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 A
It's a tricky problem because it's fundamentally unsolvable, so you need to work around the tradeoffs to do your best. There've been several good points made on the technical side including: (a) don't waste your time thinking compiling to Flash, Windows, Silverlight, JVM, or anything will actually help, (b) first transmit the encrypted real puzzle payload, then as the actual bottleneck transmit the key alone, (c) the latency even on 56k of sending a couple hundred bytes is negligible compared to human reaction time.
One thing I haven't seen mentioned is this:
Use after-the-fact auditing and tracking of users. This is how real casinos work. This is, I am told, a big part of how PayPal made their money. In both cases, rather than doing a lot of before-the-fact security, they keep very close tabs on everything about their players, use a lot of technology (statistics, pattern detection, etc) to flag suspicious players and they investigate. In both casinos and PayPal, you can't get your money right away. You have to cash in your chips or wait for the money to make it out of the PayPal system into your real bank. Your system should work the same way-- they can't actually get the money for at least a few days at minimum (longer if you are unable to set up a sufficiently speedy auditing system), giving you time to potentially impound their winnings. You have a lawyer, right? Also, casinos and PayPal know your real life identity (a must for dealing in money) so they can go after you legally-- or more importantly, deter would-be attackers since they could go after them legally.
Combined with the other tips, this may be sufficient to eliminate cheating entirely.
If you find it is not, make your goal not to totally eliminate cheating but to keep it to an acceptable level. Kind of like having 99.99% uptime. Yes, as one poster said, if even one person can compromise it everyone is screwed, but with a good auditing system the attacker won't be able to consistently cheat. If they can cheat 1 in 1000 times if they're lucky and they find they can't cheat more than once or twice before being caught, it won't be a problem since very few will cheat and any given honest user will have an extremely low chance of being affected by an extremely small amount of cheating. It'll be imperceptible. If you ever have a real cheating occurence that hurts an honest user, go out of your way to make the honest user feel satisfied with the outcome to a degree out of proportion to the value of that single customer. That way everyone will be confident in your security. They know they don't have to worry about anything.
People problems are not always solvable with technology solutions alone. You sometimes need to use people solutions. (The technology can help those people solutions work a lot better though.)