I've mostly read about them in passing, but a quick google search turns up some results. They seem to rely on at least partially homomorphic encryption.
Interestingly, the NSW iVote seems to share some ideas with helios. They both appear to use ElGamel encryption, which is a [partially] homomorphic algo.
I don't know anything close to enough about ElGamel to comment on their implementation with any authority whatsoever, except to note that it looks very different to others I've seen. The challenge/proof parts in particular look unusual to me - I haven't spent a lot of time looking into their implementation, so it could just be parsing failure on my part, but it doesn't appear at first sight to use the usual fiat-shamel method other ElGamel implementations I've seen tend to.
Interestingly https://vote.heliosvoting.org/faq gives the answer no to "Should we start using Helios for public-office elections?" on the grounds the people's computers are too easily compromised for this to viable. So perhaps the issue is not the protocol at all?
according to the technical paper they don't even attempt to provide any form of coercion-resistance, so that would already fail one of the criteria usually required of public elections.
But yes, computer security certainly is a problem. But I think it's not intractable. We manage to get online-banking to work with acceptably low compromise rates despite huge monetary incentives to attack them.
So maybe if they handed out small, non-personalized cryptographic devices (similar to TAN generators) that can do all the essential operations and talk to a smartphone to retrieve a ballot and submit the vote then e-voting could work.
It would essentially be your own little portable voting booth. It's important though that the device should be separate from the key used to vote, so you could swap devices and re-cast your vote if you consider it compromised for any reason.
