So What Do Sea Shells Have To Do With Computer Security?

A Fibonacci sequence is defined by:

and where the current term is the sum of the two previous values. For example, if we start at zero and one, we end up with the sequence of:

0,1,1,2,3,5,8,13,21,34,55...

This series was named after Fibonacci (and who also defined the concept of zero). If we plot the lengths in the spirals get the following:

This type of shape is seen in nature, such as:

The problem we have in computer security is to generate random numbers that cannot be predicted, as we will often generate encryption keys for our tunnelled connections and for encrypted data. We thus need to create a random seed value — typically generated from a truly random event — and then use this to generate a sequence of random values.

We can then generalise the Fibonacci sequence by selecting offset values of j and k, and then defining an operator: