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No, they don't. That's the point. The voter can lie about the salt. Only the voter knows they are lying, because they were alone in the polling booth.



Then how can they be sure their vote was counted correctly?


By comparing their private knowledge of 1) who they voted for and 2) the salt they were shown in the booth with 3) the public hash of the two.

In any case it was only meant as an existence proof, not a practical system. I like aeternus's suggestion much more, since it has the useful property that everyone can see all the votes - just not whose is whose. (Although I'm not sure what function the receipt serves)




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