Have Alice generate a list of N numbers and encrypt the list with a private key. Alice then sends the list to Bob. Bob can’t look at the list yet, because he doesn’t know the secret key yet. Bob then picks a number between 0 and N-1 and sends it to Alice. Alice replies with the secret key and Bob decrypts the list. The random number is the index in Alice’s list that Bob picked.

(Take from http://www.everything2.com/index.pl?node_id=1342791 – the same method is also described in the book “Applied Cryptography” by Bruce Schneier)

This method works well over the phone, or in another circumstance where two parties are physically separated (like over the Internet!).

Alice and Bob agree on a hash function H which compresses its input to an N-bit result. H should have a result long enough to prevent a mortal from finding two inputs which hash to the same result. It should also be free of shortcuts for doing so. In other words, it should be a cryptographic hash.

One of the two people picks a random number, hashes it with H(x), and tells y=H(x) to the other party. The recipient of y guesses whether the random input was even or odd. After this, the party who generated the random number reveals this secret number. The recipient can compute H(x) and verify that it equals y, thus, that x is almost certainly the original random number. After this it is obvious to both sides whether the guess was correct.