It's not secret to the administrator though, as they could know who was assigned what secret. I think it could work like: before voting, you go to an office whe

It's not secret to the administrator though, as they could know who was assigned what secret. I think it could work like: before voting, you go to an office where they verify your identity and let you randomly pick envelope containing unique number from a box. After voting all votes are published and you can verify your vote was counted, but nobody else knows your number.