Another complexity is ensuring there aren't superfluous votes. Everyone can verify their own, but what if there were several million "hacked" extra votes.
This is a pretty easy one to solve since the number of votes is not privileged information. Simply publicly record the number of votes as each person goes into vote. This can be verified/observed by whoever wishes to do so. You could even require a large public display at each station. Pair that with a camera record that can also be verified. One person enters, the display should go up by one. And from there you have simple math:
The sums of the polling stations should equal the district.
The sums of the districts should equal the state.
The sums of the states should equal the nation.
I have to say it also makes me wonder what in the world darpa is thinking. Modern technology possible, somewhat trivially, elections that would be nearly impossible to fake in any way, shape, or form. And I'm certain this isn't exactly a secret to darpa.
You'd want a system where each citizen receives an ID/key, and there is no way to who a particular ID/key voted for, but if you know your ID/key, you can look up whether you voted. This should deter anyone from voting in anyone else's name, since they'd be likely to be exposed if they did it at an impactful scale.
The only other way to forge votes would be to invent new people that don't really exist, or maybe piggyback on recently deceased people. These are both problems that should be fairly straightforward to address if you have decently efficient administrations keeping track of things.
A simple way would be to use a public key ID that can be used to check if that key voted, and a private signing key. The list of all legitimate IDs is public (though not linked to identities). Anyone can see the total number of legitimate keys, and anyone can check to see how many of those keys voted, and verify that the number of voting keys from the national list is in fact equal to the global vote total. That same total and be cross-checked with the census and other sources of voting age population data.
