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Algebra for Applications

Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression

  • Textbook
  • © 2020

Overview

Authors:
  1. Arkadii Slinko

    1. Department of Mathematics, The University of Auckland, Auckland, New Zealand

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  • Suitable for an undergraduate applied algebra course
  • Covers a wide range of applications of algebra and number theory to information handling, such as encryption and error-correcting codes
  • Uses the free GAP software to illustrate the main concepts
  • Includes numerous worked examples and exercises

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Integers

    • Arkadii Slinko
    Pages 1-39

  3. Cryptology

    • Arkadii Slinko
    Pages 41-77

  4. Groups

    • Arkadii Slinko
    Pages 79-127

  5. Fields

    • Arkadii Slinko
    Pages 129-146

  6. Polynomials

    • Arkadii Slinko
    Pages 147-170

  7. Secret Sharing

    • Arkadii Slinko
    Pages 171-190

  8. Error-Correcting Codes

    • Arkadii Slinko
    Pages 191-234

  9. Compression

    • Arkadii Slinko
    Pages 235-255

  10. Appendix A: GAP

    • Arkadii Slinko
    Pages 257-274

  11. Appendix B: Miscellania

    • Arkadii Slinko
    Pages 275-279

  12. Solutions to Exercises

    • Arkadii Slinko
    Pages 281-361

  13. Back Matter

    Pages 363-368
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, The University of Auckland, Auckland, New Zealand

    Arkadii Slinko

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.

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