You have to make sure every link in the chain is secure.
That means:
1) Secured military-grade with strong anti-tamper machines, built on open-source OS software and hardware, that'll sign votes with a one-time-only HSM with strong anti-tamper (i.e., acid to burn off everything inside it if someone attempts to open it). Every HSM's public key will be competely open to the public, and the public will verify that the number of booth is what it's supposed to be.
2) Real life humans verifying the identity of the person voting (citizenship status, age, etc.), and verifying that they're alone in the booth.
3) Technology that uses biometrics (combination of voice, fingerprint, retina, DNA, whatever) to make a GUID for every person - this will also assure they haven't voted twice.
4) Open counting of the votes, booth by booth. Again, this will be completely open so the public can verify that all booths are accounted for and the vote counting is correct.