So the other approach for solving this is what's known as an auditing mix net,
and the idea here is that each participant in the mix net can audit some of the outputs of the next step.
So to do that, we need to provide extra inputs.
So instead of the voter just providing the vote as encrypted to party A,
they'll provide it to party B as well.
All of the incoming votes go to the next two steps.
And now B going to audit A and it does that by picking some random set of inputs.
So let's say it picks this one and it picks this one, and it picks some of the ones in here.
So that means it's looking at some A's ouputs, and we'll call these y values.
So this would be y2, this would be y something else, and this would be y of n-1.
All right.  And this would be y of n.
So for each of the n inputs, Bob picks some number to audit.
And what B does is ask A to prove that y2 is a valid input.
In order to prove this, what does A need to provide?
What must A provide to B in order to prove that y2 is a valid output from A's mix net?
