If it's possible to burn a ballot (i.e. associate the set of bar codes to actual candidates), shouldn't it be possible to "burn" a ballot after the fact as well?
i.e. we have 4 barcodes, I need a way to associate each barcode with a candidate to burn it, so why couldn't this happen after the fact as well?
I assume homomorphic encryption might help here, I just am missing it.
If the keys are destroyed after a valid election, as one would expect, then there is no possibility for that.
One way to better ensure the keys are destroyed is to use secret-sharing schemes so that multiple parties that are adversaries would have to lie similarly about destroying the keys, then conspire to work together to decrypt ballots after the fact. But I hope you see that this is all chasing social problems that must be solved as a precondition to have fair elections in the first place.
Though I tend to agree, its more of a social issue that technology can't really solve and hence why I'm more concerned about a user (and hence others) being able to verify that their vote was recorded correctly than doing out utmost to discourage "vote buying" schemes as at the end of the day, I don't think technology can really solve that problem but having more faith in the electoral system as a whole by being individually verifiable has more value (even if it can make vote buying more common). but I understand I might be in the minority on that.
UPDATE ballots
SET status = "burned"
WHERE contents = :ballot AND status = "unused"
UPDATE ballots
SET status = "used"
, voter_id = :voter
, choice = :choice
WHERE contents = :ballot
AND status = "unused"
AND region = :region
If you allow people to access the decryption oracle without going through that first pathway, which simultaneously checks if the ballot was not spent and immediately spends it into the "burning" pathway, then either of those opens up the space to attacks which decrypt individual ballots. With that said, just about any auditing mechanism applied to the decryption oracle would be revealing the existence of those attacks anyway so you can still get a measure of security without this.
You can potentially even distribute the database (e.g. over a blockchain among several political parties), but as far as I can tell the decryption authority would still need to be centralized and could be a single-point of failure. (In this case it would be a program which is watching that blockchain and interacting with it via some “I publish a burned ballot onto the ledger after I think the blockchain has passed N blocks ahead of the ledger request to burn that ballot” algorithm, and nodes in the network need to reject requests to cast ballots that they think have been requested to be burnt.)