Us "computer folks" convincing ourselves is the easy part. Maybe after enough studying of the system, I'd be absolutely sure that my vote was counted, but what would the other 90 % of the population think? This not a "people are stupid" argument, a brain surgeon or nuclear physicist or philosopher isn't going to put in the effort to understand fully homomorphic cryptography, hardware-based security, etc. Why should they?
The alternative works perfectly fine and it's so easy to explain. It's obvious to anyone, no matter their level or field of education, how their vote makes it from their hand into the tally, what prevents it from being misused and what they can do to further reduce that already tiny probability.
You can see, feel and experience the technical measures keeping your vote safe. The people keeping their eyes on the ballot box alp day may literally be your neighbours, as are the people counting. You can reason about their motivations, you can theorise in your head about what lengths you'd have to go to in order to change even a few votes and how unlikely you would be to succeed.
The biggest danger to elections, ultimately, isn't the risk of cheating. It's the risk of losing the people's trust.
(I'm in the local election commission (that's layer 2 out of 4 in our particular election management hierarcy), we just had a big referendum, everyone keeps asking me about online elections so this rant was fresh on my mind)
It's funny too - 15 years ago on HN people would discuss blockchain voting systems or ways to make it 100% secure. It seems like lately a lot of people carrying water for the potential that one party is associated with 95% of the fraud - and don't wish to discuss the vote being fair.
In any system, I suspect it is possible. There are strategies that allow doing private set intersections (or similar): https://en.wikipedia.org/wiki/Private_set_intersection (i.e. a set with one member is "you", and you can check to see if you're in that 764, without knowing who the others are)
I'm not sure what strategies would also allow you to not reveal to the vote collectors where your vote went, but there might be something.
> Private set intersection is a secure multiparty computation cryptographic technique[1] that allows two parties holding sets to compare encrypted versions of these sets in order to compute the intersection. In this scenario, neither party reveals anything to the counterparty except for the elements in the intersection.
Revealing even elements in the intersection, if that means revealing individual votes, breaks ballot secrecy.
Are there any voting systems that have both of those qualities? I'm not sure, but I hope so, and the relatively-widespread existence of both seems like there's at least some possibility that one could be built.
1: https://dl.acm.org/doi/10.1145/3573428.3573750
2: message repudiation: https://en.wikipedia.org/wiki/Signal_Protocol
However, how do you know you're one of the X votes displayed in the final tally ?
Faking paper ballots is totally doable, but you can take various precautions to make that very difficult. For example, you can deliver ballots to polling locations in sequentially-numbered packs and shuffle them at the voter sign-in desk: by shuffling the packs before delivery, by having the elections judges record which packs they got and which numbers went unused, by making them sign ballots prior to placing them on the sign-in table, and so on, you can make it very difficult for elections administration staff to later replace those paper ballots. But you're going to need timely, partial or full hand-count audits in order to make it necessary to replace paper ballots in order to replace results.
Election security is pretty expensive, but compared to the _value_ of elections, it's nothing.
I think that is the essential point. How much is it worth for Russia or China or even Iran to change an election outcome? It could be existential. How about to a corporation, or of course a political party or well-resourced individual? Do you think some of those individuals might have the ability and resources, and the amorality and lust for power?
Remember that the task is not changing tens of millions of votes across the country; you only need to change a small proportion in the right localities to swing the electoral college. And you don't necessarily need to even change numbers there; just create errors that dissuade enough people from voting or add votes of registered voters who didn't show up to the polls. (And you can get ahead of these tasks with disinformation.)
Defending against them are relatively small manufacturers - i.e., this isn't Apple securing iPhones - and local election operations. Can Savannah, Georgia handle these attackers? Imagine being the national CSO for US elections (if there was one) and being asked to secure this absurd, distributed, decentralized system. All I would say is, 'we're switching to paper'.
I think such a system could still work, but just like the voter has to go to the booth alone to vote, they must go the booth alone to verify.
That being said I think the Estonian voting system does a decent job of being trustworthy. Publishing the source code is a big step to the better as well. As far as I knew the system was written in Java but seems like they have upgraded it in Go. Good job! Probably the best in the world.
BTW, the source code we're talking about could easily be enormous, especially if you want the machines' firmware to be open too. Reviewing that source code would be a huge task. And you still have the problem of being unable to validate that the actual object code run in production corresponds to the source code you reviewed. And the public won't believe any of it anyway.
However, the Estonian governement has made a different choice and I salute that they are at least trying to do everything by the book and in the right way. Publishing the source code is a part of that. Estonia is a high-trust society (which is an incredible achievement in itself, considering they were a province of the Soviet Union only forty years ago) and they have the most functional e-identity system in the World. Voting is just a part of it. It does make many things easier and also helps economy if you can trust - and verify - your fellow man.
I might be missing something obvious but I'm not quite seeing the logical inconsistency between their two goals. Note they're only asking to verify their own vote, not to verify every other person's vote. For that, isn't it enough for authorities to announce a product of large primes, letting each person verify that their own prime was in the set? At each stage, the machines only report the product of primes up the chain, not the individual ones.
It seems to me the difficulty is with the fact that we have so many places to hide malicious things with modern technology (tiny electronics, firmware, etc.), not a logical incompatibility between the goals. If you had some sort of abacus that did all this mechanically without reprogrammability... or a large computer whose logic was fully verifiable... then everyone could inspect the machine and verify that it behaves correctly prior to elections, and e.g. a camera/observers/etc. can ensure no tampering occurred with the machine until the tallies were conducted.
Still, if you had the authorities to announce a product of large primes - whatever that means - how do you know they announced the correct primes and not something they made up? I'm afraid any clever cryptographic scheme you come up with falls the victim of the same dilemma: if you can check that your vote was counted right, you lose anonymity. Also how do you check no fake votes were added?
As far as I know, the Estonian voting system works in two stages. First there is an authenticator, that verifies that each given vote is signed properly, is only given once and can be counted, without looking at the payload. Then it anonymizes the votes and signs the result file which is transferred to another system which counts the votes. The communication is unidirectional so that the front-end doesn't get any feedback from the back end save some data transfer acks.
As I said, a decent job. It's not perfect in any meaning of the word. It's practical and it works. People trust it because they trust the people who designed it and run it.
My take is that one should be able to check that a blockchain has not been altered/substituted, and the way to do that is by being able to record encrypted running tally blockchain heads, but this gives you no indication that the published blockchain faithfully represents the cast votes so you have to add paper ballots and an immediate partial manual audit of the paper ballots checked against the digital cast vote record.
Note, obviously I was not attempting to detail a cryptographic voting system here. My only point was that I don't see what you said as being obviously true, if it is true at all. For the purposes of that point, even an incorrect scheme that isn't trivially disprovable would prove my point.
That said, to answer your question as I think through the details right now...
- Authorities preassign N-digit primes to everybody, one per option on the ballot.
- Find a way to validate the total number of ballots cast in the election. (Assume for simplicity that every question has exactly one answer selected.) Exercise for the reader on how to do this; this ought to be easy. This is important to know how many digits to expect in the product(s).
- You "vote" by submitting the primes corresponding to the option you select, one per question.
- Authorities announce the products of primes corresponding to each option.
- If your prime isn't included in the product, then it's obviously trivial to prove it... you just reveal your number and show the result fails divisibility.
- If they included extra fake primes, then this is harder to prove, but I think you can catch this by looking at how many digits are in the result. I think you can make the error margin arbitrarily sharp by making all the primes lead with 10000000000..., for example, adding however many zeros you need to make sure a single fake number adds a detectable number of digits to the product.
This is just a sketch; fix & fill in details as appropriate. The biggest flaw I see right now is that it's susceptible to whatever eventual algorithm (quantum or otherwise) ends up breaking factoring and leaking everyone's votes. But otherwise, it sounds plausible to me, and there's probably another trapdoor function that can mitigate that better. And as mentioned initially, if you can't easily prove it's impossible to make it work, that's sufficient for my point, even if it is in fact wrong.
Which has always been my biggest beef about digital vote. I'm all trusting the people writing voting software to do their best, actually. Being a Software engineer myself, I'm more concerned about bugs and hacks than deliberate tampering by the government. Especially in an age where AI agents can access pretty much anything ever connected to an electric plug...
You are aware of malicious hacking.
Hanlon's razor, etc...
This, and the need for everyday Joe to be able to understand what is done at every step.
In code, you have no insight into what actually happens.
trivia: did you know that a tear in any of the pages of your passport renders it invalid?
How? Any possible scheme I can think of that could theoretically allow a tabulation machine to behave differently on audit ballots than it does on real ballots, can also theoretically be mitigated via audit procedures.
An audit will only mitigate that if a) you have paper ballots you can check, b) the audit happens very soon after the closing of the polls. If an audit takes place a month later, that's a lot of time for the elections administration to create all new ballots to replace the originals with, so the audit has to come very soon after the election.