Non invertible functions — The Daily PPILL #117

This is quite a nerdy one.

One of the things used quite a lot in cryptography, is what are called “non invertible functions”. These are mathematical functions that by operating on something they give you a result, but the inverse function either doesn’t exist, or its output is undefined (meaning that is not unique). Non-invertible functions are used -for example- to encrypt passwords. Before storing a password, you can encrypt it, and if the function utilized is a non-invertible, it would be impossible to know what the password is, the only thing that can be done, is to run the function on the password someone has entered, and check if it matches what it’s in storage.

It is part of what makes passwords secure.

Many of the concepts utilized in cybersecurity come from ages-old concepts and techniques adapted to the modern technology.

That’s how we got “man in the middle”, “bastion”, and -believe it or not- two-factor authentication. Remember the stories about King Arthur or some other powerful being going undercover and then showing a tattoo and a passphrase? What do you think that was about?

So this got me thinking on non-invertible functions outside of these complex mathematical functions. Most of the functions we learn through school are all invertible, making algebra possible. You know, sum has subtraction, sine has arc-sine, etc., so I was hard pressed, except, I was looking in all the wrong places.

It looks like in real life -actually- non-invertible functions are more common than the other type. The typical one is when you recognize that “it is pretty hard to put the toothpaste back into the tube”. When you burn something, it is pretty hard to undo that from the ashes. How could we use this property for other purposes?

As published on The Channelmeister