There have been many proposals for direct democracy via the Internet, and they always run into the same two issues: anonymity and fraud.
This scheme works as follows:
1) Distribute Unique "election keys" on paper at polling stations
On the day of "national election key distribution", you go
to what used to be your "polling station". After checking in, you walk through a hallway with 12 (the number could change) tumblers containing little pieces of paper, each tumbler representing a month of the year. You reach in with your own hands and pick a single piece of paper from each tumbler (or are handed such a piece of paper pulled from the tumbler by a Vanna-White-look-alike election worker). The pieces of paper are sealed and can't be distinguished from each other.
2) Vote at home, make "election keys" and their votes public, optionally destroy your own key
Now you have in your possession 12 differently colored pieces of paper with long numbers (and an optional barcode) printed on them. You put these in the safest place you know in your house. Each of these numbers is YOUR unique authentication key for that month's election, but the number is NOT associated with you.
That night, the government publishes 12 large encrypted files for anyone to download. These files contain a list of all authentication keys by region, and the decryption key will not be published until after the election.
When it's time for that month's election, you log on to your government's elections web site using only that month's "election key." (using something like TOR, of course). You fill out a form with that month's election questions, candidates, etc. What is submitted to the "national election system" is a plaintext representation of the form containing your unique ID which you get to verify. It looks something like
1234 1 0 1 5
(Your unique ID, yes on issue 1, no on issue 2, yes on issue 3, candidate #5 for mayor). This will go into another publicly available file that anyone can download.
After voting, you have a choice to make: you can destroy your "election key" for that month and ensure your anonymity, or write down your selections on the back and hold on to it for your part in a distributed recount.
3) Distributed Validation and Challenge
Once the election is over, the government publishes two things:
a) The key to that month's encrypted file containing unique "election keys"
b) Plaintext results of all votes as given above (e.g,, 1234 1 0 1 5)
Validation can then be done by the government and repeated by anyone who is interested to do so. Individuals who chose to keep their pieces of paper with their votes written on it can challenge the election at the expense of their anonymity -- if enough individuals object the election can be declared invalid and the officials responsible punished.