I read some e-voting questions here, but most deal with simple things like securing the connection from external attackers. But they usually put implicit trust on the central voting authority to be honest.
So assume you have 1000 Voters, and a single person (the Tallier) who tallies (i.e. counts) the votes. Each Voter knows what his own vote is (incomplete information), but only the Tallier knows how everyone voted (the complete picture). The Tallier wants to lie about the results, however.
Because the Voters don't trust the Tallier to be honest, they require him to provide them with some sort of a log. Each Voter then examines that log.
Can we make the system in such a way that it is impossible for the Tallier to provide a fraudulent log without a large percentage of Voters becoming aware that something is wrong?
I imagine something similar to SHA1 checksums, where a server cannot provide a file such that the SHA1 checksum will. Only in this case each voter has incomplete information (he only knows about his own vote).
Also, voters would need to detect if the Taller has invented non-existent voters.
Is there any research on the subject?