Cyclic Redundancy Check
One way to verify the integrity of a file which has been moved to a different computer is the cyclic redundancy check (CRC). This is mainly a bit shifting and exclusive or process, not very different from the digital noise generator circuit. However, given modern computing resources, a hardware implementation is hardly necessary, and a few lines of code will do.
This is a program which will check a single file, and some code, too. There are many ways of generating a CRC, of course: Data transfers are verified with a high probability, however, for several different variants of CRC. This is not a way to look for versions of a file which are essentially the same, though: The cyclic redundancy check will almost certainly give a different figure even if a single space is appended to the file.