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Codes, Cryptology and Curves with Computer Algebra

Codes, Cryptology and Curves with Computer Algebra

Autorzy
Wydawnictwo Cambridge University Press
Data wydania 2017
Liczba stron 606
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9780521520362
Kategorie Algebra
342.30 PLN (z VAT)
$77.00 / €73.39 / £63.71 /
Produkt na zamówienie
Dostawa 5-6 tygodni
Ilość
Do schowka

Opis książki

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. 'The book under review is intended as an introduction to the field for beginning graduate students. The authors do a good job of covering a wide range of topics and keeping the discussion detailed while still as elementary as one can hope to make it.' Darren Glass, MAA Reviews 'While 'coding' may commonly connote confidential communication and security for sensitive data, coding also enters the engineering of information transmission and retrieval, simply for efficient resilience against mechanical error and corrupting noise. From these two purposes rise the two distinct subjects of cryptology and error-correction, receiving here an unusual, unified treatment. Good codes spring from diverse directions, since so many branches of mathematics inform their development: combinatorics, linear algebra, finite fields, ring theory, algebraic geometry, and computer algebra. The girth of this volume reflects the reasonably detailed exposition of all this background material, most of it likely new to engineering students (but students of pure mathematics should also read this book for practical applications of seemingly abstract material they have likely studied). The authors maintain a high level of rigor, keeping all proofs short by astute organization without ever stinting on detail.' D. V. Feldman, Choice 'This book provides a fine exposition of the topics to those students who are novices to the field. At the same time it will also be of interest to readers who are already familiar with some of the concepts discussed in the book. It provides a valuable schematic summary and consolidated overview of the field.' S. V. Nagaraj, SIGACT News I was impressed by the scope of the book: many topics in algebraic coding theory are addressed and now collected in one book. Someone reading the entire book, will obtain a very good overview of algebraic coding theory. Peter Beelen, Nieuw Archief voor Weskunde

Codes, Cryptology and Curves with Computer Algebra

Spis treści

Preface Ruud Pellikaan; 1. Error-correcting codes Ruud Pellikaan and Xin-Wen Wu; 2. Code constructions and bounds on codes Ruud Pellikaan and Xin-Wen Wu; 3. Weight enumeration Relinde Jurrius, Ruud Pellikaan and Xin-Wen Wu; 4. Cyclic codes Ruud Pellikaan; 5. Polynomial codes Ruud Pellikaan; 6. Algebraic decoding Ruud Pellikaan and Xin-Wen Wu; 7. Complexity and decoding Stanislav Bulygin, Ruud Pellikaan and Xin-Wen Wu; 8. Codes and related structures Relinde Jurrius and Ruud Pellikaan; 9. Cryptology Stanislav Bulygin; 10. Groebner bases for coding and cryptology Stanislav Bulygin; 11. Codes on curves Ruud Pellikaan; 12. Coding and cryptology with computer algebra Stanislav Bulygin; References; Index.

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