diffiejs

Diffie Hellman implementation in JavaScript

A bit about the Diffie–Hellman key exchange protocol

Suppose you're a person that wants to send a message to your friend, or a secure bank server that wants to send a message to your client. However, you're stuck with a government monitored, unsecure internet connection. How would you make sure that your message goes across without the Rothschild family reading your bank statement? Well, the answer is pretty easy: encryption. So suppose we use the standard AES, Rijndael cipher, this is all good and all, but since this is symmetric encryption you and your partner need to share a common key. Well, that poses another problem, how do you get a key across to your friend without being sniffed? You could use RSA, but no one wants to waste their time with RSA libraries, extra prime number generation, and blah blah blah. Instead we use the Diffie–Hellman key exchange protocol.

Now Diffie–Hellman is not a protocol that enables you to transfer a key across securely, rather, it allows you and the person you're trying to communicate with to generate a unique key that only you and they will know. This is as good if not better, than generating a key and transferring it via asymmetric encryption.

So, is Diffie–Hellman very math heavy? Nope! Diffie–Hellman is probably easier to understand than RSA. The only thing you need to know is how to calculate modulus' and exponents.

4 steps of Diffie–Hellman

Step 1: Choosing some common parameters

Well, to begin, you and your partner need to agree upon a common base and modulus, let's call them g and p, respectively. It's very important that p is prime and that g is less than p. You can send these numbers to each other over an unsecure channel as they are public knowledge.

Although it's easy to implement on your own I made it a bit easier to do this using the diffiejs library

//Share this string with your friend
var commonNums = diffie.gen();
// Some code where you send the above string to your friend
// Some function where you recieve a similar string from your friend

// This callback is called when you get your friend's data
function onFriendString(data){
  diffie.update(data);
}

All the above code does, is generate a key file and then once the partner's keyfile is recieved, it sees which is bigger and adjusts accordingly

Step 2: Keeping your secret

Now you and your friend have to generate secret keys. Note: THIS IS YOUR PRIVATE KEY, YOU NEVER EVER SHARE THIS. Any information of the key should not leave your computer. The diffiejs library does this automatically on construction. Also, for the sake of documentation we'll refer to this as S.

Step 3: Making a public shared key

So, here's where a bit of the math begins. You take your base, g, and raise it to the power of secret number, s. Then, you take the modulus of this and modulus number we talked about earlier, g. This is an operation known as modular exponentiation. Since these numbers are so large diffiejs uses the bigjs Big Integer library to do this operation. In common math notation it can be written in JS as the following:

  var yourPublicKey = Math.pow(g,s) % p;

You can now send this to your friend, over the unsecure channel as this is public knowledge as well. Your friend will send this to you as well.

Step 4: Recieving a public key, and generating the final secure key.

So, let's suppose your friend sent you their public key call it P. Now you do a modular exponentation, only this time using P as your base instead of g. This new number is your secret key. Your friend will have the exact same key This can be written in JS math as:

  var secretKey = Math.pow(P,s) % p;
  // When you expand it out on your side it looks like this
  Math.pow(((Math.pow(g,friendSecret)) % p),s) % p;
  // Your friend will calculate:
  Math.pow(((Math.pow(g,s)) % p),friendSecret) % p;
  // Thanks to the nature of modular arithmetic, these 2 numbers are the exact same
  Math.pow(((Math.pow(g,friendSecret)) % p),s) % p == Math.pow(((Math.pow(g,s)) % p),friendSecret) % p
  // ^this is true!!

The diffiejs library was onestep ahead of you and already computed it, when you did the .update() in Step 3. To access it, just check out the key attribute

var secretKey = diffie.key //This will give you your secret shared key 

For more details check out the Wikipedia article on it: https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange

Elliptic Curve Diffie-Hellman

Although the previous, vanilla, version of Diffie Hellman

##How to use diffie.js