This is a really fascinating area of Maths which pretty well everyone uses multiple times every day and is generally totally unaware that they are doing so.
While encryption brings to mind spies and covert communications, probably with sinister overtones, the everyday uses are much more important to everyone and indeed the safety and security of lots of things we do are totally reliant on it.
I’m talking about RSA encryption, which is quite likely a term you’ve never heard of, but is the vital tool that protects your financial transactions, emails, telephone calls among other things.
People have been using codes and ciphers for centuries to keep information private between sender and intended recipient. They started with rather crude methods that were not very secure and gradually evolved with an ongoing battle between code makers and code breakers.
In the early 70s a chap working at GCHQ in the UK came up with an ingenious mathematical method to encipher information which is based on the fact that the mathematical operation of factorisation is actually very very hard to do.
You may think this is nonsense as clearly you are able to factorise numbers easily. Well you’re right to a degree. When numbers are ‘small’ then factorisation is indeed easy as you will either know an answer or can use a calculator and some basic strategies to work it out.
However, if you had a really big number, say 600 digits long, and were simply told this was the product of two large prime numbers, then there is no way you could factorise it. Actually the fastest current supercomputer couldn’t do it either. Well not without an infeasibly long time to work on the problem.
The issue is that mathematicians have not come up with a method to do this other than trial and error despite working on the problem for centuries. And with a really big number there are a massive number of possibilities to try out…
Unfortunately the GCHQ employee who thought up the method did so a bit early as computers in the early 70s were not powerful enough even to encrypt messages via the method, let alone decrypt them. GCHQ archived the method and it was forgotten as a nice theoretical curiosity. Oh, and it was covered by the official secrets act, so remained known to just a handful of GCHQ employees.
A few years later three Americans came up with the same method completely independently. Computers had developed enough by then to be able to deal with the method. They patented it and made millions. It is the encryption method used everywhere today. Called RSA encryption as these are the initial letters of the surnames of the three inventors.
While the Maths gets a bit hairy in places I think it is well worth the effort to try and understand. It’s a classic case of maths that was developed over centuries that was never thought to have any real world application, which eventually has become absolutely essential worldwide. You can access a presentation I put together a couple of years ago which takes you through how RSA encryption works here