One of the most fascinating areas of information and network security, in my opinion, is the area of cryptography.  In truth, many aspects of cryptography still baffle me but it also the one area that really piques my interest.  I recall my first steps into the cryptographic realm and wondered how anyone was able to comprehend it all.  At the time, my mathematical foundation was weak so understanding the ideas presented to me were confusing.  Much of cryptography, from a mathematical perspective, has its roots in number theory which is the branch of pure mathematics concerned with the properties of numbers in general (integers in particular).  To be more precise, the sub-field of computational number theory which is the study of algorithms relevant in number theory, specifically fast algorithms for prime testing (3, 5, 7, etc.) and integer factorization, is where cryptography resides in the mathematical world.

So, what is cryptography and why should anyone care about it?  Cryptography is the art of transforming a message into an intermediate form that contains the same information as the original message but is hidden or secret to anyone who does not know how to reverse the transformation.  In layman’s terms, it is the science writing in secret code.  Before I supply an example let me use and clarify the proper terminology for this meaning.  A message exists in plain text which means anyone who understands the language the message was written in is able to understand it.  This is how all messages exist prior to the cryptographic process taking place.  The information is always used and understood in plain text form to one or more persons.  Once a message has undergone the cryptographic process of transforming it from a plain text message into a secret message, it is called a cipher text.  Let’s review this quickly.  A message existing in plain text undergoes a cryptographic process and becomes cipher text.

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