**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

AMS Member Price: $39.20

MAA member Price: $44.10

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

List Price: $49.00

AMS Member Price: $39.20

MAA member Price: $44.10

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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
or Steven.Miller.MC.96@ya.yale.edu.

#### Readership

Undergraduate students interested in cryptography and elementary number theory.

#### Reviews & Endorsements

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

-- MAA Reviews

#### 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