【算法笔记】RSA_算法简单实践
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这篇文章简单的整理了RSA算法的简单实践。
1.RSA加密算法
我们先看看维基百科的解释
RSA加密算法是一种非对称加密算法，在公开密钥加密和电子商业中被广泛使用。
2.密钥对生成步骤
RSA算法是利用了两个大素数相乘容易，公式分解困难的原理。
因此公开乘积公开作为加密密钥。
2.1 秘钥对生成步骤
- 随机选择两个不想的的质数p和q
- 计算p和q的乘积N
- 计算p-1和q-1的乘积φ(N)
- 随机选个整数e，e与m要互质，且0 < e < φ(N)
- 计算e的模范元素d(使得ed-1是(p-1)*(q-1)的倍数)
- 公钥是(N,e) 私钥是(N,d)
2.2 加解密步骤
- 假设一个明文m (0 <= m < N)
- 对明文m加密成密文c a.c = m ^ e mod N
- 对密文c解密成明文m a.m = c ^ d mod N
3.模拟RSA
import org.junit.Test;
/**
* @author : 李明燮
* @since : 2022/11/1
* create at : 2022/11/1 10:32 PM
*/
public class RsaUtil {
public static void Rsatest() {
int p = 11, q = 3;
int N = 0, F = 0, c = 0, d = 0, e = 0, m = 0;
N = p * q;
F = (p - 1) * (q - 1);
for (int i = 2; i < N; i++) {
if ((F + 1) % i == 0) {
e = i;
break;
}
}
d = (F + 1) / e;
//公钥: (N,e) 私钥：(N,d)
//公钥: (33,3) 私钥：(33,7)
m = 8;
//1.计算c
c = (int) (Math.pow(m, e) % N);
System.out.println("c = " + c);
m = (int) (Math.pow(c, d) % N);
System.out.println("m = " + m);
}
@Test
public void test() {
Rsatest();
}
}
4.java实现RSA加解密
package org.example;
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import org.junit.Test;
import javax.crypto.Cipher;
import java.security.*;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.Base64;
/**
* @author : 李明燮
* @since : 2022/11/1
* create at : 2022/11/1 10:33 PM
*/
public class RsaUtil {
public static void createKeyPairs() {
Security.addProvider(new BouncyCastleProvider());
try {
KeyPairGenerator generator = KeyPairGenerator.getInstance("RSA");
generator.initialize(512, new SecureRandom());
KeyPair pair = generator.generateKeyPair();
PrivateKey privateKey = pair.getPrivate();
PublicKey publicKey = pair.getPublic();
String strPublicKey = new String(Base64.getEncoder().encode(publicKey.getEncoded()));
String strPrivateKey = new String(Base64.getEncoder().encode(privateKey.getEncoded()));
System.out.println(strPublicKey);
System.out.println(strPrivateKey);
} catch (Exception e) {
e.printStackTrace();
}
}
public static String pubKeyEncrytData(String data, PublicKey publicKey) {
try {
Cipher cipher = Cipher.getInstance("RSA");
cipher.init(Cipher.ENCRYPT_MODE, publicKey);
byte[] encData = cipher.doFinal(data.getBytes("utf-8"));
String result = Base64.getEncoder().encodeToString(encData);
return result;
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static String privKeyDecrytData(String data, PrivateKey privateKey) {
try {
Cipher cipher = Cipher.getInstance("RSA");
cipher.init(Cipher.DECRYPT_MODE, privateKey);
byte[] decData = cipher.doFinal(Base64.getDecoder().decode(data));
String result = new String(decData, "utf-8");
return result;
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static String privKeyEncrytData(String data, PrivateKey privateKey) {
try {
Cipher cipher = Cipher.getInstance("RSA");
cipher.init(Cipher.ENCRYPT_MODE, privateKey);
byte[] encData = cipher.doFinal(data.getBytes("utf-8"));
String result = Base64.getEncoder().encodeToString(encData);
return result;
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static String pubKeyDecrytData(String data, PublicKey pubKey) {
try {
Cipher cipher = Cipher.getInstance("RSA");
cipher.init(Cipher.DECRYPT_MODE, pubKey);
byte[] decData = cipher.doFinal(Base64.getDecoder().decode(data));
String result = new String(decData, "utf-8");
return result;
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
@Test
public void testResult() {
//createKeyPairs();
String strPubKey = "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAKgi54xoLp9XLdxKrdTK18kkFThuX0PTeMwu+BpOfY8dUUj+/iF4eaANACvlw1NruUBJad66DjnzHnyMZ6hfZJ0CAwEAAQ==";
String strPriKey = "MIIBVAIBADANBgkqhkiG9w0BAQEFAASCAT4wggE6AgEAAkEAqCLnjGgun1ct3Eqt1MrXySQVOG5fQ9N4zC74Gk59jx1RSP7+IXh5oA0AK+XDU2u5QElp3roOOfMefIxnqF9knQIDAQABAkA7sxkQS7WyMhxAieurENMJwlwei2IcDSxpI4xImvIOLD6RW05NyOdQViNJUCSCIw7hUjL4MjfiXUid8iP9dOlpAiEA/G8kpjGmSuaczv4sRy4RUp7b/hYKIo7PBs94QXvDVPMCIQCqguwPLyzX0pI790ZCaHc8LvVIpDdB7yj8/tT6/NUELwIgHyc4Rqpp82RyhbkojcBJswCX9cuShKFLO3PvS2WSvbECICJbMN86XSm7ZvWoNELrM6MvvwJ8/BlP7A1V92n/CZjHAiEAgVVKXN98r/n/Rto9Z1RiH2Tdb37F/M65H0gBUXWmbpE=";
String data = "做加密测试了~~";
try {
//公钥对象
X509EncodedKeySpec x509EncodedKeySpec = new X509EncodedKeySpec(Base64.getDecoder().decode(strPubKey.getBytes()));
//私钥对象
PKCS8EncodedKeySpec pkcs8EncodedKeySpec = new PKCS8EncodedKeySpec(Base64.getDecoder().decode(strPriKey.getBytes()));
KeyFactory keyFactory = KeyFactory.getInstance("RSA");
PublicKey publicKey = keyFactory.generatePublic(x509EncodedKeySpec);
PrivateKey privateKey = keyFactory.generatePrivate(pkcs8EncodedKeySpec);
//1.公钥加密数据
String encData = pubKeyEncrytData(data, publicKey);
System.out.println("公钥加密：" + encData);
//2.私钥解密
String decData = privKeyDecrytData(encData, privateKey);
System.out.println("私钥解密：" + decData);
//3.私钥加密数据
String encData2 = privKeyEncrytData(data, privateKey);
System.out.println("私钥加密：" + encData2);
//4.公钥解密
String decData2 = pubKeyDecrytData(encData2, publicKey);
System.out.println("公钥解密：" + decData2);
} catch (Exception e) {
e.printStackTrace();
}
}
}
欢迎大家的意见和交流
email: li_mingxie@163.com