The mathematics behind the security features that the computing industry takes for granted

Throughout this paper I aim to explain mathematical/encryption concepts that are fundamental to security as it was in the past, as it is today and my vision for the future. I shall explain and in some cases actually prove how this theory is applied. Many computing professionals may well have heard of the RSA or the DES algorithm and may even frequently use GUI's (Graphical User Interfaces) to encrypt/decrypt data but may be unaware of the beauty of the mathematics behind it. Without documents like this, the comparatively unprofitable world of mathematical cryptography will not receive the human investment needed to push the boundaries of this frontier. I believe that whilst writing about this subject I must pay tribute to the heroes who founded it. Most importantly I will concentrate on a real world example and go from (or at least close to) the axioms taken for granted right through to the final application.