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Algebra for Applications

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

  • 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 Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Arkadii Slinko
    Pages 1-39
  3. Arkadii Slinko
    Pages 41-77
  4. Arkadii Slinko
    Pages 79-127
  5. Arkadii Slinko
    Pages 129-146
  6. Arkadii Slinko
    Pages 147-170
  7. Arkadii Slinko
    Pages 171-190
  8. Arkadii Slinko
    Pages 191-234
  9. Arkadii Slinko
    Pages 235-255
  10. Arkadii Slinko
    Pages 257-274
  11. Arkadii Slinko
    Pages 275-279
  12. Arkadii Slinko
    Pages 281-361
  13. Back Matter
    Pages 363-368

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 computationally hard 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.


public key cryptography Secret key cryptography RSA Cryptosystem BCH Code Elgamal Cryptosystem Shamir’s Secret Sharing Scheme digital signature Diffie-Hellman ideal secret sharing scheme Huffman compression code Fitingof Compression Code Error-Correcting Codes Euler Totient Function Fingerprinting Codes Lagrange Interpolation Linear Secret Sharing Scheme Miller-Rabin Pseudoprimality Test Prefix Codes Primality Testing Reed-Solomon Codes

Authors and affiliations

  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand

About the authors

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.

Bibliographic information