The aim of this book is to provide a comprehensive introduction to cryptography without using complex mathematical constructions. The themes are conveyed in a form that only requires a basic knowledge of mathematics, but the methods are described in sufficient detail to enable their computer implementation. The book describes the main techniques and facilities of contemporary cryptography, proving key results along the way. The contents of the first five chapters can be used for one-semester course.

There are two basic methods of error control for communication, both involving coding of the messages. With forward error correction, the codes are used to detect and correct errors. In a repeat request system, the codes are used to detect errors and, if there are errors, request a retransmission. Error detection is usually much simpler to implement than error correction and is widely used. However, it is given a very cursory treatment in almost all textbooks on coding theory. Only a few older books are devoted to error detecting codes. This book begins with a short introduction to the theory...

Covers error-correcting codes, automorphism groups of codes, the key equation for codes from order domains, codes over rings, and theta functions of certain codes. This book contains articles on cryptography - small dimensional varieties, Jacobians of curves, theta functions of hyperelliptic curves, and elliptic curve cryptography.

Presents the successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of information due to interferences in the telecommunications. This book is useful for mathematicians and computer scientists.

The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.

All of the chapters are integrated in a...

This is the proceedings volume of the International Centre for Pure and Applied Mathematics Summer School course held in Ankara, Turkey, in August 2008. Contributors include Greferath, Honold, Landgev, Ling, Lopez, Nebe, Nechaev, zbudak, Sol, Wolfmann and Wood. The aim is to present a survey in fundamental areas and highlight some recent results.