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If I know the initial state and the time window that the first player pressed the button, I can just run the LFSR up to and through that time window. The first player's token will match one of these states, which means you know the LFSR state after player 1 has gone. You can repeat this to find the token for player 2, since applying the inversion gives you ...


Here is an attack that I think will, with excellent odds, allow certain determination of which value is on the ticket of colluding players; and consequently give an advantage on guessing the tickets of these colluding players, and a (typically lesser) advantage on guessing the tickets of honest players. I'm assuming: The adversary knows the value on every ...

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