You're voting for who?!?

Recently there has been a lot of complaining about having to publicly announce your party of choosing on primary day. Although I agree that this should be kept private, I think that there is another issue that is more important. There is no proof that your vote even was recorded. No paper trail. Now, I use a computer (obviously). I know that more than once I've saved something on my computer only to find out later that it never saved. I've had computers lose files. I've even had once lose an entire hard drive. I'm sure you've had similar problems. My point is that these all-electronic machines have no back-ups. What if someone bumps the machine and it loses memory? What if someone for whatever reason walks up to the machine with a magnet, erasing the entire day's worth of votes? It has already been proven that a virus could be uploaded to the machines to alter the outcomes of an election.
My proposal is this: We need a machine that gives out a hard copy for voters to check over themselves. These hard-copies are then used to count the vote, NOT THE MACHINES. You can verify a person, you can not verify a computer.