Every time there are elections in USA, questions of the security vulnerabilities and hacking/tampering with voting machines are raised (I'm sure that it's not US-only phenomenon, either).
Obviously, preventing hardware level hacks is a whole different kettle of fish, but if we assume that the machine is physically secure - if for no other reason, because there are just so many, all over entire USA, so it's nearly impossible to tamper with meaningful enough amount even only counting swing states), would the following approach be a reasonably reliable way to prevent non-physical tampering/hacking of a voting machine?
Have a real ROM (non-writeable) storing the checking code
Checking code verifies that the voting machine software is valid (presumably, by computing checksum, and verifying the checksum against known valid values - for example, stored on a website of Federal election office).
- Use public key encryption for ensuring that the check-sums retrieved are indeed sourced correctly (using federal election office's public key).
If checksum fails, use separate hardware NOT controlled by the rest of the electronics in voting machine, to at least signal malfunction, or even lock out voting functionality.
Since the checking code is 100% in ROM, it would require physical access to the machine to mess with (and if it's sufficiently well protected, e.g. within a welded compartment, would be extra hard to screw with).