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BGonline.org Forums
Allaying concerns about dice hacking.
Posted By: Timothy Chow In Response To: Allaying concerns about dice hacking. (mamabear)
Date: Monday, 4 April 2016, at 4:32 p.m.
First let me assume that you understand how the coin-flipping protocol that I described elsewhere in this thread addresses concerns about cheating. It remains to explain how to implement such a protocol electronically.
The problem is solved if there exists an encryption algorithm that both sides trust to have the following two properties:
A. It can't be cracked without the password.
B. There's no way to provide a "fake" password that causes encrypted messages to decrypt to something other than the original message.
Given such an algorithm, we proceed as follows.
1. Each player secretly generates a long list of random numbers ("coin flips") ahead of time and encrypts the list with a secret password.
2. The encrypted list is given to the opponent.
3. During play, each player reveals the next random number from his or her list as needed, and the two random numbers are combined to produce the overall dice roll.
4. After the game is over, the passwords are revealed and each player verifies that the decrypted list of random numbers matches the random numbers that appeared during actual play.
There do exist encryption algorithms that are widely believed to have properties A and B. However, we could reach an impasse if someone refuses to trust such an algorithm.
Note, however, that it's not necessary for both players to use the same encryption algorithm. If we use different algorithms, I just have to be confident that my algorithm has property A and that my opponent's algorithm has property B.
Most people are to come up with an algorithm that they feel has property A, so the sticking point is trusting that the opponent's algorithm has property B. As an honest person, I can request that my opponent use a bit-commitment protocol. If they're willing to do this then I am happy.
The only remaining sticking point is convincing a suspicious player that the bit-commitment protocol really works, and that it prevents me from repudiating. Convincing suspicious people is never a guaranteed thing, but at least in this case, all that is required is to follow a relatively short logical argument. There is no need to trust a complicated piece of hardware or software that one has no hope of being able to understand completely.
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