I've always been fascinated by encryption & compression, but my favorite is probably the cryptographic hash function. A hash function is a one-way algorithm that takes an input of any size and always produces the same size output. It is one-way in that there is information loss -- you can't easily go from the output to the input again. The cryptographic hash is a more secure version of the hash function. It is most often used in signing to validate that data hasn't been modified.  ...