Oh, it is a sort of computer term. I'm not sure how it works, but they feed the input data into a system which outputs a unique number that is specific to the input provided. It's used for encryption stuff mostly. I was kinda jokingly tossing that out there.
Maybe a checksum is more appropriate to what I was talking about, but that is where you read all the bits of a big file, and I guess they add it all up to produce one "sum" value which represents the file, and if any single bit of the file is different from the original, the checksum values differ and you can tell that there was a problem with a transfer or something.
I had not read your notes when I commented. It looks like you have put a lot of thought into the system you came up with, I hope you catch the eye of someone who can really interpret and appreciate what you are trying to say there.
Here is one explanation of "hashing" that I found: http://www.webopedia.com/TERM/H/hashing.html