How to export RSA private key from Java as XML?

Question

Java

Hi all!
Help me out, already tormented. I was banned on Google - I can not find any answer.
In general, the question is this. In Java (Android) I generate a private-public key pair. In Android, everything goes fine - it encrypts and decrypts the strings as it should. But now I need to export this pair to .NET (C#). Public is exported as needed in the form

<RSAKeyValue><Modulus>AKfPOw...OZASeVM0qkuWp3</Modulus><Exponent>AQAB</Exponent></RSAKeyValue>

But there is a problem with exporting the private key. RSAPrivateKeySpec allows you to get only the module and the private exponent. But .NET also needs parameters P, Q, DP, DQ, InverseQ (D is a private exponent). Where can I get them? Calculate using formulas from wikipedia? But after all there should be a ready decision. It's just that I can't find it. Help.
The code:

KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
kpg.initialize(1024);
KeyPair kp = kpg.genKeyPair();
PublicKey publicKey = kp.getPublic();
PrivateKey privateKey = kp.getPrivate();

String xmlPublic = getPublicKeyAsXml(publicKey);
String xmlPrivate = getPrivateKeyAsXml(privateKey);

public String getPrivateKeyAsXml(PrivateKey privateKey) throws Exception {
  KeyFactory kf = KeyFactory.getInstance("RSA");
  RSAPrivateKeySpec ks = kf.getKeySpec(privateKey, RSAPrivateKeySpec.class);
  BigInteger modulus = ks.getModulus();
  BigInteger exponent = ks.getPrivateExponent();

  byte[] modByte = modulus.toByteArray();
  byte[] expByte = exponent.toByteArray();

  String encodedModulus = Base64.encodeToString(modByte, Base64.NO_WRAP);
  String encodedExponent = Base64.encodeToString(expByte, Base64.NO_WRAP);

  String publicKeyAsXML = "<RSAKeyValue>" +
      "<Modulus>" + encodedModulus + "</Modulus>" +
      "<Exponent>AQAB</Exponent>" +
      "<P></P>" +
      "<Q></Q>" +
      "<DP></DP>" +
      "<DQ></DQ>" +
      "<InverseQ></InverseQ>" +
      "<D>" + encodedExponent + "</D>" +
      "</RSAKeyValue>";

  Log.d(TAG, "getPrivateKeyAsXml: " + publicKeyAsXML);
  return publicKeyAsXML;
}

Answer 1

I forgot to write that I solved the problem

public String getPrivateKeyAsXml(PublicKey publicKey, PrivateKey privateKey) throws Exception
    {
        KeyFactory kf = KeyFactory.getInstance("RSA");
        RSAPublicKeySpec ksPublic = kf.getKeySpec(publicKey, RSAPublicKeySpec.class);
        RSAPrivateKeySpec ksPrivate = kf.getKeySpec(privateKey, RSAPrivateKeySpec.class);

        BigInteger n = ksPublic.getModulus();
        BigInteger e = ksPublic.getPublicExponent();
        BigInteger d = ksPrivate.getPrivateExponent();

        BigInteger p = findFactor(e, d, n);
        BigInteger q = n.divide(p);
        if (p.compareTo(q) > 1) {
            BigInteger t = p;
            p = q;
            q = t;
        }

        BigInteger dp = d.mod(p.subtract(BigInteger.ONE));
        BigInteger dq = d.mod(q.subtract(BigInteger.ONE));
        BigInteger inverseQ = q.modInverse(p);

        String publicKeyAsXML = "<RSAKeyValue>" +
                "<Modulus>" + convertToString(n) + "</Modulus>" +
                "<Exponent>" + convertToString(e) + "</Exponent>" +
                "<P>" + convertToString(p) + "</P>" +
                "<Q>" + convertToString(q) + "</Q>" +
                "<DP>" + convertToString(dp) + "</DP>" +
                "<DQ>" + convertToString(dq) + "</DQ>" +
                "<InverseQ>" + convertToString(inverseQ) + "</InverseQ>" +
                "<D>" + convertToString(d) + "</D>" +
                "</RSAKeyValue>";

        Log.d(TAG, "getPrivateKeyAsXml: " + publicKeyAsXML);
        return publicKeyAsXML;
    }

    private String convertToString(BigInteger n) {
        return Base64.encodeToString(n.toByteArray(), Base64.NO_WRAP);
    }

Answer 2

If on the java side it is possible to make the key in the form of pem, pass it in this form.