CRC and How to Reverse It

This essay consists of a CRC tutorial and a way of how to reverse it. Many Coders/Reversers don't know exactly how CRC works and almost no one knows how to reverse it, while this knowledge could be very usefull. First the tutorial will learn you how to calculate CRC in general, you can use it as data/code protection. Second, the reverse part will learn you (mainly) how to reverse CRC-32, you can use this to break certain CRC protections in programs or over programs (like anti-virus). There seem to be utilities who can 'correct' CRCs for you, but I doubt they also explain what they're doing. I'd like to warn you, since there is quite some math used in this essay. This wont harm anyone, and will be well understood by the avarage Reverser or Coder. Why? Well. If you dont know why math is used in CRC, I suggest that you click that button with a X at the top-right of this screen. So I assume the reader has knowledge of binair rithmetic.