java - 为给定的模数和指数生成 RSA key

Question

我被要求使用给定的 modulus 和 exponent 值生成 RSA key 。但我只知道如何在不指定模数和指数的情况下生成 key 。无论我给出什么值，似乎都是大整数值。我在网上搜索了这个并解决了一些问题，但它无法成功。

所以如果有人以前这样做过，他们能给我一些提示吗？

这是我们用给定值尝试过的示例程序。

import java.io.UnsupportedEncodingException;
import java.math.BigInteger;
import java.security.KeyFactory;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.spec.RSAKeyGenParameterSpec;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;

public class Sample {
        public static void main( String args[] ) {

                BigInteger modulus  = new BigInteger("350871044328208704010580786055405681");
                BigInteger exponent = new BigInteger("545161406957801571");

                try {                    
                        RSAPublicKeySpec spec = new RSAPublicKeySpec(modulus, exponent);
                        RSAPrivateKeySpec privateSpec = new RSAPrivateKeySpec(modulus, exponent);

                        KeyFactory factory = KeyFactory.getInstance("RSA");

                        PublicKey pub = factory.generatePublic(spec);
                        PrivateKey priv = factory.generatePrivate(privateSpec); 

                        System.out.println("Public Key : "+ byteArrayToHexString( pub.getEncoded() ));
                        System.out.println("Private Key : "+ byteArrayToHexString( priv.getEncoded() ));
                }                        
                catch( Exception e ) {   
                        System.out.println(e.toString());       
                }                        
        }         
        public static String byteArrayToHexString(byte[] bytes)          
        {         
                StringBuffer buffer = new StringBuffer();
                for(int i=0; i<bytes.length; i++)
                {                        
                        if(((int)bytes[i] & 0xff) < 0x10)       
                                buffer.append("0");                               
                        buffer.append(Long.toString((int) bytes[i] & 0xff, 16));
                }                        
                return buffer.toString();
        }         
}

错误:

java.security.spec.InvalidKeySpecException: java.security.InvalidKeyException: RSA keys must be at least 512 bits long

Answer 1

我给你一些关于 RSA 的信息。首先在 RSA key 中 modulus = p·q 其中 p 和 q 是不同的质数，模数长度是 key 长度。因此，当您收到异常时:

java.security.spec.InvalidKeySpecException: java.security.InvalidKeyException: RSA keys must be at least 512 bits long

这意味着您的模数至少必须为 512 位长。

除了您的代码中还有另一个错误，您对公钥和私钥使用了相同的指数，但这些指数必须是不同的数字。

在简历中，您必须按照 RSA key 生成算法使用 java.math.BigInteger 计算模数、公共(public)指数和私有(private)指数，以生成正确的 key 。我从你的代码中给你一个例子:

import java.math.BigInteger;
import java.security.KeyFactory;
import java.security.PrivateKey;
import java.security.PublicKey;
import java.security.SecureRandom;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;

public class Sample {
    public static void main( String args[] ) {

        int keySize = 512;  
        SecureRandom random = new SecureRandom();
        // Choose two distinct prime numbers p and q.
        BigInteger p = BigInteger.probablePrime(keySize/2,random);
        BigInteger q = BigInteger.probablePrime(keySize/2,random);
        // Compute n = pq (modulus)
        BigInteger modulus = p.multiply(q);
        // Compute φ(n) = φ(p)φ(q) = (p − 1)(q − 1) = n - (p + q -1), where φ is Euler's totient function.
        // and choose an integer e such that 1 < e < φ(n) and gcd(e, φ(n)) = 1; i.e., e and φ(n) are coprime.
        BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
        BigInteger publicExponent = getCoprime(m,random);
        // Determine d as d ≡ e−1 (mod φ(n)); i.e., d is the multiplicative inverse of e (modulo φ(n)).
        BigInteger privateExponent = publicExponent.modInverse(m);


        try {                    
            RSAPublicKeySpec spec = new RSAPublicKeySpec(modulus, publicExponent);
            RSAPrivateKeySpec privateSpec = new RSAPrivateKeySpec(modulus, privateExponent);

            KeyFactory factory = KeyFactory.getInstance("RSA");

            PublicKey pub = factory.generatePublic(spec);
            PrivateKey priv = factory.generatePrivate(privateSpec); 

            System.out.println("Public Key : "+ byteArrayToHexString( pub.getEncoded() ));
            System.out.println("Private Key : "+ byteArrayToHexString( priv.getEncoded() ));
        }                        
        catch( Exception e ) {   
            System.out.println(e.toString());       
        }                        
    }         

    public static BigInteger getCoprime(BigInteger m, SecureRandom random) {
        int length = m.bitLength()-1;
        BigInteger e = BigInteger.probablePrime(length,random);
        while (! (m.gcd(e)).equals(BigInteger.ONE) ) {
            e = BigInteger.probablePrime(length,random);
        }
        return e;
    }


    public static String byteArrayToHexString(byte[] bytes)          
    {         
        StringBuffer buffer = new StringBuffer();
        for(int i=0; i<bytes.length; i++)
        {                        
            if(((int)bytes[i] & 0xff) < 0x10)       
                buffer.append("0");                               
            buffer.append(Long.toString((int) bytes[i] & 0xff, 16));
        }                        
        return buffer.toString();
    }         
}

希望对您有所帮助，