>>> ... but how you will distinguish fake votes from real ones?

Easy. Serial numbers. Like any other anonymous system (paper money, raffle tickets etc) you assign a number to every valid ballot. Should the same number appear twice, or not appear, then you know something fishy is happening. Any extra fake ballots should be discovered, so long as the originals are not removed from the systems. Throw the numbers around randomly and creating undetectable fakes become very difficult.

> Yep, you can recount fake paper votes, but how you will distinguish fake votes from real ones?

You already have a log of who showed up to vote. Compare the number of shows S with the number of ballots V which must be <= S due to poorly marked/unreadable ballots. Simple.

Edit: and this all statistically correlates with exit polls. It's very, very hard to fake all three of these in order to rig an election.

Explain "fake paper votes". I'm not sure that this is a real problem with normal auditing -- record all voters that come into a precinct, what time they appear, and compare to the number of received ballots. Comparing signatures of voters to the file signature is common for absentee voting. It's just far harder and riskier to mess around with compromising paper ballots than a mistake (or "mistake") in a line of code.