Cryptographic protocols, again

I've mentioned cryptographic protocols as one way to address the suspicion
that backgammon websites cheat with the dice. The responses I received
revealed that many people don't understand what I mean by cryptographic
protocols, so I thought I would give a brief explanation. The idea is
taken from the "Mental Poker" article that I mentioned previously.

The website and I agree on some publicly known cryptographic algorithm.
To roll the dice, I secretly choose a key, and encrypt thirty-six phrases:
"one one," "one two," "one three," etc. With a good algorithm, this
produces thirty-six random-looking strings of the same length. I send
these thirty-six strings to the website in some random order chosen by me,
without of course revealing my secret key. The website picks one of the
strings and sends it back to me. Upon receiving the chosen string, I
publicly reveal my secret key, and the thirty-six strings are publicly
decrypted (to prove that I really did encrypt all thirty-six dice rolls).
The (decrypted) chosen string is the dice roll.

It is hard for the website to cheat with the dice under such conditions.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

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