Seriously one of the most important area of mathematics for democracies in an online world.
Homomorphic encryption promises a hidden and verifiable online voting system that does not rely on trusting third party.
Homomorphic encryption promises a hidden and verifiable online voting system that does not rely on trusting third party.
https://www.chaum.com/publications/AccessibleVoterVerifiabil...
The major problem with online voting is that people can be coerced into voting against their wishes outside the watchful eye of election authorities. This may be worth the increase in voting ease, but it's where the real debate is.
Do you just mean the ballots are filled out at home where a government authority is not looking over my shoulder? Because everything else is controlled by the government. The ballots and booklets are printed by the government (who authorize what can be on the ballot and in the booklet), are mailed by a government agency, are checked by a government authority, etc.
I don't think this is currently happening, so I don't think it is a major issue.
Imagine constructing a system that can thwart a abusive, tyrannical father who insists that his wife and children vote for a particular candidate (to make it concrete.) If you can get past him, your voting system passes the first test. Now imagine someone is offering $50 if you vote in a particular way. If there's no way to figure out how someone would claim it, it passes the second test.
The abusive father can literally just fill out all of his family's ballots, and the $50 could be claimed by filling out the ballot in front of the buyer. You could thwart this with allowing multiple votes but only accepting the first, but then the father or buyer could just have the ballots filled out immediately at the first legal moment.
I don't know that it's a thing that can be done without totally private environment around the voter and the record; meaning that the actions of the voter cannot be observed.
There are also countries where turnout is consistently above 70% and there is no mail voting. In the US the obstacles to voting are not having to go to a polling station: voter registration due to not having a federal ID, voting on a Tuesday rather than during the weekend, gerrymandering due to political bodies bring able to affect the redistricting process, and so on.
The only difference I see, is, the mail is sent via the postal service and the online vote is sent via my personal computer and internet connection.
To get around this, the government could issue verified voting tablets that are locked down and use secured connections.
Otherwise, people can force me to vote different without the authorities noticing already.
You cannot easily encrypt your voting information when sent by regular mail. If you have a unique unforgeable id, like a private key, and a secure voting device then your vote can be submitted and counted securely online. Granted, you could print your encrypted vote and mail it in.
The main problem is guaranteeing one vote per eligible voter.
Coercion is a related but smaller problem. It's much harder to coerce most of the people most of the time than it is to stuff the ballot.
Imagine trying to hack the British general election, it would be impossible without hiring millions.
Helios [1], for instance uses an homomorphic scheme.
There are alternatives to it though which preserve voter privacy but allow vote tallying. Shuffling is one of them. Cothority [2] implements an e-voting scheme based on Neff Shuffles
1. https://heliosvoting.org/ 2. https://github.com/dedis/cothority/tree/master/evoting
P.S. I contributed to the latter