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Quickly understand the commonly used asymmetric encryption algorithm, and no longer have to worry about the interviewer's thorough inquiry

2022-06-23 13:17:00 【51CTO】

interviewer ： Tell me about your common encryption algorithms ？

Encryption algorithms are usually divided into two types ： Symmetric encryption algorithm and Asymmetric encryption algorithm . among , Symmetric encryption algorithm uses the same key for encryption and decryption ; Asymmetric encryption algorithm uses different keys for encryption and decryption , It is divided into public key and private key . Besides , There is also a class called Message digest algorithm , It is an irreversible algorithm for summarizing data .

This time we will learn about asymmetric encryption algorithm .

Asymmetric encryption algorithm

Asymmetric encryption algorithm uses two different keys for encryption and decryption , One of the keys that can be made public is called Public key , Another fully secret key is called Private key . Only the same public key and private key pair can be encrypted and decrypted normally .

For the same public and private key pair , If you use the public key to encrypt the data , Only the corresponding private key can be used for decryption ; If you use a private key to encrypt data , Only the corresponding public key can be used for decryption .

The common asymmetric encryption algorithms are ：RSA Algorithm 、DSA.

RSA Algorithm

RSA The algorithm is the most influential public key encryption algorithm at present , It consists of Ron Rivest、Adi Shamir and Leonard Adleman Three big men are 1977 It was put forward together when working at the Massachusetts Institute of technology in ,RSA It's a combination of the three of them .

Quickly understand common asymmetric encryption algorithms , No longer have to worry about the interviewer's thorough inquiry _ encryption algorithm

in addition ,1973 year , A mathematician working at the British government communications headquarters Clifford Cocks An equivalent algorithm is proposed in an internal file , But the algorithm is classified , until 1997 It was only in .

RSA The algorithm utilizes two number theoretic properties ：

p1、p2 For two prime numbers , n=p1 * p2. It is known that p1、p2 seek n Simple , It is known that n seek p1、p2 It is difficult to .
(m^e) mod n=c, It is known that m、e、n seek c Simple , It is known that e、n、c seek m It is difficult to .

Public and private key generation process ： Randomly select two prime numbers p1、p2,n=p1 * p2, And then randomly select one and φ(n) Coprime and less than φ(n) The integer of e, And then calculate e about φ(n) The modulo inverse elements of d, Finally get n and e For public key ,n and d For private key .

The encryption process ：(m^e) mod n = c, among m In plain text ,c For the cipher ,n and e For public key .

The decryption process ：(c^d) mod n = m, among m In plain text ,c For the cipher ,n and d For private key .

We use it Java Write an example ：

import javax.crypto.Cipher;
import java.nio.charset.Charset;
import java.nio.charset.StandardCharsets;
import java.security.GeneralSecurityException;
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.Base64;

public class RsaUtil {

    private static final String RSA = "RSA";
    private static final Charset CHARSET = StandardCharsets.UTF_8;

    /** *  encryption  * * @param input  Plaintext  * @param publicKey  Public key  * @return  Ciphertext  * @throws GeneralSecurityException */
    public static String encrypt(String input, String publicKey) throws GeneralSecurityException {
        Cipher cipher = Cipher.getInstance(RSA);
        PublicKey pubKey = KeyFactory.getInstance(RSA)
                .generatePublic(new X509EncodedKeySpec(Base64.getDecoder().decode(publicKey)));
        cipher.init(Cipher.ENCRYPT_MODE, pubKey);
        byte[] data = cipher.doFinal(input.getBytes(CHARSET));
        return Base64.getEncoder().encodeToString(data);
    }

    /** *  Decrypt  * * @param input  Ciphertext  * @param privateKey  Private key  * @return  Plaintext  * @throws GeneralSecurityException */
    public static String decrypt(String input, String privateKey) throws GeneralSecurityException {
        Cipher cipher = Cipher.getInstance(RSA);
        PrivateKey priKey = KeyFactory.getInstance("RSA")
                .generatePrivate(new PKCS8EncodedKeySpec(Base64.getDecoder().decode(privateKey)));
        cipher.init(Cipher.DECRYPT_MODE, priKey);
        byte[] data = cipher.doFinal(Base64.getDecoder().decode(input));
        return new String(data, CHARSET);
    }

    public static void main(String[] args) throws GeneralSecurityException {
        //  Generate public key ／ Private key pair :
        KeyPairGenerator kpGen = KeyPairGenerator.getInstance(RSA);
        kpGen.initialize(1024);
        KeyPair keyPair = kpGen.generateKeyPair();
        String publicKey = Base64.getEncoder().encodeToString(keyPair.getPublic().getEncoded());
        String privateKey = Base64.getEncoder().encodeToString(keyPair.getPrivate().getEncoded());
        System.out.println(" Public key ：" + publicKey);
        System.out.println(" Private key ：" + privateKey);

        String msg = " I like you , Can you be my girl friend? ？";
        System.out.println(" Before encryption ：" + msg);
        String pwd = RsaUtil.encrypt(msg, publicKey);
        System.out.println(" After encryption ：" + pwd);
        System.out.println(" After decryption ：" + RsaUtil.decrypt(pwd, privateKey));
    }
}

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The operation results are as follows ：

 Public key ：MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDd4brSm8gdJqFi04m3aW8kjVYbd/T4ymyc7l3c2WmwOhVPlZO1eaZJpTvas61rW0HPf267CRIhc52Zp2+e1hoknApvT0gKeRkfSwC5aws/yoT2vZ9J627QbCFkFc8mmfP8LJ5V/rCpmUE12dIW4xVlEYtWPzmNK2iTMzuR99Jq9wIDAQAB
 Private key ：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
 Before encryption ： I like you , Can you be my girl friend? ？
 After encryption ：tRt5hdF0XB8V2wk6BWC2i8UWVQj/jOCRZn3wIfGYqVaYJ9OjC/+VRUI3c5WgpZlKCZd5zrHo3g1LuQ02G934Gcb51cKH4uhWxRY8oxUgs/fibkvc9+w1X7FQarFwAGCs5SddHIL/vYUxHIvQslelyP9l9/EFpgSs0WWSfOfKcUc=
 After decryption ： I like you , Can you be my girl friend? ？

     
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RSA The algorithm solves the problem that the security of symmetric algorithm depends on the same key . however ,RSA The algorithm is computationally quite complex , Poor performance 、 Far less than symmetric encryption algorithm . therefore , In general practice , Asymmetric encryption algorithms are often used to randomly create temporary symmetric keys , Then a large number of... Are transmitted through symmetric encryption 、 Subject data .

DSA

DSA（Digital Signature Algorithm, Digital signature algorithm ） yes Schnorr and ElGamal A variety of signature algorithms , Complexity based on modulo arithmetic and discrete logarithm .

National institute of standards and technology （NIST） On 1991 Proposed in DSA For its DSS（DigitalSignature Standard, Digital signature standard ）, And in 1994 It was regarded as FIPS 186 use .

and RSA The algorithm uses public key encryption and private key decryption in different ways ,DSA Use the private key to encrypt the data to generate a digital signature , Then the decrypted data is compared with the original data using the public key , To verify the digital signature .

Digital signatures provide information authentication （ The recipient can verify the source of the message ）, integrity （ The receiver can verify that the message has not been modified since it was signed ） And non repudiation （ Senders cannot falsely claim that they have not signed the message ）.

We use it Java Write an example ：

import java.nio.charset.Charset;
import java.nio.charset.StandardCharsets;
import java.security.GeneralSecurityException;
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.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.Base64;

public class DsaUtil {

    private static final String DSA = "DSA";
    private static final String SHA1withDSA = "SHA1withDSA";
    private static final Charset CHARSET = StandardCharsets.UTF_8;

    /** *  Signature  * * @param data  data  * @param privateKey  Private key  * @return  Signature  * @throws GeneralSecurityException */
    public static String sign(String data, String privateKey) throws GeneralSecurityException {
        PrivateKey priKey = KeyFactory.getInstance(DSA)
                .generatePrivate(new PKCS8EncodedKeySpec(Base64.getDecoder().decode(privateKey)));
        Signature signature = Signature.getInstance(SHA1withDSA);
        signature.initSign(priKey);
        signature.update(data.getBytes(CHARSET));
        return Base64.getEncoder().encodeToString(signature.sign());
    }

    /** *  verification  * * @param data  data  * @param publicKey  Public key  * @param sign  Signature  * @return  Whether the verification is passed  */
    public static boolean verify(String data, String publicKey, String sign) throws GeneralSecurityException {
        try {
            PublicKey pubKey = KeyFactory.getInstance(DSA)
                    .generatePublic(new X509EncodedKeySpec(Base64.getDecoder().decode(publicKey)));
            Signature signature = Signature.getInstance(SHA1withDSA);
            signature.initVerify(pubKey);
            signature.update(data.getBytes(CHARSET));
            return signature.verify(Base64.getDecoder().decode(sign));
        } catch (Exception e) {
            throw new RuntimeException(e);
        }
    }

    public static void main(String[] args) throws GeneralSecurityException {
        //  Generate public key ／ Private key pair :
        KeyPairGenerator kpGen = KeyPairGenerator.getInstance(DSA);
        kpGen.initialize(1024);
        KeyPair keyPair = kpGen.generateKeyPair();
        String publicKey = Base64.getEncoder().encodeToString(keyPair.getPublic().getEncoded());
        String privateKey = Base64.getEncoder().encodeToString(keyPair.getPrivate().getEncoded());
        System.out.println(" Public key ：" + publicKey);
        System.out.println(" Private key ：" + privateKey);

        String msg = " I like you , Can you be my girl friend? ？";
        System.out.println(" data ：" + msg);
        String sign = DsaUtil.sign(msg, privateKey);
        System.out.println(" Signature ：" + sign);
        System.out.println(" Verify pass ：" + DsaUtil.verify(msg, publicKey, sign));
    }

}

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The operation results are as follows ：

 Public key ：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
 Private key ：MIIBSwIBADCCASwGByqGSM44BAEwggEfAoGBAP1/U4EddRIpUt9KnC7s5Of2EbdSPO9EAMMeP4C2USZpRV1AIlH7WT2NWPq/xfW6MPbLm1Vs14E7gB00b/JmYLdrmVClpJ+f6AR7ECLCT7up1/63xhv4O1fnxqimFQ8E+4P208UewwI1VBNaFpEy9nXzrith1yrv8iIDGZ3RSAHHAhUAl2BQjxUjC8yykrmCouuEC/BYHPUCgYEA9+GghdabPd7LvKtcNrhXuXmUr7v6OuqC+VdMCz0HgmdRWVeOutRZT+ZxBxCBgLRJFnEj6EwoFhO3zwkyjMim4TwWeotUfI0o4KOuHiuzpnWRbqN/C/ohNWLx+2J6ASQ7zKTxvqhRkImog9/hWuWfBpKLZl6Ae1UlZAFMO/7PSSoEFgIUA1HUKjMiSvazMzpKczR6w6DDbeM=
 data ： I like you , Can you be my girl friend? ？
 Signature ：MCwCFHhnd/3yRCIygyD1GPa1K9ZVQ+4rAhR8zAtlrBim9KKEkv+Fxz47opvSuA==
 Verify pass ：true

     
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adopt Java You can see the example of , The private key will not be directly encrypted to the data , Instead, the data is summarized through the information summarization algorithm , Then encrypt the private key of the summary information .

summary

Asymmetric encryption algorithm uses two different keys for encryption and decryption , They are called public key and private key respectively , Only the same public key and private key pair can be encrypted and decrypted normally .

The common asymmetric encryption algorithms are ：RSA Algorithm 、DSA.RSA The algorithm mainly encrypts the data with public key ,DSA Mainly for signature verification of data .

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