Let's say you have two text files that are 50 pages long. You want to know whether they are the same or different. One way you could do this would be to hash them. Hashing (or a hashing function) is a mathematical procedure by which any input is turned into a fixed-length output. There are many of these functions, the most common being SHA-1, SHA-2, and MD5. For instance, here is the output of a hashing function called MD5 with an input of two pages of text:
9a137a78cf0c364e4d94078af1e221be
What's powerful about hashing functions is what happens when I add a single character to the end and run the same function:
8469c950d50b3394a30df3e0d2d14d74
As you can see, the output is completely different. If you want to quickly prove that some data has not been changed in any way, a hash function will do it. For our discussion, here are the important parts...