如何通过在Java中指定不同的输入来生成有效的RSA 1024位公钥和私钥？

Question

(if you're coming new to the question, jump to the EDIT, EDIT section)

I can generate random valid RSA 1024 bit public and private keys by using the following code:

KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA");    
keyPairGenerator.initialize(1024);
KeyPair keyPair = keyPairGenerator.generateKeyPair();
PublicKey publicKeyGenerated = keyPair.getPublic(); //Sun RSA public key, 1024 bits
PrivateKey privateKeyGenerated = keyPair.getPrivate(); //sun.security.rsa.RSAPrivateCrtKeyImpl@fffbfe07

The comments in the above code give the details from the debugger.

Rather than randomly generating the public and private keys I'd like to specify inputs to generate valid keys. Something like ( link which is in the comments below):

SecureRandom secureRandom = new SecureRandom();
BigInteger p = new BigInteger("41");
BigInteger q = new BigInteger("13");
BigInteger g = new BigInteger("17");
//http://www.javadocexamples.com/java_source/sun/security/provider/DSAKeyPairGenerator.java.html
//copying the methods generateKeyPair, generateX, generateY
KeyPair keyPair = generateKeyPair(p, q, g, secureRandom);
PublicKey publicKeyGenerated = keyPair.getPublic(); //Sun DSA Public Key
PrivateKey privateKeyGenerated = keyPair.getPrivate(); //DSAPrivateKey@fffa5e6a

Using the above code I don't get valid RSA keys like in my first example.

How can I generate my own valid RSA 1024 bit public and private keys by specifying different inputs in java?

EDIT , in response to Robert:

Yes, I wish to create public and private keys using user defined values, not random. In response to the link you provided I wrote this:

BigInteger q = new BigInteger("114...15741");  //big prime number
BigInteger g = new BigInteger("65537"); //modulus
RSAPublicKeySpec publicSpec = new RSAPublicKeySpec(q, g);
RSAPrivateKeySpec privateSpec = new RSAPrivateKeySpec(q, g);
KeyFactory kf = KeyFactory.getInstance("RSA");
PublicKey publicKey = kf.generatePublic(publicSpec);
PrivateKey privateKey = kf.generatePrivate(privateSpec);

I created random keys then put the values for the exponent and modulus I got for the public key in the variables q and g above. I get the same public key but I don't get the same private key. I tried adding another large prime, instead of q but I'm not really getting the answer I'd expect. The debugger shows a difference. How do I create a valid public and private key?

EDIT , EDIT , after response to mnistic

To pull things a bit more together

//randomly generate public and private keys
KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA");    
keyPairGenerator.initialize(1024);
KeyPair keyPair = keyPairGenerator.generateKeyPair();
PublicKey publicKeyGenerated = keyPair.getPublic(); //Sun RSA public key, 1024 bits
PrivateKey privateKeyGenerated = keyPair.getPrivate(); //sun.security.rsa.RSAPrivateCrtKeyImpl@fffbfe07

//pull out the exponents and modulus
BigInteger publicExponent = ((RSAPublicKey)keyPair.getPublic()).getPublicExponent();
BigInteger privateExponent = ((RSAPrivateKey)keyPair.getPrivate()).getPrivateExponent();
BigInteger modulus = ((RSAPublicKey)keyPair.getPublic()).getModulus();

//generate public and private keys using the above details
RSAPublicKeySpec publicSpec = new RSAPublicKeySpec(modulus, publicExponent);
RSAPrivateKeySpec privateSpec = new RSAPrivateKeySpec(modulus, privateExponent);
KeyFactory kf = KeyFactory.getInstance("RSA");
PublicKey publicKey = kf.generatePublic(publicSpec);
PrivateKey privateKey = kf.generatePrivate(privateSpec);

//check to see that the keys are the same
System.out.println((new BigInteger(publicKeyGenerated.getEncoded())).toString());
System.out.println((new BigInteger(publicKey.getEncoded())).toString());
System.out.println((new BigInteger(privateKeyGenerated.getEncoded())).toString());
System.out.println((new BigInteger(privateKey.getEncoded())).toString());
//the private keys are different :(

The private keys are different, what's happening here?

Answer 1

You are passing the public exponent to both RSAPublicKeySpec and RSAPrivateKeySpec , which is wrong. RSAPrivateKeySpec expects the private exponent. If you want to regenerate the key from your first code snippet, you can obtain the modulus and the exponents with:

BigInteger publicExponent = ((RSAPublicKey)keyPair.getPublic()).getPublicExponent();
BigInteger privateExponent = ((RSAPrivateKey)keyPair.getPrivate()).getPrivateExponent();
BigInteger modulus = ((RSAPublicKey)keyPair.getPublic()).getModulus();

And then regenerate the key with:

RSAPublicKeySpec publicSpec = new RSAPublicKeySpec(modulus, publicExponent);
RSAPrivateKeySpec privateSpec = new RSAPrivateKeySpec(modulus, privateExponent);
KeyFactory kf = KeyFactory.getInstance("RSA");
PublicKey publicKey = kf.generatePublic(publicSpec);
PrivateKey privateKey = kf.generatePrivate(privateSpec);

Note: To get the private key encoding to match, you can try the following (using RSAPrivateCrtKeySpec :

BigInteger crtCoefficient = ((RSAPrivateCrtKey)keyPair.getPrivate()).getCrtCoefficient();
BigInteger primeExponentP = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPrimeExponentP();
BigInteger primeExponentQ = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPrimeExponentQ();
BigInteger p = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPrimeP();
BigInteger q = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPrimeQ();
BigInteger publicExponent = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPublicExponent();
BigInteger privateExponent = ((RSAPrivateCrtKey)keyPair.getPrivate()).getPrivateExponent();
RSAPrivateCrtKeySpec crtKeySpec = new RSAPrivateCrtKeySpec(modulus, publicExponent, privateExponent, p, q, primeExponentP, primeExponentQ, crtCoefficient);
...
PrivateKey privateKey = kf.generatePrivate(crtKeySpec);