# Algebra for Applications

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

Textbook

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

1. Front Matter
Pages i-xiv
Pages 1-36
Pages 37-71
Pages 73-116
Pages 117-131
Pages 133-151
Pages 153-170
Pages 171-211
Pages 213-228
Pages 229-248
Pages 249-251
Pages 253-328

### Introduction

This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory.

This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.

### Keywords

BCH Codes Cryptography Cryptology Elgamal Cryptosystem Elliptic Curves Error-Correcting Codes Euler Totient Function Factorisation Fingerprinting Codes Finite Field Fitingof’s Compression Code Integers Lagrange Interpolation Linear Codes Linear Secret Sharing Scheme Miller-Rabin Pseudoprimality Test Permutation Groups Polynomial Prefix Codes Primality Testing Primes RSA Cryptosystem Reed-Solomon Codes Secret Sharing Scheme Shamir’s Threshold Secret Sharing Scheme

#### Authors and affiliations

• 1
1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-21951-6
• Copyright Information Springer International Publishing Switzerland 2015
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-21950-9
• Online ISBN 978-3-319-21951-6
• Series Print ISSN 1615-2085
• Series Online ISSN 2197-4144
• Buy this book on publisher's site