Algebra for Applications: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression

by Arkadii Slinko

Overview

Modern societies are awash with data that needs to be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorised access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory and can only be properly understood with a good knowledge of these fields. This textbook provides the mathematical tools and applies them to study key aspects of data transmission such as encryption and compression.

Designed for an undergraduate lecture course, this textbook provides all of the background in arithmetic, polynomials, groups, fields, and elliptic curves that is required to understand real-life applications such as cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. It explains in detail how these applications really work. The book uses the free GAP computational package, allowing the reader to develop intuition about computationallyhard problems and giving insights into how computational complexity can be used to protect the integrity of data.

The first undergraduate textbook to cover such a wide range of applications, including some recent developments, this second edition has been thoroughly revised with the addition of new topics and exercises. Based on a one semester lecture course given to third year undergraduates, it is primarily intended for use as a textbook, while numerous worked examples and solved exercises also make it suitable for self-study.

Product Details

ISBN-13:	9783319219516
Publisher:	Springer-Verlag New York, LLC
Publication date:	08/19/2015
Series:	Springer Undergraduate Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
File size:	10 MB

About the Author

Arkadii M. Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand. Before taking this position in 1993 he was a Senior Research Fellow of the interdisciplinary Institute of Systems Analysis of Russian Academy of Sciences in Moscow. He has published extensively in a wide range of journals in mathematics, computer science, economics, and politics. His current research focuses on the mathematics of social choice, game theory, and secret sharing.

Table of Contents

1 Integers.- 2 Cryptology.- 3 Groups.- 4 Fields.- 5 Polynomials.- 6 Secret Sharing.- 7 Error-Correcting Codes.- 8 Compression.- Appendix A: GAP.- Appendix B: Miscellanea.- Solutions to Exercises.- Index.

Editorial Reviews

Brief, but thoughtful, exercise sets are presented throughout the text with worked answers to all exercises provided in an appendix. Overall, this book, part of the ‘Springer Undergraduate Mathematics’ series, is an excellent introduction to modern applications of algebra and number theory for advanced students. Summing Up: Highly recommended. Upper-division undergraduates and graduate students.” (D. S. Larson, Choice, Vol. 53 (10), June, 2016)

“The different topics are well motivated and many examples are interweaves through the text as well as small programs in the computer packages GAP. Appendix A describes this package and gives instructions on how to use it. Also a list of exercises are proposed at the end of each subsection and solutions are provided at the end of the book. Biographical and bibliographical references are given as footnotes and at the end of some chapters.” (Juan Tena Ayuso, zbMATH 1345.94002, 2016)

From the Publisher