Codes and Cryptography on Algebraic Curves

This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

Ruud Pellikaan has tenure at the Technische Universiteit Eindhoven, The Netherlands where his research has shifted from a devotion to coding theory, particularly algebraic geometry codes and their decoding, to code-based cryptography. He previously served as an associate editor of the IEEE Transactions of Information Theory and has organised several conferences.

Xin-Wen Wu is a Senior Lecturer at the School of Information and Communication Technology, Griffith University, Queensland. His research interests include coding theory and information theory, cyber and data security, applied cryptography communications and networks. He has published extensively in these areas and is a senior member of Institute of Electrical and Electronics Engineers (IEEE).

Stanislav Bulygin works as a technology specialist and product manager in the field of IT security and banking services. He previously worked as a researcher focusing on cryptology and IT security at the Technical University of Darmstadt, Germany. His main research activities were connected to the theory of error-correcting codes and their use in cryptography, quantum resistant cryptosystems and algebraic methods in cryptology.

Relinde Jurrius is an Assistant Professor at the Université de Neuchatel, Switzerland. Her research interests are in coding theory, network coding and its connection with other branches of mathematics such as matroid theory, algebraic and finite geometry, and combinatorics. Apart from research and teaching, she is active in organising outreach activities, including a math camp for high school students, a public open day for the Faculty of Science and extra-curricular activities for elementary school children.