生成给定模数和指数的RSA密钥

Question

我被要求使用给定值modulus和exponent值生成RSA密钥.但我只想知道生成密钥而不指定模数和指数.无论我给出的值是什么,似乎都是大整数值.我在网上搜索了这个并制定了一些东西,但它无法通过成功.

所以,如果有人之前已经这样做了,他们可以给我一些提示吗？

这是我们尝试使用给定值的示例程序.

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密钥长度必须至少为512位

Answer 1

我给你一些关于RSA的信息.首先在RSA中键入modulus = p·qwhere p和q不同的素数,模数长度就是它key length.所以当你收到例外时:

java.security.spec.InvalidKeySpecException:java.security.InvalidKeyException:RSA密钥长度必须至少为512位

这意味着您的模数至少必须为512位长.

除了在你的代码中还有另一个错误,你对公钥和私钥使用相同的指数,但这个指数必须是不同的数字.

在简历中,您必须java.math.BigInteger按照RSA密钥生成算法计算模数,公共指数和私有指数,以生成正确的密钥.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 ?(n) = ?(p)?(q) = (p ? 1)(q ? 1) = n - (p + q -1), where ? is Euler's totient function.
        // and choose an integer e such that 1 < e < ?(n) and gcd(e, ?(n)) = 1; i.e., e and ?(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 ?(n)); i.e., d is the multiplicative inverse of e (modulo ?(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();
    }         
}

希望这有帮助,