POW?

The idea isn't new. It's a technique that asks the client to perform proof-of-work in order to increase the costs associated with spamming a website. For a single user the workload shouldn't be an issue at all, but a spammer (or indeed a brute-forcing hacker) might run into problems with being able to maintain a high throughput of requests. Validating the proof of work is trivially computational and hence will not put your server under the same amount of stress.

POWJS on my laptop takes 17 seconds to solve the problem in Chrome (50 seconds in IE 11) with 22 bits required to be zero. The workload can be started as soon as the user opens the page and will run asyncronously in the background (in a web worker if the browser supports them).

POWJS uses CryptoJS, but won't pollute your global namespace with it. This can't be used (as-is) to farm bitcoins or what-have-you, it merely performs a random POW.

Usage

Your server will need to generate a challenge and needs to be able to verify that it created a challenge, a trivial example could be an expiring challenge:

validUntil = utcfiletime() + 3600;
token = pack(validUntil, generateRandomBytes(32));
challenge = hmac(token, secretServerPassword);

Or just store a nonce in the user's session. Whatever you do, I recommend that you use HMAC to authenticate the token.

The server might then send something like this to the client (hexadecimal, please):

<input type="hidden" id="pow-token" value="<token>" />
<input type="hidden" id="pow-challenge" value="<challenge>" />
<input type="hidden" id="pow-solution" value="" />

The server can also indicate how many zero-bits it wants by including them in the challenge:

<!-- Expect the first byte to have only zeros. -->
<input type="hidden" id="pow-challenge" value="<challenge>;8" />

On the client POWJS is then used to calculate the proof of work:

$(function() {

	var pow = PowJS.start({
	    js: 'pow.js', // The path to the POWJS file. This is optional, but if omitted web workers will not be used.
	    challenge: $('#pow-challenge').val(), // The challenge from the server.
	    work: 800, // Only used when web workers are unavailable. How many attempts to make per invocation of the solver.
	    delay: 30, // Only used when web workers are unavailable. How many milliseconds between each call to the solver.
	    blurfactor: 30, // If the browser incurs limits on setTimeout for some reason (e.g. tab changed), multiply work by this.
	    complete: function(result) {
	    	if (result < 0) {
	    	  alert("cancelled!");
	    	  return;
	    	}
	    	$('#pow-solution').val(result);
	    	$('#submit-button').prop('disabled', false);
	    }
	});
	
	// Solves the problem drastically faster but risks lagging the web page, use this
	// if the user has reached the submit button and no solution has been found.
	if (pow.canSpeedUp) pow.speedUp();
	
	// For whatever reason.
	pow.cancel();
});

When the form is submitted the server can then validate it:

token = getinput('pow-token');
challenge = hmac(token, secretServerPassword); // Don't trust the challenge from the client!

// Has the token expired?
date = unpackint(token);
if (date < utcfiletime()) return false;

solutionCount = getinput('pow-solution'); //32bit uint
solution = sha1(pack(solutionCount, challenge));

// The solution from the client must have 22 zero bits at the start.
return firstBitsAreZero(22, solution));