You walk up to the thing and press a big red button. It spits out a confirmation code, like 564263563165465561654 . Just a long ol' string of paper the thing spits out for you.
Because you could lounge around in the line area for a long time, there's no way for anyone to find out what your confirmation code is or who voted how.
You vote and the machine prints a certificate, something hard to forge, detailing your votes and reiterating your confirmation code.
From here you have two options. On the way out of the voting place, there is a confetti shredder you can dump your papers into. Activist groups can lounge around and offer to take your vote, and make sure its on the list. You can do this if you are concerned about your privacy, don't want a paper trail, or just don't care to check up on things.
Anyone who wants to tinker with the machines has no way of knowing who is going to check thier votes and who won't.
The software creates a simple web page with the confirmation codes and how each one voted. Under president, it would say just the last name. Under each ballot measure, it would have the number then yes, the number then no, or the number then null.
Just want to make sure your vote registered correctly? No problem! Just type in your confirmation code 564263563165465561654 and hit find in frame to check it out.
Want to joyfully confirm that only 3 people in your voting district chose Bush? All you gotta do is hit edit, select all, copy, and paste it into Microsoft Word. Then go to search/replace. Replace the word Bush with idiots. A window will pop up saying "Word has made 3 replacements." You can print and manually count, or there's a few other ways, but thats the easiest I can think of. Check for your district, or any district, that its re-reported correctly on the state info, check everything!
The only way I can see that this would be hacked would be to create additional codes but it would be easy for the government to prove it hadn't done that, and therefore hard for it to hide it if it had. How come theres three times more people voting in this pricinct than last year? Can we see the list of names of people who voted here and make sure they are all alive?
Why does it give you the number twice, you ask? Otherwize, it would be easy to hack and program it to assign everyone who votes a certain way the same code and this would prevent that. If you have a dozen things to vote on with five choices each, that would mean that there are only 60 possible combinations of how one would vote. Without the number coming out twice, it would be easy to hack everyone (or large groups) of people who have the exact same choices with the same code each time creating a bogus silent code that votes how the hacker wants.