**Mathematical World**

Volume: 29;
2013;
332 pp;
Softcover

MSC: Primary 94; 68; 01;

Print ISBN: 978-0-8218-8321-1

Product Code: MAWRLD/29

List Price: $49.00

Individual Member Price: $39.20

**Electronic ISBN: 978-1-4704-1594-5
Product Code: MAWRLD/29.E**

List Price: $49.00

Individual Member Price: $39.20

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#### Supplemental Materials

# The Mathematics of Encryption: An Elementary Introduction

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*Margaret Cozzens; Steven J. Miller*

How quickly can you compute the remainder when dividing \(109837^{97}\) by 120143? Why would you even want to compute this? And what does this have to do with cryptography?

Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online.

This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

A complete solution key is available for instructors upon
request. Send email to
Steven.J.Miller@williams.edu

#### Table of Contents

# Table of Contents

## The Mathematics of Encryption: An Elementary Introduction

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Acknolwedgments xi12 free
- Preface xiii14 free
- Historical introduction 120 free
- Classical cryptology: Methods 1938
- Enigma and Ultra 5170
- Classical cryptography: Attacks I 81100
- Classical cryptography: Attacks II 113132
- Modern symmetric encryption 133152
- Introduction to public-channel cryptography 171190
- Public-channel cryptography 213232
- Error detecting and correcting codes 239258
- Modern cryptography 269288
- Primality testing and factorization 289308
- Solutions to selected exercises 317336
- Bibliography 325344
- Index 329348 free
- Back Cover Back Cover1354

#### Readership

Undergraduate students interested in cryptography and elementary number theory.

#### Reviews

The authors have done an excellent job of presenting this material in as painless and accessible way as possible.

-- MAA Reviews