Here's the idea: you collect the votes from the voters. Those are inputs to a random permutation.
Let's say this is controlled by the Apple Party,
and what the permutation does is randomly scramble the order of the votes.
Now the position of the votes that came in
doesn't match the position of the votes that came out.
We'll also do some encryption, and we'll get to that in the next question part.
Those are passed along to the next party. Let's call that the Blue Party.
The Blue Party also scrambles the votes in some random permutation,
and then those are passed along to the next one and we'll call this one the Crazy Party.
Our parties start with the letters A, B, and C, and the Crazy Party does the same thing.
It selects some other random permutation where it randomly selects a permutation,
and it scrambles the positions of the votes.
In order for this to work, we want at the end of this to know what the actual votes are.
The question is what value should we use for x to enable this chain.
Our security assumption is that the Apple, the Blue, and the Crazy Party all hate each other.
They wouldn't possibly collude, so they can be trusted not to collude with the other parties.
But otherwise they can't be trusted, they'll want to try to change the election,
change the votes, and do everything they can.
The question is which one of these would be the best choice for the xi values?
Neither of these are the correct choice.  Neither of these will work securely.
We're going to have to do some other things, but which one of these is the best starting choice?
