RSA加密问题
定义
RSA公开密钥密码体制是一种使用不同的加密密钥与解密密钥，“由已知加密密钥推导出解密密钥在计算上是不可行的”密码体制
原理
RSA公开密钥密码体制的原理是：根据数论，寻求两个大素数比较简单，而将它们的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
算法原理
RSA算法的具体描述如下： （1）任意选取两个不同的大素数p和q计算乘积 （2）任意选取一个大整数e，满足 ，整数e用做加密钥； （3）确定的解密钥d，满足 ，即 是一个任意的整数；所以，若知道e和，则很容易计算出d （4）公开整数n和e，秘密保存d （5）将明文m（m<n是一个整数）加密成密文c，加密算法为
（6）将密文c解密为明文m，解密算法为
然而只根据n和e（注意：不是p和q）要计算出d是不可能的。因此，任何人都可对明文进行加密，但只有授权用户（知道d）才可对密文解密
实例
随机生成或者在线获取秘钥对：http://web.chacuo.net/netrsakeypair
-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCzcZWZ22Wo2J11tbsbGGr8ZY3S
geMEa0MyyML/MQQ9R2bgxVuP6mdDgoy5rtLbEJmASHK1eu+/NyI6QAeZeQW0SxjP
jdvlNAQiPKAbJGoA82gDpcm1h0WDryE/zRlt/jzCR9sGbkQ3oArLaZhtMlUb4zsj
MKnRUnbxb7UpfpJlEQIDAQAB
-----END PUBLIC KEY-----
-----BEGIN PRIVATE KEY-----
MIICdwIBADANBgkqhkiG9w0BAQEFAASCAmEwggJdAgEAAoGBALNxlZnbZajYnXW1
uxsYavxljdKB4wRrQzLIwv8xBD1HZuDFW4/qZ0OCjLmu0tsQmYBIcrV67783IjpA
B5l5BbRLGM9dpDY+pwM7AmdnT9WTMC4PYpYYm8nDKqrljET/11eCk3G4aPaVsZpg
SUhcm5q4xfEwqdFSdvFvtSl+kmURAgMBAAECgYEAlKHklIhR8EVcR3+793mGRIGp
s0+6xpJCGvKH8fCb3lYiNNPEP7SczCJ6heL07FcXjlZ0DTZDF1OHmlAm+0xvF760
MeyXaPUKw8/YwFnbFPoLnHtr6EAhKLsmSaZh/IrJVwXE8WaqWpdIUTwblwIiDNIg
hzrxx1LV5aMsfiVbPHECQQDs5f2Sw5h2a0FGAUBSEYnTF+Lt6t3gpFrsMH/7JHwe
KHBBDViy+9XT7rYFDRcxkSJPT5qBoPGbr5x8WKDtRqHjAkEAwemgC4k7bKa2Cq0h
8JMrX/ZiJimzXtaMpJ2ZdD6cNWRFEdFK5hhBBmlhjZjzBdYqhc7g8ExqDs9dlc5Z
49F/ewJBALWGPlm5exgyc1/bEZhRTBTu1rqMH9xE1E7rkwW0HU9WmT2fpnnvsxek
cOFJ+J3Ioku3qaLu2nP7iqNVnmpylxUCQByn/tvVku+Sj3JydYKM7SsISSbkoLpS
MISfOa9BFWqaf86LRGtOiEV/S0hWowtow+30Ta+VS1MW9/iMfyI4soMCQHpY2Xgt
XXQ2PqcDOwJnZ0/VkzAuD2KWGJvJwyqq5YxE/9dXgpNxuGj2lbGaYElIXJuauMax
Y3opGNCbp1MxUYg=
-----END PRIVATE KEY-----
调用
/**
* 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;
public static final String KEY_ALGORITHM = "RSA";
private static KeyFactory keyFactory = null;
static {
try {
keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
} catch (NoSuchAlgorithmException e) {
e.printStackTrace();
}
}
/**
* 解密方法
* @param dataStr 要解密的数据
* @return 解密后的原数据
* @throws Exception
*/
public static String decrypt(String dataStr,String PrivateKey) throws Exception{
//对私钥解密
Key decodePrivateKey = getPrivateKeyFromBase64KeyEncodeStr(PrivateKey);
//Log.i("机密",""+decodePrivateKey);
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.DECRYPT_MODE, decodePrivateKey);
byte[] encodedData = Base64Utils.decodeFromString(dataStr);
byte[] decodedData = cipher.doFinal(encodedData);
String decodedDataStr = new String(decodedData,"utf-8");
return decodedDataStr;
}
public static Key getPrivateKeyFromBase64KeyEncodeStr(String keyStr) {
byte[] keyBytes = Base64Utils.decodeFromString(keyStr);
// 取得私钥
PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(keyBytes);
Key privateKey=null;
try {
privateKey = keyFactory.generatePrivate(pkcs8KeySpec);
} catch (InvalidKeySpecException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
return privateKey;
}
/**
* 获取base64加密后的字符串的原始公钥
* @param keyStr
* @return
*/
public static Key getPublicKeyFromBase64KeyEncodeStr(String keyStr) {
byte[] keyBytes = Base64Utils.decodeFromString(keyStr);
X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(keyBytes);
Key publicKey = null;
try {
publicKey = keyFactory.generatePublic(x509KeySpec);
} catch (Exception e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
return publicKey;
}
/**
* 公钥加密方法
* @param dataStr 要加密的数据
* @param dataStr 公钥base64字符串
* @return 加密后的base64字符串
* @throws Exception
*/
public static String encryptPublicKey(String dataStr,String publicKey) throws Exception{
//要加密的数据
System.out.println("要加密的数据:"+dataStr);
byte[] data = dataStr.getBytes();
// 对公钥解密
Key decodePublicKey = getPublicKeyFromBase64KeyEncodeStr(publicKey);
// 对数据加密
Cipher cipher = Cipher.getInstance(KEY_ALGORITHM);
cipher.init(Cipher.ENCRYPT_MODE, decodePublicKey);
byte[] encodedData = cipher.doFinal(data);
String encodedDataStr = new String(Base64Utils.encode(encodedData));
System.out.println("公钥加密后的数据:"+encodedDataStr);
return encodedDataStr;
}
/**
* 使用公钥进行分段加密
* @param dataStr 要加密的数据
* @return 公钥base64字符串
* @throws Exception
*/
public static String encryptByPublicKey(String dataStr,String publicKey)
throws Exception {
//要加密的数据
byte[] data = dataStr.getBytes();
// 对公钥解密
Key decodePublicKey = getPublicKeyFromBase64KeyEncodeStr(publicKey);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
// 对数据加密
Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
cipher.init(Cipher.ENCRYPT_MODE, decodePublicKey);
int inputLen = data.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, offSet, MAX_ENCRYPT_BLOCK);
} else {
cache = cipher.doFinal(data, offSet, inputLen - offSet);
}
out.write(cache, 0, cache.length);
i++;
offSet = i * MAX_ENCRYPT_BLOCK;
}
byte[] encryptedData = out.toByteArray();
out.close();
String encodedDataStr = new String(Base64Utils.encode(encryptedData));
return encodedDataStr;
}
/**
* 使用私钥进行分段解密
* @param dataStr 使用base64处理过的密文
* @return 解密后的数据
* @throws Exception
*/
public static String decryptByPrivateKey(String dataStr,String PrivateKey)
throws Exception {
byte[] encryptedData = Base64Utils.decodeFromString(dataStr);
KeyFactory keyFactory = KeyFactory.getInstance(KEY_ALGORITHM);
Key decodePrivateKey = getPrivateKeyFromBase64KeyEncodeStr(PrivateKey);
Cipher cipher = Cipher.getInstance(keyFactory.getAlgorithm());
cipher.init(Cipher.DECRYPT_MODE, decodePrivateKey);
int inputLen = encryptedData.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(encryptedData, offSet, MAX_DECRYPT_BLOCK);
} else {
cache = cipher.doFinal(encryptedData, offSet, inputLen - offSet);
}
out.write(cache, 0, cache.length);
i++;
offSet = i * MAX_DECRYPT_BLOCK;
}
byte[] decryptedData = out.toByteArray();
out.close();
String decodedDataStr = new String(decryptedData,"utf-8");
return decodedDataStr;
}
// RSAUtils.decryptByPrivateKey(d,pr);
// RSAUtils.encryptByPublicKey(d,pu);