The Code Book - The Evolution of Secrecy from Mary, Queen of Scots to Quantum Cryptography, by Simon Singh
If you have any interest in the history of codemaking and codebreaking (or more accurately ciphermaking and cipherbreaking ), this would be a great place to start. Singh begins with early codebreaking ingenuity such as the Caesar shift (yes, that Caesar) where alphabets are substituted for others, and the powerful technique of frequency analysis for breaking substitution ciphers.
What is frequency analysis? It is a way of breaking codes by looking at the frequency with which alphabets occur in the English language. What is the most frequent letter in the English language? E. In most long passages E will occur more frequently than most, or all other letters. So regardless of which of the other 25 letters are substituted for E, this can always be figured out. Using this basic idea and its variations, frequency analysis cracks any kind of substitution cipher.
From there Singh works all the way up to modern encryption systems, such as those that make internet commerce secure. To make credit card transactions secure, an encryption system called RSA (after its inventors' initials) is currently used. It uses factoring of large prime numbers and the lack of processing power in current computers to maintain security. However as one of the RSA inventors (Adi Shamir of MIT) recently pointed out, manufacturing flaws in computer chips can in fact make the system vulnerable If that were to happen, internet commerce could potentially disappear overnight! Will there ever be an unbreakable cipher? Singh finishes his tale with an interesting description of quantum cryptography and how it could be potentially unbreakable because the very act of trying to break it could destroy the message. Of course, to get there we would need quantum computers and we are quite far away from that day. At least we think we are since no one has publicly acknowledged building one, and in the secret world of codes that is no guarantee that one hasn't been already built.
As an added bonus, there is a Cipher Challenge presented at the end of the book which is a series of increasingly difficult problems with a $10,000 prize. This generated a good amount of interest and was solved one year after publication, but don't let that stop you from trying. The book's website has plenty of related information that will keep you occupied for a long time.
Simon Singh has a PhD in Physics from the University of Cambridge, is an award winning documentary film maker and was made a Member of the Order of the British Empire (MBE) in 2003. He is also the best-selling author of Fermat's Enigma.