I am designing a web site in which users solve puzzles as quickly as they can. JavaScript is used to time each puzzle, and the number of milliseconds is sent to the server via AJAX when the puzzle is completed. How can I ensure that the time received by the server was not forged by the user?

I don't think a session-based authenticity token (the kind used for forms in Rails) is sufficient because I need to authenticate the source of a value, not just the legitimacy of the request.

Is there a way to cryptographically sign the request? I can't think of anything that couldn't be duplicated by a hacker. Is any JavaScript, by its exposed, client-side nature, subject to tampering? Am I going to have to use something that gets compiled, like Flash? (Yikes.) Or is there some way to hide a secret key? Or something else I haven't thought of?

Update: To clarify, I don't want to penalize people with slow network connections (and network speed should be considered inconsistent), so the timing needs to be 100% client-side (the timer starts only when we know the user can see the puzzle). Also, there is money involved so no amount of "trusting the user" is acceptable.