crypto.createSign() using DH private key use case

example.js

/* Bob's environment */
var crypto = require('crypto');
var rsa = require('ursa');

crypto.DEFAULT_ENCODING = 'hex'

var dhBob = crypto.getDiffieHellman('modp18')
  , kBob = dhBob.generateKeys()
  , keysBob = {
      pubKey: dhBob.getPublicKey(),
      privKey: dhBob.getPrivateKey()
    };

/* Alice's envrionment setup (different computer emulation) */
var dhAlice = crypto.getDiffieHellman('modp18')
  , kAlice = dhAlice.generateKeys()
  , keysAlice = {
      pubKey: dhAlice.getPublicKey(),
      privKey: dhAlice.getPrivateKey()
    };
  

/* Bob recieves Alice's public key & generates a shared secret */
var secret = dhBob.computeSecret(keysAlice.pubKey);

/* Bob uses shared secret to generate RSA keys */
var k = rsa.generatePrivateKey();
var pk = rsa.createPrivateKey(k.toPrivatePem().toString('utf8'), secret, 'utf8');
var keys = {
  privKey: pk.toPrivatePem().toString('utf8'),
  pubKey: pk.toPublicPem().toString('utf8')
}

/* Bob uses shared secret to create cipher text */
try {
  var cipher = crypto.createCipher('aes-256-cbc', secret)
    , ct = [];

  ct.push(cipher.update('This is a secret message for Alice'));
  ct.push(cipher.final());
  var result = ct.join('');
} catch(e){
  throw new Error('Could not create encryption object');
}

/* Bob then computes a digest of the cipher text */
var digest = crypto.createHmac('sha256', secret);
digest.update(result);
var hmac = digest.digest();

/* Create object of ct & hmac and stringify it */
var sendToAlice = JSON.stringify({ message: result, digest: hmac });

/* Bob's DH privKey needs to be an RSA key */
var sig = crypto.createSign('RSA-SHA256');
sig.update(sendToAlice);
var signature = sig.sign(keys.privKey);

console.log('PAYLOAD: '+sendToAlice);
console.log('SIGNATURE '+signature);

/* Verify signature of payload with Bob's public key */
var v = crypto.createVerify('RSA-SHA256');
v.update(sendToAlice);
var verify = v.verify(keys.pubKey, signature);

console.log('VERIFY '+verify);

This was helpful, thanks!