n；B=A^e1 mod n；（公钥加密体制中，一般用公钥加密，私钥解密）
e1和e2可以互换使用，即：
A=B^e1 mod n；B=A^e2 mod n;
3、算法实现：
RSA算法实现较简单，没有什么需要特别注意的地方，以下代码仅进行了私钥加密，公钥解密，可用作数字签名使用；
public abstract class RSACoder {
private static final String KEY_ALGORITHM= "RSA";
private static final int KEY_SIZE=512;
private static final String PUBLIC_KEY = "RSAPublicKey";
private static final String PRIVATE_KEY = "RSAPrivateKey";
public static Map initKey() throws NoSuchAlgorithmException{
KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance(KEY_ALGORITHM);
keyPairGen.initialize(KEY_SIZE);
KeyPair keyPair = keyPairGen.generateKeyPair();
//生成密钥当然要生成最丰富的啦
RSAPublicKey publicKey = (RSAPublicKey)keyPair.getPublic();
RSAPrivateKey privateKey = (RSAPrivateKey)keyPair.getPrivate();
Map keyMap = new HashMap(2);
keyMap.put(PUBLIC_KEY, publicKey);
keyMap.put(PRIVATE_KEY, privateKey);
return keyMap;
}
public static byte[] encryptByPrivateKey(byte[] data,byte[] priKey) throws NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, InvalidKeyException, IllegalBlockSizeException, BadPaddingException{
PKCS8EncodedKeySpec x509EncodedKeySpec = new PKCS8EncodedKeySpec(priKey);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
PrivateKey privateKey = keyFactory.generatePrivate(x509EncodedKeySpec);
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.ENCRYPT_MODE, privateKey);
return cipher.doFinal(data);
}
public static byte[] decryptByPublicKey(byte[] data,byte[] pubKey) throws NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, InvalidKeyException, IllegalBlockSizeException, BadPaddingException{
X509EncodedKeySpec pkcs8EncodedKeySpec = new X509EncodedKeySpec(pubKey);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
PublicKey publicKey = keyFactory.generatePublic(pkcs8EncodedKeySpec);
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.DECRYPT_MODE, publicKey);
return cipher.doFinal(data);
}
public static byte[] getPrivateKey(Map keyMap){
RSAPrivateKey privateKey = (RSAPrivateKey) keyMap.get(PRIVATE_KEY);
return privateKey.getEncoded();
}
public static byte[] getPublicKey(Map keyMap){
RSAPublicKey publicKey = (RSAPublicKey)keyMap.get(PUBLIC_KEY);
return publicKey.getEncoded();
}
} public class RSACoderTest {
private byte[] privateKey;
private byte[] publicKey;
@Before
public void initKey() throws NoSuchAlgorithmException{
Map keyMap = RSACoder.initKey();
publicKey = RSACoder.getPublicKey(keyMap);
privateKey = RSACoder.getPrivateKey(keyMap);
System.err.println("公钥：\n"+Base64.encodeBase64String(publicKey));
System.err.println("私钥：\n"+Base64.encodeBase64String(privateKey));
}
@Test
public void test() throws InvalidKeyException, NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, IllegalBlockSizeException, BadPaddingException{
System.err.println("\n--私钥加密，公钥解密--");
String input1 = "RSA加密算法";
System.err.println("原文：\n"+input1);
byte[] data1 = input1.getBytes();
byte[] encodedata1 = RSACoder.encryptByPrivateKey(data1, privateKey);
System.err.println("加密后：\n"+Base64.encodeBase64String(encodedata1));
byte[] decodedata1 = RSACoder.decryptByPublicKey(encodedata1, publicKey);
System.err.println("解密后：\n"+Base64.encodeBase64String(decodedata1));
String output1 = new String(decodedata1);
System.out.println("结果：\n"+output1);
assertEquals(input1,output1);
}
} 公钥：
MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAIVn3mmbLJ35bRW51IM6voFzBcpIhhts85OlQJDTSdisfaEt9BRHOoTy2ND31oirr2gA/fGEEVWZvFgVyoz/8Y8CAwEAAQ==
私钥：
MIIBVAIBADANBgkqhkiG9w0BAQEFAASCAT4wggE6AgEAAkEAhWfeaZssnfltFbnUgzq+gXMFykiGG2zzk6VAkNNJ2Kx9oS30FEc6hPLY0PfWiKuvaAD98YQRVZm8WBXKjP/xjwIDAQABAkARdQYly6iLA5jCvw6QHZ/QULzxO4xRCnDVYUqRqRSAxeEtUGv7rTdzvmD4e7sNnnmgdzJA4Tw6WFqI32e1UtgBAiEAxn8AWQuJ1LjC/Uvk90bh1J9rvLZAn22SV9z0TS3I45kCIQCsDZfV5Zl7vTT4cwXe+lcC7z6504R8i7aHyaPcRoq3ZwIgCYQxOhOpif9JqecnlQta7FywR53dP0d7iqbXN5QIW5ECIQCmWdo1aHH2ruC5W1UQ21EnuDQYrYcKeHc6YN56ywWx/wIgRzHu0AmIjaG94ihMBWvAywO/xetdY9tSQZpSHFSKLnU=
--私钥加密，公钥解密--
原文：
RSA加密算法
加密后：
BltYXEfVGzfd78ejw70kIQ3eapFzZmb69i4LYdU5gopS4FtDNnshhkMiNTkzO8MVLKyHtsp6XCg+8fZ0GHcSUw==
解密后：
UlNBvNPD3Mvjt6g=
结果：
RSA加密算法
小结：
1、RSA算法公钥远远小于私钥；
2、Cipher.init()中参数第二为Key类型即可，还原Key类型即可；
3、getPrivateKey及getPublicKey都是通过传入Map参数取得结果的；
4、PKCS8EncodedKeySpec是还原私钥的，尽管PKCS是这个The Public-Key Cryptography Standards
二、ElGamal密码体系：
本部分注重一个问题：ElGamal密钥的生成
JAVA7不支持。引入BouncyCastle
下面是教程提供的基于DHParameterSpec算法参数材料创建密钥
public static Map initKey() throws NoSuchAlgorithmException, InvalidParameterSpecException, InvalidAlgorithmParameterException{
Security.addProvider(new BouncyCastleProvider());
AlgorithmParameterGenerator apg =AlgorithmParameterGenerator.getInstance(KEY_ALGORITHM);
apg.init(KEY_SIZE);
AlgorithmParameters params = apg.generateParameters();
DHParameterSpec dhParams = params.getParameterSpec(DHParameterSpec.class);
KeyPairGenerator keyPairGene = KeyPairGenerator.getInstance(KEY_ALGORITHM);
keyPairGene.initialize(dhParams, new SecureRandom());
KeyPair keyPair = keyPairGene.generateKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
Map keyMap = new HashMap(2);
keyMap.put(PUBLIC_KEY, publicKey);
keyMap.put(PRIVATE_KEY, privateKey);
return keyMap;
} 经过试验，按照往常的套路，这样的代码也是可行的：
public static Map initKey() throws NoSuchAlgorithmException, InvalidParameterSpecException, InvalidAlgorithmParameterException{
Security.addProvider(new BouncyCastleProvider());
KeyPairGenerator keyPairGene = KeyPairGenerator.getInstance(KEY_ALGORITHM);
keyPairGene.initialize(KEY_SIZE, new SecureRandom());
KeyPair keyPair = keyPairGene.generateKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
Map keyMap = new HashMap(2);
keyMap.put(PUBLIC_KEY, publicKey);
keyMap.put(PRIVATE_KEY, privateKey);
return keyMap;
} 而两种方法的关键都在于KeyPairGenerator类的init()函数：
Class KeyPairGenerator
- java.lang.Object
-
- java.security.KeyPairGeneratorSpi
-
- java.security.KeyPairGenerator
void |
initialize(AlgorithmParameterSpec params)
Initializes the key pair generator using the specified parameter set and the
SecureRandomimplementation of the highest-priority installed provider as the source of randomness.
|
void |
initialize(AlgorithmParameterSpec params, SecureRandom random)
Initializes the key pair generator with the given parameter set and source of randomness.
|
void |
initialize(int keysize)
Initializes the key pair generator for a certain keysize using a default parameter set and the
SecureRandom implementation of the highest-priority installed provider as the source of randomness.
|
void |
initialize(int keysize, SecureRandom random)
Initializes the key pair generator for a certain keysize with the given source of randomness (and a default parameter set).
|
Interface AlgorithmParameterSpec
-
- All Known Subinterfaces:
- C14NMethodParameterSpec, DigestMethodParameterSpec, SignatureMethodParameterSpec, TransformParameterSpec
- All Known Implementing Classes:
- DHGenParameterSpec, DHParameterSpec, DSAGenParameterSpec, DSAParameterSpec, ECGenParameterSpec, ECParameterSpec, ExcC14NParameterSpec, GCMParameterSpec, HMACParameterSpec, IvParameterSpec, MGF1ParameterSpec, OAEPParameterSpec, PBEParameterSpec, PSSParameterSpec, RC2ParameterSpec, RC5ParameterSpec, RSAKeyGenParameterSpec, XPathFilter2ParameterSpec, XPathFilterParameterSpec, XSLTTransformParameterSpec
public class AlgorithmParameters
extends Object
两者没有半毛钱关系
再需要注意的是ElGamal需要随机数的，详细可参照加密原理，传输密钥对有乙方选择的随机数k
最后，实现代码如下：
public abstract class ElGamalCoder {
public static final String KEY_ALGORITHM="ElGamal";
private static final int KEY_SIZE=256;
private static final String PUBLIC_KEY="ElGamalPublicKey";
private static final String PRIVATE_KEY = "ElGamalPrivateKey";
public static byte[] decryptByPrivateKey(byte[] data,byte[]key) throws NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, InvalidKeyException, IllegalBlockSizeException, BadPaddingException{
Security.addProvider(new BouncyCastleProvider());
PKCS8EncodedKeySpec pkc = new PKCS8EncodedKeySpec(key);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
Key privateKey = keyFactory.generatePrivate(pkc);
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.DECRYPT_MODE, privateKey);
return cipher.doFinal(data);
}
public static byte[] encryptByPublicKey(byte[] data,byte[]key) throws NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, InvalidKeyException, IllegalBlockSizeException, BadPaddingException{
Security.addProvider(new BouncyCastleProvider());
X509EncodedKeySpec x509 = new X509EncodedKeySpec(key);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
Key publicKey = keyFactory.generatePublic(x509);
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.ENCRYPT_MODE, publicKey);
return cipher.doFinal(data);
}
public static Map initKey() throws NoSuchAlgorithmException, InvalidParameterSpecException, InvalidAlgorithmParameterException{
Security.addProvider(new BouncyCastleProvider());
AlgorithmParameterGenerator apg =AlgorithmParameterGenerator.getInstance(KEY_ALGORITHM);
apg.init(KEY_SIZE);
AlgorithmParameters params = apg.generateParameters();
DHParameterSpec dhParams = params.getParameterSpec(DHParameterSpec.class);
KeyPairGenerator keyPairGene = KeyPairGenerator.getInstance(KEY_ALGORITHM);
keyPairGene.initialize(dhParams, new SecureRandom());
// keyPairGene.initialize(KEY_SIZE, new SecureRandom());
KeyPair keyPair = keyPairGene.generateKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
Map keyMap = new HashMap(2);
keyMap.put(PUBLIC_KEY, publicKey);
keyMap.put(PRIVATE_KEY, privateKey);
return keyMap;
}
public static byte[] getPrivateKey(Map keyMap){
Key key = (Key) keyMap.get(PRIVATE_KEY);
return key.getEncoded();
}
public static byte[] getPublicKey(Map keyMap){
Key key = (Key) keyMap.get(PUBLIC_KEY);
return key.getEncoded();
}
} public class ElGamalCoderTest {
private byte[] privateKey;
private byte[] publicKey;
@Before
public void initKey() throws NoSuchAlgorithmException, InvalidParameterSpecException, InvalidAlgorithmParameterException{
Map keyMap = ElGamalCoder.initKey();
publicKey = ElGamalCoder.getPublicKey(keyMap);
privateKey = ElGamalCoder.getPrivateKey(keyMap);
System.err.println("公钥：\n"+Base64.encodeBase64String(publicKey));
System.err.println("私钥：\n"+Base64.encodeBase64String(privateKey));
}
@Test
public void test() throws InvalidKeyException, NoSuchAlgorithmException, InvalidKeySpecException, NoSuchPaddingException, IllegalBlockSizeException, BadPaddingException{
System.err.println("\n--公钥加密，私钥解密--");
String input1 = "ElGamal加密算法";
System.err.println("原文：\n"+input1);
byte[] data1 = input1.getBytes();
byte[] encodedata1 = ElGamalCoder.encryptByPublicKey(data1, publicKey);
System.err.println("加密后：\n"+Base64.encodeBase64String(encodedata1));
byte[] decodedata1 = ElGamalCoder.decryptByPrivateKey(encodedata1, privateKey);
System.err.println("解密后：\n"+Base64.encodeBase64String(decodedata1));
String output1 = new String(decodedata1);
System.err.println("结果：\n"+output1);
assertEquals(input1,output1);
}
}