In this chapter we consider some aspects of cryptology that have received considerable attention over the last few years. Cryptology is concerned with the designing and the breaking of systems for the communication of secret information. Such systems are called cryptosystems or cipher systems or ciphers. The designing aspect is called cryptography, the breaking is referred to as cryptanalysis. The rapid development of computers, the electronic transmission of information, and the advent of electronic transfer of funds all contributed to the evolution of cryptology from a government monopoly that deals with military and diplomatic communications to a major concern of business. The concepts have changed from conventional (private-key) cryptosystems to public-key cryptosystems that provide privacy and authenticity in communication via transfer of messages. Cryptology as a science is in its infancy since it is still searching for appropriate criteria for security and measures of complexity of cryptosystems.

Conventional cryptosystems date back to the ancient Spartans and Romans. One elementary cipher, the Caesar cipher, was used by Julius Caesar and consists of a single key K = 3 such that a message M is transformed into M + 3 modulo 26, where the integers 0, 1, …, 25 represent the letters A, B, …, Z of the alphabet. An obvious generalization of this cipher leads to the substitution ciphers often named after de Vigenère, a French cryptographer of the 16th century.