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

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Arkadii Slinko

Algebra for Applications

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

Arkadii Slinko

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English

Springer International Publishing AG
21 May 2025

Discrete mathematics; Algebra; Mathematical theory of computation

Series: Springer Undergraduate Mathematics Series

This textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information.

The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study.

This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version.

By: Arkadii Slinko
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Third Edition 2025
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031826252
ISBN 10: 3031826256
Series: Springer Undergraduate Mathematics Series
Pages: 395
Publication Date: 21 May 2025
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Arkadii Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand.