Hash, CRC, MD5, SHA1, rsync, PowerPC

The idea of hashing predates diff and patch
Theoretically, a hash is an injective, non-invertible, math function
In practice, it's something that represents a file with a number
It's a basic concept people study (and forget) in the first CS course
CRC32: polynomial algorithm run on a bit sequence
The CRC in the "cksum" command is a Posix standard
MD5: message digest, by Dan Rivest
Hash algorithm returning 128 bits, decently secure
SHA1: secure hash algorithm (one)
Hash algorithm returning 160 bits, more secure

rsync is a remarkable application of the hash idea
It allows synchronization of files or file trees
It only exchanges the differences, limiting network traffic
Even PowerPC virtual memory is based on a hash table
Page tables are just one level (on x86 it was 2 levels, now 3)
Memory size, and thus conflict rate, is configurable