Preventing non-registered voters is the easy problem. Some signature systems allow blind signatures: I can create a ballot and encrypt the ballot. The governm

Preventing non-registered voters is the easy problem. Some signature systems allow blind signatures: I can create a ballot and encrypt the ballot. The government can sign the ballot, and then knowing my secret encryption key, I can decrypt the ballot and transform the government signature so that it matches the decrypted ballot. The signed but decrypted ballots can then be published using mixnets, Tor, or some other anonymous publishing mechanism. As I remember, it's still an open problem to set things up (without requiring trusted hardware or trusting the government to destroy a private homomorphic encryption key) so that I can't later prove to Dr. Evil's jackbooted thugs that I voted for Dr. Evil. Though, maybe there's some mechanism where I actually generate ballots for all candidates and only submit one of the ballots and it's impossible for me to prove which one I actually submitted, and I could cheat by submitting more than one ballot but there's a zero-knowledge proof that my ballots were for all of the N candidates, so in an American-style first-past-the-post voting system, submitting all of my ballots has the same effect as submitting none of my ballots.