Fully software, even a combo of software and hardware, cannot by itself make elections secure. Think of the Reflections On Trusting Trust problem, the need to verify firmware, etc. You can't ensure that machines _will_ work correctly, but you _can_ verify that they _did_. To do verify the machines' functioning after the fact you have to do it very soon after closing of the polls, and you have to devise a manual, statistical random sampling method where you manually check randomly sampled, marked paper ballots, against the digital cast vote record, then do a digital risk limiting audit to check that the CVR totals up to the machines' reported results. The sooner after closing of the polls you do this, the better the likelihood that any cheating will be caught. I.e., an immediate manual, partial audit of enough randomly-selected polling locations.
That still leaves tons of other technical problems to address, like security of mail-ballots / absentee ballots, the security of ballot boxes used for early voting (because you probably cannot run the above manual partial audit due to then having nightly results available to the public; or maybe you accept that), voter registration, etc.
himata4113 3 hours ago [-]
You solve all of these with cryptography.
Your ID card contains a private key, you use that key to sign a transaction. It doesn't matter that machine you are running on is compromised as these details can be verified at a later date.
Example A:
You vote for candidate A, but software changes to candidate B and software displays that you voted for candidate A. At any later time you can check with an independent device and look at the transaction finding out that it was altered with and retract your vote / change it.
Example B:
How do you know your vote was counted? Publish a hash and the signature of every vote, recompute the final tally and compare with all the votes. If your vote is not in the final tally the hash will be different and you can visibly see your vote in the dataset as every transaction is published. To preserve privacy each round has a number, private key + number -> new key so each fingerprint will be unique between votes.
cryptonector 3 hours ago [-]
> You solve all of these with cryptography.
I've spent a lot of time thinking about this problem, and my conclusion is that cryptography alone is not the solution, for reasons like:
1. The public needs to believe it, and hypertechnical solutions are a hard sell.
2. Any blockchain approach needs to preserve the secrecy of the ballot, otherwise you get all the problems you can expect of non-secret votes (coercion, vote buying, shaming network effects).
3. You still need to have the cryptographic rubber meet the physical road _somewehere_ -- it has to, otherwise the need for vote secrecy means that the results can be entirely fictitious and pre-programmed and there is no way to check!
I.e., you can have a paperless blockchain solution IFF you abandon vote secrecy. That is a very tough to swallow pill.
On the other hand, if you accept paper ballots and manual partial audits as part of the solution, then blockchain can have a role to play. For example, the machines could display a blockchain head every 50 ballots cast, and voters take a copy of the blockchain head visible to them, then after the election the public can verify the integrity of the blockchain, and the fact that you only get running tallies every 50 ballots means you get vote secrecy.
A system that uses paper ballots and partial manual audits can be explained to the public, and the public can develop confidence in it. Blockchains can then add a good deal of confidence: the blockchain tells you that the tallies were not modified after the fact, and the partial manual audit tells you to an acceptable level of statistical confidence that the digital cast vote record contains the actual paper ballots _as marked and cast_ by voters.
sigmoid10 2 hours ago [-]
>I.e., you can have a paperless blockchain solution IFF you abandon vote secrecy. That is a very tough to swallow pill.
This is false. I know this is a common thought on HN because some formerly popular youtuber did a video about this topic that is still regularly reposted here, but he was already wrong in theory back then and it is certainly wrong in practice today. Secrecy/anonymity and verifiability are no longer mutually exclusive as anyone who is well versed in modern cryptography will be able to tell you.
cryptonector 2 hours ago [-]
I'd appreciate some references. That's not because I'm trying to put you down with a request for references, but clearly you have seen them, and I'd like to see them.
Also, you still have to convince the public.
sigmoid10 2 hours ago [-]
I agree that convincing the public is a separate issue. But on a technical level, these problems are solved. See e.g. this modern implementation: https://github.com/vocdoni/davinci-paper This is a pretty recent one, but the mathematical foundation dates back to the late 80s.
Thanks. Right, this is zero-knowledge proofs. I expected as much. I think that ZK can be made to work for secure voting, though I don't believe that the public can be expected to understand it. I'll have to read this, but I suspect that there is a way for possessors of secret keys to choose to decrypt ballots and violate ballot secrecy.
mariofdistrust 2 hours ago [-]
the issue isn't that people won't believe it or that blockchain can't preserve secrecy of ballots (it can). it is, in part, that crypto eventually has to meet the real world, but mainly that crypto is hard and governments might not be up to the task. for example, last year the IACR (which had been doing online voting via crypto for more than a decade, and still is) had to void their elections because one of the trustees lost their private key and the results were impossible to decrypt. while it was ultimately fine because the IACR isn't really a high-stakes operation, how would you feel if your government just said "sorry folks, there's been some technical issues and elections will have to be redone"? would you believe them or suspect they're up to no good? what if this happens in a very contended and heated election?
varispeed 2 hours ago [-]
> The public needs to believe it, and hypertechnical solutions are a hard sell.
Public doesn't need to know the details. Production of paper, printers is quite complex and so production of the pen. Yet people are not concerned about that when voting and we don't publish schematics of a printer that printed the ballots.
cryptonector 2 hours ago [-]
> Public doesn't need to know the details. Production of paper, printers is quite complex and so production of the pen. Yet people are not concerned about that when voting and we don't publish schematics of a printer that printed the ballots.
Except that people know what paper looks and feels like, they know how it absorbs ink, they know its various properties, they can _read_ whatever is printed on them, and they can see that the marks they make (or a ballot marking device does for them) are faithfully visible on the paper. With paperless machines there is nothing comparable.
emil-lp 2 hours ago [-]
A major problem is that if you are able to verify who you vote for, you can either sell your vote or be coerced (by, say, your abusive husband) to vote a specific way.
rustyhancock 2 hours ago [-]
We have the solution it's just not practicable. Cryptocurrencies and hardware wallets have solved this problem. But they operate at the scale of people in their bedrooms not hundreds of millions of people voting over one day all over a country.
Passports would need to become like hardware wallets with screens such as Trezor. Who's firmware and design are open source.
The screen means I can see what I'm signing and later be shown what I signed.
Now, I don't want people to know who I vote for. So we make it e-passport gate so that no one can enter with me.
Now I want to be able to verify my vote at a later date but not let others know it was me.
Well this too is solved by multiple cryptocurrencies like monero and z-cash.
I can go to my local town hall enter a room alone using a e-passport style gate and check my vote at the machine. My device can verify my vote.
Someone with the vote can only see that 1 of N voters did it. Where N is so large they can't identify me.
No duplicate vote is possible.
Literally no one would agree to this however.
dpkirchner 33 minutes ago [-]
As long as you can see your own vote, someone can force/coerce you to show them your vote.
cryptonector 2 hours ago [-]
Cryptocurrencies mostly are pseudonymous, and, really, not even that. Certainly bitcoin is at best pseudonymous.
rustyhancock 1 hours ago [-]
There is a reason monero and z-cash are being banned in Europe.
I can't claim to be a crypto expert.
But hiding a transaction and it's value among other transactions is perfect for voting.
As I understand it Monero uses ring signatures to make it so it's not possible to know which individual of a group initiated a transaction, and it's zero knowledge proof system means it can be verified that a particular transaction is valid despite this.
To my layman mind that seems to be good enough, every vote can be verified by any party as valid (no double spending or double voting took place).
You can never narrow down who made a particular vote beyond a large pool of people.
You can't tell where any transaction went (you don't know who was voted for).
At the same time with my private key I can see my vote.
The only thing needed for voting is the e-passport style gates.
Certainly it won't just get a case of use monero, they would need to design the system for voting.
ifwinterco 32 minutes ago [-]
True for bitcoin but Monero is legitimately quite anonymous
himata4113 2 hours ago [-]
You can always include a nonce to decode the votes true value or provide an alternative for people that are vulnerable to coerction. If you need an example: monero crypto currency is the pinnacle of it.
spiddy 2 hours ago [-]
retraction of vote with a new vote solves this.
Since I'm able to retract my vote, I cannot sell it.
And since I can retract my vote, I cannot be coerced in any way.
cryptonector 2 hours ago [-]
Elections results have to be final at some point, and after that point no further retraction/changes can be made, therefore you can be coerced.
himata4113 2 hours ago [-]
coerced at the time of voting, but then you can go back and simply change it again
cryptonector 1 hours ago [-]
And then you can be coerced again, and again, until the vote is final.
spiddy 11 minutes ago [-]
there is a limit of how many people you can be physically present to coerce up to end of election, making it inviable en mass, thus impractical.
himata4113 10 minutes ago [-]
how would one know? they're they know a transaction happened, but they do not see the contents of a transaction
resist_futility 2 hours ago [-]
You could have verification be done in person and not online with no way to share it.
cryptonector 2 hours ago [-]
You'd have to go to your elections authority's location, and very few could do it w/o overwhelming the vote verification rate capacity, and very few would.
matheusmoreira 2 hours ago [-]
> software displays that you voted for candidate
This enables coercion of voters. It must be impossible to attribute any vote to any specific person.
himata4113 2 hours ago [-]
this is out of context, nobody would see who they have voted for in practice
matheusmoreira 1 hours ago [-]
> At any later time you can check with an independent device and look at the transaction finding out that it was altered
This implies there is a record establishing a relationship between person A and vote X.
The fact most people won't bother to check it in practice is irrelevant. It must be impossible, because otherwise people are going to die.
There is no problem that electronic voting solves that paper ballots and scanners do not, and the latter are not only more secure but are seen to be more secure. Trust is essential in a voting system and only paper ballots provide the necessary level of trust.
sam1714 2 hours ago [-]
There are problems that electronic voting does solve: in some countries, moving paper ballots are problematic and subject to tampering. This shows up in mail-in voting, where there's always a risk of loss and delay. Overseas voters are an issue, e.g. deployed military.
There is a specific problem with mail-in voting and disabled voters, for example elderly people who can't go to the polls and can't get an electronic ballot marker. 25 US states deliver ballots electronically and 15 allow electronic voting for this specific case [1].
Registration of such voters can be audited and checked carefully to limit their numbers (since they must be inherently limited), and ballots can be delivered to them, or voting equipment can be brought to them (e.g., elderly care homes). I'm not sure much can be done to make voting by the permanently confined secure. For military the military itself can help a great deal. For civilians overseas, either come back to vote, vote at a consulate, or don't vote -- I don't think it's necessary to bend over backwards for civilians who choose to be overseas unless a country has a huge proportion of its population residing abroad.
sam1714 59 minutes ago [-]
Intentionally limiting access to accessible voting is problematic.
You also have issues of deanonymization if you only get a couple of ballots in via one method. In Maryland, for example, they're supposed to encourage at least 100 random people to use the accessible ballot marker per precinct for this reason.
It's not reasonable to tell people "too bad," fly back to the US as much as 3 times per year. They pay taxes and are subject to US law even though they're overseas, so they get to vote.
Ballot management becomes error prone. My county alone has 25 ballots due to the different combinations of state house, senate, Federal house, municipalities, and _all_ the special districts. (4 members to the board of directors of the Anytown West Memorial District, a.k.a. cemetery, because they had a property tax assessment when they built the thing in 1950)
cryptonector 40 minutes ago [-]
> Intentionally limiting access to accessible voting is problematic.
I offered nothing of the kind, except as to civilians residing abroad, and even then, I don't think there should be any obligation to provide online voting -- having to travel to a consulate is not too unreasonable.
> It's not reasonable to tell people "too bad," fly back to the US as much as 3 times per year. They pay taxes and are subject to US law even though they're overseas, so they get to vote.
Vote... where? In what state, in what county, in what precinct? The correct answer is that they should not have to pay income taxes while residing abroad, but also not get to vote while residing abroad.
For military the situation is simpler even if the personnel have no US-side residence: use the state/county/precinct of last residence. The same can apply to civilians, but I'd rather let them not pay state and federal income taxes while residing abroad.
> Ballot management becomes error prone. My county alone has 25 ballots due to the different combinations of state house, senate, Federal house, municipalities, and _all_ the special districts. (4 members to the board of directors of the Anytown West Memorial District, a.k.a. cemetery, because they had a property tax assessment when they built the thing in 1950)
That's a small county :)
eastbound 50 minutes ago [-]
> You solve all of these with cryptography.
Or ballot boxes. Where citizen can keep their eyes on their ballot until it is counted.
Even back in 2002, TV channels in France (60m inhabitants) broadcast the winner at 20:00:30, using statistical models.
But recently, they removed the ability for citizen to stay during the counting, relying on designated persons, which breaks the chain of trust. Might as well cast my vote into a black bag or an electronic machine, no trust at all.
Trust was never the goal. As the means of coercion are higher and the capacity of communication is filtered, it becomes unnecessary to involve citizen in voting, isn't it?
mmooss 3 hours ago [-]
Who makes your ID card, generates the private key, and stores it there? Do you trust them? Did they retain a copy of the key? Did they implement security effectively (a very difficult task, considering the resources of attackers)? What about securing the manufacturing process?
In the end, you always must trust humans.
vincnetas 2 hours ago [-]
So if someone else knows my private key and voted for me not the same way i intended to vote, this will be visible in final results. And then you can start asking questions. If they have my private key and voted the way i intended, then its no problem :)
drdexebtjl 2 hours ago [-]
Why would others trust you to be telling the truth and not just lying to attempt to cause mistrust in the election?
Naive solutions have naive problems.
thfuran 2 hours ago [-]
I’m not sure what you’re trying to say. That the “solution” to that is just to ignore both votes in the case of multiple votes per id?
drdexebtjl 2 hours ago [-]
That this is too simplistic. There are obviously many solutions with different trade offs, but this one sacrifices secrecy to help catch fraud, and it’s not even effective at catching fraud.
cryptonector 3 hours ago [-]
Indeed. The rubber hose always beats cryptography. Always.
thaumasiotes 3 hours ago [-]
> Example A: You vote for candidate A, but software changes to candidate B and software displays that you voted for candidate A. At any later time you can check with an independent device and look at the transaction finding out that it was altered with and retract your vote / change it.
This seems to make a pretty dramatic change to the election protocol, no?
Consider example A': You vote for candidate A, but later realize that you hate candidate A. You repudiate your recorded vote for candidate A.
What should happen?
devin 2 hours ago [-]
How much later? Cryptographic systems certainly have methods for allowing revoting up to a deadline, but endlessly mutable voting is insane. It's also not really any different from today. I can say I didn't vote for candidate A 12 months after the upcoming election and it means... well... nothing.
sam1714 2 hours ago [-]
You can do A' in some US states... you can vote by mail/early vote, and then later request they spoil that ballot and do it again, or by voting on election day the mail-in is invalidated.
grg0 2 hours ago [-]
The US voting system is probably not a good starting point for modeling such systems :)
cryptonector 1 hours ago [-]
There is no "US voting system". Each of the 50 States have their own systems, often several systems, and where there are several systems it's the counties that pick a system that suits them.
sam1714 2 hours ago [-]
I'm confused. Can you explain the exact issues created by this repudiation system practiced by US states? Maybe there's a real issue that hasn't been addressed that I am unaware of.
Or is this a knee-jerk America Bad?
bel8 2 hours ago [-]
But Brazilian gov says their electronic election system is unhackable... Yeah.
Only a selected few orgs and groups are allowed to audit and in a very controlled environment because they also rely on security through obscurity. The source code is not available to the citizens.
If by any chance I'm wrong and someone can point me a source code repo, please enlighten me.
In my country we still rely on a paper process - which is very hard to tamper with but also has a bunch of problems - recently we needed to repeat local state elections because of such problems including shortages of ballot papers, unusually long queues to vote, ballots being delivered to the wrong locations, and in some cases voters being turned away.
Many of these problems go away with digital voting - but then you have other issues.
I don’t think a perfect solution can exist
matheusmoreira 2 hours ago [-]
One would think they'd have the balls to put up a billion dollar bounty.
bel8 2 hours ago [-]
That would require at least access to the ballots, which citizens don't have.
Not even a remote access to a demo ballot machine.
matheusmoreira 2 hours ago [-]
Yeah. The audits are a joke. In the end it amounts to nothing but an idiotic judge-god-king proudly declaring that the machines are UNQUESTIONABLE.
Our congress has determined that a paper trail must be implemented but the judges aren't having it.
Source code is a red herring too. If there's no reproducible builds that cryptographically establish source-executable correspondence, showing us the source code would prove nothing and only serve to embarrass us. Supply chain attacks could compromise it without any source code vulnerability. What they need to do is publish the signed executables that ran on election day as well as every executable used to construct those artifacts. Our AIs will make short work of the binaries.
In any case, the prevailing theory is that the mesários are partidarian and simply impersonate people who didn't show up to vote in order to boost their candidate's numbers. Very low tech, can be fixed with surveillance: have people from all parties everywhere observing everything. It boggles my mind that this isn't being done already.
atoav 2 hours ago [-]
While these all are problems, the REAL problem is that the goal of elections isn't to get scientifically or mathematically verifiably correct results. The goal is to produce agreeable consent.
That means it doesn't matter one bit how correct you are if the regular Joe does believe you tricked. Adding computers into the mix always makes this worse. And again, this is not something you can fix with clever solutions and cryptography (that admittedly fascinates me nonetheless), the problem is that people can't see electricity generally and I something at the scale of a computer, even if you could it would be utterly meaningless.
This is why the paper ballot system is so glorious in its stupid inefficiency, because it spreads the trust in a way any adult who has mastered object permanence can verify for themselves. Invite the conflicting parties to monitor and have them begrudgingly admit their defeat in the face of the simple, inefficient but agreeable process.
This is why I as a cryptography fan, programmer and hardware guy think electronic voting is not up to the task for high stakes elections.
llukas 1 hours ago [-]
> glorious in its stupid inefficiency, because it spreads the trust
What is the goal? Having fancy crypto or people being confident about elections?
If spreading the trust is the goal what makes you say "inefficient". It is orders of magnitude better then any crypto system.
icantevenhold 30 minutes ago [-]
As I wrote in another comment we had to repeat local state elections because of problems in the paper process - including shortages of ballot papers, unusually long queues to vote, ballots being delivered to the wrong locations, and in some cases voters being turned away.
While I’m a proponent of the paper process let’s not pretend it immediately means you can be confident about the election
llukas 4 minutes ago [-]
Oh, you absolutely can and it worked in your state. There were problems with the process and you had to repeat the election for people to be confident. People can understand all problems of the above.
With some abstract math and computers? Any real or imaginary issues are incomprehensible to most of the voters and concerns can be easily shooed away.
cryptonector 35 minutes ago [-]
GP means inefficient in the sense of cost. Paper ballots add costs. Partial manual audits / hand-counts add costs. Full audits / hand-counts add a lot of cost, and in particular hand-counts require a lot of staff in order to yield results on election night.
The costliest item is counting by hand, so... don't. Use ballot scanning and counting machines and then implement a timely partial manual audit to demonstrate that the BMDs and BSCDs functioned correctly.
llukas 8 minutes ago [-]
Full hand count is a feature not a cost. The more people involved and see democracy happen and have actual agency in making it happen the better.
Automating any of the process is (imho) harmful to above.
caaqil 3 hours ago [-]
> Think of the On Trusting Trust problem, the need to verify firmware, etc.
I mean that's too abstract and philosophical of a problem when talking about voting machines/software: there are much more prevalent and concrete risks including but not limited to APT-grade breach/espionage if your country is important enough, and the various other issues (some in your comment itself).
cryptonector 3 hours ago [-]
Yes, of course. See my reply to sibling comment about why a software solution is insufficient, even a soft/hardware solution is insufficient. Cryptography does not save the day. A modicum of physically auditable paper trail is required.
kuratkull 30 minutes ago [-]
I'm Estonian. E-voting is widely accepted and used here. We've been doing it since 2001, and extensivelly (first parliamentary e-voting) since 2007.
The fact that it's open source is long known (at least in the IT community) and highly appreciated.
There's no inherent doubt about its validity in the local expert and international community.
AndroTux 45 minutes ago [-]
Living in Estonia, I have a hard time deciding how I feel about this voting system.
Currently, with people trusting the government, this system is great. I can just cast my vote online, like I do everything else here, and I can be reasonably sure that my vote is counted thanks to the aforementioned trust in the system.
But I really fear the day that trust erodes.
On the other hand, though, once the trust is gone, I think it doesn’t really matter whether it’s an analog or digital count. People won’t trust the system anyways.
Then again, there’s a lot of nuances and different levels of trust, which is the reason why I don’t know what the right answer is.
wavemode 24 minutes ago [-]
The advantage of paper ballots is that the possible ways that the system can be rigged are technologically limited. Either ballots are forged or ballot are miscounted. Both are mitigated by having election officials physically present who validate that voter registrations are valid and that counting is being done accurately, and having those officials be made up of representatives from each participating political party.
Then the defense-in-depth is that paper ballots are inherently decentralized. Even if you manage to pull off a complex operation to rig ballots at a local voting location, you'd have to do the same at hundreds or thousands of other locations to affect the results of the election.
cryptonector 31 minutes ago [-]
It's easier to restore the security of elections run with paper ballots because people can get involved locally. It's not possible to steal numerous paper-based elections in a row -- at some point the thieves' energy/funding runs out and security can be restored. With a digital system, if the system is changed to be vulnerable, or if it always was, then there is no way to recover.
kuratkull 16 minutes ago [-]
I don't agree with this statement. If the system is corrupt (take for example Russia), then the voting system doesn't simply matter. Having absolute access to millions of votes, either digital or on paper, allows any dictator to decide the outcome.
Millions of slips of paper are very easy to burn, and print...
E-votes just make it cheaper/easier to vote in free countries. I don't think we have invented a truly dictator-proof voting system available yet.
icantevenhold 27 minutes ago [-]
> at some point the thieves' energy/funding runs out
I don’t see why that should be the case. If you can influence gov elections every couple of years that seems like a pretty big deal.
On the other hand having the voting source code public and auditable seems like a good way to build trust
devin 2 hours ago [-]
There are a lot of folks who, whenever this topic comes up, seem to have no knowledge of the systems which already exist and have actually been used in real elections already. For instance, ElectionGuard has been used in several real elections in the US since 2020[1].
There's issues that are pretty fundamental with the black-box approach that the electronic ballot becomes. Paper and transparent ballots can be scrutinized pretty easily, but once you have a black box that might also be connected to the internet there's nothing you can really trust.
devin 2 hours ago [-]
[dead]
samat 3 hours ago [-]
Interesting that there are no updates for almost a year. Cool stable software, I guess?
jeff_vader 3 hours ago [-]
Explanation is in the README:
> The intention behind this repository is to make source code of the Estonian online voting system available for public review.
> The repository is not used for active development, but will be kept up to date, so the code that can be found here is the code that is used for election.
3 hours ago [-]
piiritaja 3 hours ago [-]
from README
The repository is not used for active development, but will be kept up to date, so the code that can be found here is the code that is used for election. As the voting system used for legally binding elections must strictly follow the legislation, the actual development of Estonian I-voting system and I-vote verification application is supervised by State Electoral Office of Estonia. Please refer to www.valimised.ee for further information.
cryptonector 2 hours ago [-]
But updates are promised, so GP's question is valid: where are they, and since they're not there, why? Is this the final product's source code and it has not been modified since?
Karliss 2 hours ago [-]
Parliament elections in Estonia happen once every 4 years so don't expect frequent updates. Next one should be in 2027 so there are still ~5 months for them to publish next update. There was also a municipal election in 2025 and European parliament in 2024 which matches last 3 updates in git history. No elections in 2026 so no updates this year.
AntiqueFig 2 hours ago [-]
If I understood correctly they make updates elsewhere, then update this repository only when elections happen, thus making the repository in the exact state it was used for that election.
pelagicAustral 2 hours ago [-]
The answer is paper backed by an ID, but i guess is too late for that.
3 hours ago [-]
3 hours ago [-]
phtrivier 3 hours ago [-]
I know the answer is "you don't", but suppose I vote vote electronically for candidate A. In the end, the candidate loses with 764 votes. How do I convince myself that my vote was counted in the 764 votes, and that it was not a randomly chosen number (with a RNG skewed around "plausible" scores) ?
franga2000 3 hours ago [-]
To take it one step further: how does the election authority convince everyone that their vote was counted?
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)
Groxx 3 hours ago [-]
In this system: I have no idea.
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.
cryptonector 3 hours ago [-]
From that wiki:
> 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.
phtrivier 2 hours ago [-]
Exactly, it means someone you could prove to someone else how you voted, which is the sine qua non condition for creating a vote economy. That's actually the main reason behind trying to keep the vote secret, much more than threats of intimidation for opposing parties voters, etc...
aramend 2 hours ago [-]
There is a separate verification tool I've used that lets me confirm who I voted for, and that the server has registered my vote. Also, like in elections in other places, every election has observers take part. OSCE regularly send their lot, their report on the last parliamentary election can be read here https://odihr.osce.org/odihr/elections/estonia/551179.
phtrivier 2 hours ago [-]
So there is a tool that remembers who you voted for. That's great to convince your bully that you actually did what they told you.
However, how do you know you're one of the X votes displayed in the final tally ?
segmondy 3 hours ago [-]
I think this is an easy enough problem to solve, the issue is that someone else can how force you to reveal who you voted for. Spouse, rouge employers, mafia, corrupt politicians. You can now "sell" your vote.
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.
vincnetas 3 hours ago [-]
Most likely similarly how you know in regular "paper" elections
phtrivier 2 hours ago [-]
I've been an overseer at election booths several times. I kept a good look at the transparent ballot box, along with complete strangers. In the end, once, I may even have inadvertently recognized my envelope and bulletin during the opening and counting - because we where very very few people to choose that candidate in my polling station :D And I was lucky enough to follow the president of the polling station to the town hall where armies of public servant where doing the addition, and I checked the CSV on next Monday, etc, etc...
mmooss 3 hours ago [-]
In theory, it's much easier to fake a number stored electronically in a computer than a large number of paper ballots.
cryptonector 3 hours ago [-]
In practice too. Elections are worth up to trillions of dollars. That means that agencies like state-level actors, and private actors with the necessary resources, will be tempted to mount supply chain and other attacks, and likely will succeed.
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.
juhanima 3 hours ago [-]
You convince yourself the way you do with any elections: you trust the people/system that counts the votes. If you think about it for a second, the requirements of a secret ballot (meaning it's not possible to know who voted who) and the fully verifiability you are asking for are mutually exclusive. You can have either one but not both at the same time.
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.
dataflow 2 hours ago [-]
> If you think about it for a second, the requirements of a secret ballot (meaning it's not possible to know who voted who) and the fully verifiability you are asking for are mutually exclusive.
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.
juhanima 2 hours ago [-]
Yes. Sorry for the condescending tone of "thinking about if for a second". It is actually an interesting problem worthy for a longer time.
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.
cryptonector 1 hours ago [-]
> 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?
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.
seb1204 1 hours ago [-]
You can be a observer in the room when the ballot is counted. So you can monitor if everything was done as intended.
This, and the need for everyday Joe to be able to understand what is done at every step.
cryptonector 3 hours ago [-]
All the source code in the world means nothing when it comes to elections. It's the object code, down to firmwares, BMCs/MEs, even microcode that matters. It's hard to establish trust in those things.
juhanima 2 hours ago [-]
I wouldn't say it means nothing, but you are right in that it is not a silver bullet. It is one piece of a chain of custody to build the trust. Having source code is better than not having it. Having verifiable builds is better than not having them. Having trustworthy hardware is better than not having it. You get the gist?
cryptonector 2 hours ago [-]
I'd rather have a paper-based system, with machines to do the hard labor of counting, and timely partial manual audits. Then I don't have to inspect any source code.
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.
juhanima 2 hours ago [-]
Preferring a paper-based system is your prerogative, that goes without saying. For what it's worth, I'm also partial to the manual system for its robustness.
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.
phtrivier 2 hours ago [-]
Nope. Vote tallying is public with random overseers, in transparent boxes watched by a room of people from diverse opinions, with random inspections - precisely because we DO NOT trust the system or the people who count the vote.
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...
cryptonector 1 hours ago [-]
> I'm all trusting the people writing voting software to do their best, actually.
You are aware of malicious hacking.
maccard 3 hours ago [-]
How do you convince yourself of this in a regular election?
InsideOutSanta 3 hours ago [-]
In a paper election, you have a chain of people who supervise each other. Depending on where you live, you can volunteer to be part of that and see it for yourself.
In code, you have no insight into what actually happens.
himata4113 3 hours ago [-]
Let's say you encounter a mob society that is convinced that there is a very high risk of election fraud and will apply unnecessary scrutiny to votes, a little rip in the paper or ink not matching standards.
trivia: did you know that a tear in any of the pages of your passport renders it invalid?
piiritaja 3 hours ago [-]
Believe it or not there is a chain of people who supervise each other for this e-voting system as well. Anyone can volunteer to be part of it as well.
InsideOutSanta 2 hours ago [-]
How can I volunteer to see the bits in a voting machine's RAM?
cryptonector 2 hours ago [-]
Logic tests only show that the machines worked correctly as of the logic test. It's easy enough to design them to behave correctly in all cases except actual elections.
wavemode 6 minutes ago [-]
> It's easy enough to design them to behave correctly in all cases except actual elections
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.
Rendered at 22:30:47 GMT+0000 (Coordinated Universal Time) with Vercel.
That still leaves tons of other technical problems to address, like security of mail-ballots / absentee ballots, the security of ballot boxes used for early voting (because you probably cannot run the above manual partial audit due to then having nightly results available to the public; or maybe you accept that), voter registration, etc.
Your ID card contains a private key, you use that key to sign a transaction. It doesn't matter that machine you are running on is compromised as these details can be verified at a later date.
Example A: You vote for candidate A, but software changes to candidate B and software displays that you voted for candidate A. At any later time you can check with an independent device and look at the transaction finding out that it was altered with and retract your vote / change it.
Example B: How do you know your vote was counted? Publish a hash and the signature of every vote, recompute the final tally and compare with all the votes. If your vote is not in the final tally the hash will be different and you can visibly see your vote in the dataset as every transaction is published. To preserve privacy each round has a number, private key + number -> new key so each fingerprint will be unique between votes.
I've spent a lot of time thinking about this problem, and my conclusion is that cryptography alone is not the solution, for reasons like:
1. The public needs to believe it, and hypertechnical solutions are a hard sell.
2. Any blockchain approach needs to preserve the secrecy of the ballot, otherwise you get all the problems you can expect of non-secret votes (coercion, vote buying, shaming network effects).
3. You still need to have the cryptographic rubber meet the physical road _somewehere_ -- it has to, otherwise the need for vote secrecy means that the results can be entirely fictitious and pre-programmed and there is no way to check!
I.e., you can have a paperless blockchain solution IFF you abandon vote secrecy. That is a very tough to swallow pill.
On the other hand, if you accept paper ballots and manual partial audits as part of the solution, then blockchain can have a role to play. For example, the machines could display a blockchain head every 50 ballots cast, and voters take a copy of the blockchain head visible to them, then after the election the public can verify the integrity of the blockchain, and the fact that you only get running tallies every 50 ballots means you get vote secrecy.
A system that uses paper ballots and partial manual audits can be explained to the public, and the public can develop confidence in it. Blockchains can then add a good deal of confidence: the blockchain tells you that the tallies were not modified after the fact, and the partial manual audit tells you to an acceptable level of statistical confidence that the digital cast vote record contains the actual paper ballots _as marked and cast_ by voters.
This is false. I know this is a common thought on HN because some formerly popular youtuber did a video about this topic that is still regularly reposted here, but he was already wrong in theory back then and it is certainly wrong in practice today. Secrecy/anonymity and verifiability are no longer mutually exclusive as anyone who is well versed in modern cryptography will be able to tell you.
Also, you still have to convince the public.
There have also been earlier implementations like this one: https://github.com/benadida/helios (corresponding paper https://www.usenix.org/legacy/event/sec08/tech/full_papers/a...), although it still lacked coercion resistance. But it already uses zero knowledge proofs, which is at the core of anonymous yet verifiable systems.
Public doesn't need to know the details. Production of paper, printers is quite complex and so production of the pen. Yet people are not concerned about that when voting and we don't publish schematics of a printer that printed the ballots.
Except that people know what paper looks and feels like, they know how it absorbs ink, they know its various properties, they can _read_ whatever is printed on them, and they can see that the marks they make (or a ballot marking device does for them) are faithfully visible on the paper. With paperless machines there is nothing comparable.
Passports would need to become like hardware wallets with screens such as Trezor. Who's firmware and design are open source.
The screen means I can see what I'm signing and later be shown what I signed.
Now, I don't want people to know who I vote for. So we make it e-passport gate so that no one can enter with me.
Now I want to be able to verify my vote at a later date but not let others know it was me. Well this too is solved by multiple cryptocurrencies like monero and z-cash.
I can go to my local town hall enter a room alone using a e-passport style gate and check my vote at the machine. My device can verify my vote.
Someone with the vote can only see that 1 of N voters did it. Where N is so large they can't identify me.
No duplicate vote is possible.
Literally no one would agree to this however.
I can't claim to be a crypto expert.
But hiding a transaction and it's value among other transactions is perfect for voting.
As I understand it Monero uses ring signatures to make it so it's not possible to know which individual of a group initiated a transaction, and it's zero knowledge proof system means it can be verified that a particular transaction is valid despite this.
To my layman mind that seems to be good enough, every vote can be verified by any party as valid (no double spending or double voting took place).
You can never narrow down who made a particular vote beyond a large pool of people.
You can't tell where any transaction went (you don't know who was voted for).
At the same time with my private key I can see my vote.
The only thing needed for voting is the e-passport style gates.
Certainly it won't just get a case of use monero, they would need to design the system for voting.
Since I'm able to retract my vote, I cannot sell it. And since I can retract my vote, I cannot be coerced in any way.
This enables coercion of voters. It must be impossible to attribute any vote to any specific person.
This implies there is a record establishing a relationship between person A and vote X.
The fact most people won't bother to check it in practice is irrelevant. It must be impossible, because otherwise people are going to die.
There is no problem that electronic voting solves that paper ballots and scanners do not, and the latter are not only more secure but are seen to be more secure. Trust is essential in a voting system and only paper ballots provide the necessary level of trust.
There is a specific problem with mail-in voting and disabled voters, for example elderly people who can't go to the polls and can't get an electronic ballot marker. 25 US states deliver ballots electronically and 15 allow electronic voting for this specific case [1].
[1] https://www.ncsl.org/elections-and-campaigns/electronic-ball...
You also have issues of deanonymization if you only get a couple of ballots in via one method. In Maryland, for example, they're supposed to encourage at least 100 random people to use the accessible ballot marker per precinct for this reason.
It's not reasonable to tell people "too bad," fly back to the US as much as 3 times per year. They pay taxes and are subject to US law even though they're overseas, so they get to vote.
Ballot management becomes error prone. My county alone has 25 ballots due to the different combinations of state house, senate, Federal house, municipalities, and _all_ the special districts. (4 members to the board of directors of the Anytown West Memorial District, a.k.a. cemetery, because they had a property tax assessment when they built the thing in 1950)
I offered nothing of the kind, except as to civilians residing abroad, and even then, I don't think there should be any obligation to provide online voting -- having to travel to a consulate is not too unreasonable.
> It's not reasonable to tell people "too bad," fly back to the US as much as 3 times per year. They pay taxes and are subject to US law even though they're overseas, so they get to vote.
Vote... where? In what state, in what county, in what precinct? The correct answer is that they should not have to pay income taxes while residing abroad, but also not get to vote while residing abroad.
For military the situation is simpler even if the personnel have no US-side residence: use the state/county/precinct of last residence. The same can apply to civilians, but I'd rather let them not pay state and federal income taxes while residing abroad.
> Ballot management becomes error prone. My county alone has 25 ballots due to the different combinations of state house, senate, Federal house, municipalities, and _all_ the special districts. (4 members to the board of directors of the Anytown West Memorial District, a.k.a. cemetery, because they had a property tax assessment when they built the thing in 1950)
That's a small county :)
Or ballot boxes. Where citizen can keep their eyes on their ballot until it is counted.
Even back in 2002, TV channels in France (60m inhabitants) broadcast the winner at 20:00:30, using statistical models.
But recently, they removed the ability for citizen to stay during the counting, relying on designated persons, which breaks the chain of trust. Might as well cast my vote into a black bag or an electronic machine, no trust at all.
Trust was never the goal. As the means of coercion are higher and the capacity of communication is filtered, it becomes unnecessary to involve citizen in voting, isn't it?
In the end, you always must trust humans.
Naive solutions have naive problems.
This seems to make a pretty dramatic change to the election protocol, no?
Consider example A': You vote for candidate A, but later realize that you hate candidate A. You repudiate your recorded vote for candidate A.
What should happen?
Or is this a knee-jerk America Bad?
Only a selected few orgs and groups are allowed to audit and in a very controlled environment because they also rely on security through obscurity. The source code is not available to the citizens.
If by any chance I'm wrong and someone can point me a source code repo, please enlighten me.
https://international.tse.jus.br/en/electronic-ballot-box/pr...
You just need to find the right balance.
In my country we still rely on a paper process - which is very hard to tamper with but also has a bunch of problems - recently we needed to repeat local state elections because of such problems including shortages of ballot papers, unusually long queues to vote, ballots being delivered to the wrong locations, and in some cases voters being turned away. Many of these problems go away with digital voting - but then you have other issues.
I don’t think a perfect solution can exist
Not even a remote access to a demo ballot machine.
Our congress has determined that a paper trail must be implemented but the judges aren't having it.
https://news.ycombinator.com/item?id=36543423
Source code is a red herring too. If there's no reproducible builds that cryptographically establish source-executable correspondence, showing us the source code would prove nothing and only serve to embarrass us. Supply chain attacks could compromise it without any source code vulnerability. What they need to do is publish the signed executables that ran on election day as well as every executable used to construct those artifacts. Our AIs will make short work of the binaries.
In any case, the prevailing theory is that the mesários are partidarian and simply impersonate people who didn't show up to vote in order to boost their candidate's numbers. Very low tech, can be fixed with surveillance: have people from all parties everywhere observing everything. It boggles my mind that this isn't being done already.
That means it doesn't matter one bit how correct you are if the regular Joe does believe you tricked. Adding computers into the mix always makes this worse. And again, this is not something you can fix with clever solutions and cryptography (that admittedly fascinates me nonetheless), the problem is that people can't see electricity generally and I something at the scale of a computer, even if you could it would be utterly meaningless.
This is why the paper ballot system is so glorious in its stupid inefficiency, because it spreads the trust in a way any adult who has mastered object permanence can verify for themselves. Invite the conflicting parties to monitor and have them begrudgingly admit their defeat in the face of the simple, inefficient but agreeable process.
This is why I as a cryptography fan, programmer and hardware guy think electronic voting is not up to the task for high stakes elections.
What is the goal? Having fancy crypto or people being confident about elections?
If spreading the trust is the goal what makes you say "inefficient". It is orders of magnitude better then any crypto system.
While I’m a proponent of the paper process let’s not pretend it immediately means you can be confident about the election
With some abstract math and computers? Any real or imaginary issues are incomprehensible to most of the voters and concerns can be easily shooed away.
The costliest item is counting by hand, so... don't. Use ballot scanning and counting machines and then implement a timely partial manual audit to demonstrate that the BMDs and BSCDs functioned correctly.
Automating any of the process is (imho) harmful to above.
I mean that's too abstract and philosophical of a problem when talking about voting machines/software: there are much more prevalent and concrete risks including but not limited to APT-grade breach/espionage if your country is important enough, and the various other issues (some in your comment itself).
Currently, with people trusting the government, this system is great. I can just cast my vote online, like I do everything else here, and I can be reasonably sure that my vote is counted thanks to the aforementioned trust in the system.
But I really fear the day that trust erodes.
On the other hand, though, once the trust is gone, I think it doesn’t really matter whether it’s an analog or digital count. People won’t trust the system anyways.
Then again, there’s a lot of nuances and different levels of trust, which is the reason why I don’t know what the right answer is.
Then the defense-in-depth is that paper ballots are inherently decentralized. Even if you manage to pull off a complex operation to rig ballots at a local voting location, you'd have to do the same at hundreds or thousands of other locations to affect the results of the election.
Millions of slips of paper are very easy to burn, and print...
E-votes just make it cheaper/easier to vote in free countries. I don't think we have invented a truly dictator-proof voting system available yet.
I don’t see why that should be the case. If you can influence gov elections every couple of years that seems like a pretty big deal.
On the other hand having the voting source code public and auditable seems like a good way to build trust
[1]: https://electionguard.vote/
There's issues that are pretty fundamental with the black-box approach that the electronic ballot becomes. Paper and transparent ballots can be scrutinized pretty easily, but once you have a black box that might also be connected to the internet there's nothing you can really trust.
> The intention behind this repository is to make source code of the Estonian online voting system available for public review.
> The repository is not used for active development, but will be kept up to date, so the code that can be found here is the code that is used for election.
The repository is not used for active development, but will be kept up to date, so the code that can be found here is the code that is used for election. As the voting system used for legally binding elections must strictly follow the legislation, the actual development of Estonian I-voting system and I-vote verification application is supervised by State Electoral Office of Estonia. Please refer to www.valimised.ee for further information.
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)
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.
However, how do you know you're one of the X votes displayed in the final tally ?
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.
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.
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.
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.
This, and the need for everyday Joe to be able to understand what is done at every step.
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.
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.
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.