People have always had a fascination with keeping information away from others. As children, many of us had magic decoder rings for exchanging coded messages with our friends and possibly keeping secrets from parents, siblings, or teachers. History is filled with examples where people tried to keep information secret from adversaries. Kings and generals communicated with their troops using basic cryptographic methods to prevent the enemy from learning sensitive military information. In fact, Julius Caesar reportedly used a simple cipher, which has been named after him.

As society has evolved, the need for more sophisticated methods of protecting data has increased. Now, with the information era at hand, the need is more pronounced than ever. As the world becomes more connected, the demand for information and electronic services is growing, and with the increased demand comes increased dependency on electronic systems. Already the exchange of sensitive information, such as credit card numbers, over the Internet is common practice. Protecting data and electronic systems is crucial to our way of living.

The techniques needed to protect data belong to the field of cryptography. Actually, the subject has three names, cryptography, cryptology, and cryptanalysis, which are often used interchangeably. Technically, however, cryptology is the all-inclusive term for the study of communication over nonsecure channels, and related problems. The process of designing systems to do this is called cryptography. Cryptanalysis deals with breaking such systems. Of course, it is essentially impossible to do either cryptography or cryptanalysis without having a good understanding of the methods of both areas.

Often the term coding theory is used to describe cryptography; however, this can lead to confusion. Coding theory deals with representing input information symbols by output symbols called code symbols. There are three basic applications that coding theory covers: compression, secrecy, and error correction. Over the past few decades, the term coding theory has become associated predominantly with error correcting codes. Coding theory thus studies communication over noisy channels and how to ensure that the message received is the correct message, as opposed to cryptography, which protects communication over nonsecure channels.

Although error correcting codes are only a secondary focus of this book, we should emphasize that, in any real-world system, error correcting codes are used in conjunction with encryption, since the change of a single bit is enough to destroy the message completely in a well-designed cryptosystem.

Modern cryptography is a field that draws heavily upon mathematics, computer science, and cleverness. This book provides an introduction to the mathematics and protocols needed to make data transmission and electronic systems secure, along with techniques such as electronic signatures and secret sharing.