Say there are two vote options, 0 and 1. We use addition modulo 2, i.e. XOR. I vote for candidate 0. The voting machine tells me the random number 1 (out of 0,

Say there are two vote options, 0 and 1. We use addition modulo 2, i.e. XOR. I vote for candidate 0. The voting machine tells me the random number 1 (out of 0, 1). When the voting results are published, I can check that next to my name it has 0^1 = 1. When someone asks me what my random number is, I can either answer 0, to pretend I voted for 0(random number)^1(public list) = 1, or 1, to say that I voted for 1(random number)^1(public list) = 0.