Overview
- 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)
Keywords
- 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
About this book
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
About the author
Bibliographic Information
Book Title: Algebra for Applications
Book Subtitle: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression
Authors: Arkadii Slinko
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-030-44074-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-44073-2Published: 02 June 2020
eBook ISBN: 978-3-030-44074-9Published: 01 June 2020
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 2
Number of Pages: XIV, 368
Number of Illustrations: 16 b/w illustrations, 1 illustrations in colour
Topics: Algebra, Information and Communication, Circuits, Discrete Mathematics