**Mathematical World**

Volume: 25;
2006;
159 pp;
Softcover

MSC: Primary 11; 94;

Print ISBN: 978-0-8218-3730-6

Product Code: MAWRLD/25

List Price: $32.00

AMS Member Price: $25.60

MAA member Price: $28.80

**Electronic ISBN: 978-1-4704-1195-4
Product Code: MAWRLD/25.E**

List Price: $32.00

AMS Member Price: $25.60

MAA member Price: $28.80

#### Supplemental Materials

# Mathematical Ciphers: From Caesar to RSA

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*Anne L. Young*

A cipher is a scheme for creating coded
messages for the secure exchange of information. Throughout history,
many different coding schemes have been devised. One of the oldest and
simplest mathematical systems was used by Julius Caesar. This is where
Mathematical Ciphers begins. Building on that simple system,
Young moves on to more complicated schemes, ultimately ending with the
RSA cipher, which is used to provide security for the Internet.

This book is structured differently from most mathematics texts. It does not
begin with a mathematical topic, but rather with a cipher. The mathematics is
developed as it is needed; the applications motivate the mathematics. As is
typical in mathematics textbooks, most chapters end with exercises. Many of
these problems are similar to solved examples and are designed to assist
the reader in mastering the basic material. A few of the exercises are
one-of-a-kind, intended to challenge the interested reader.

Implementing encryption schemes is considerably easier with the use of the
computer. For all the ciphers introduced in this book, JavaScript programs
are available from the Web.

In addition to developing various encryption schemes, this book also
introduces the reader to number theory. Here, the study of integers
and their properties is placed in the exciting and modern context of
cryptology. Mathematical Ciphers can be used as a textbook for an
introductory course in mathematics for all majors. The only prerequisite
is high school mathematics.

#### Readership

Undergraduate students interested in number theory, cryptology, and discrete mathematics.

#### Table of Contents

# Table of Contents

## Mathematical Ciphers: From Caesar to RSA

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Caesar Cipher 312 free
- Chapter 3. Terminology and Results from Number Theory 918
- Chapter 4. Modular Arithmetic 1726
- Chapter 5. Describing the Caesar Cipher Mathematically 2736
- Chapter 6. Cryptanalysis for the Caesar Cipher 3140
- Chapter 7. Multiplication Cipher 3746
- Chapter 8. Cryptanalysis for the Multiplication Cipher 4756
- Chapter 9. Multiplication-Shift Cipher 5160
- Chapter 10. Cryptanalysis for the Multiplication-Shift Cipher 5968
- Chapter 11. Non-Mathematical Substitution Ciphers 6978
- Chapter 12. Preparing to Generalize 7584
- Chapter 13. Finding Inverses Modulo n 8190
- Chapter 14. General Multiplication-Shift Cipher 8998
- Chapter 15. Security of the General Multiplication-Shift Cipher 93102
- Chapter 16. Introduction to the Exponential Cipher 103112
- Chapter 17. Deciphering the Exponential Cipher 111120
- Chapter 18. Cryptanalysis for the Exponential Cipher 119128
- Chapter 19. Mathematical Basis for the Exponential Cipher 123132
- Chapter 20. Public Key Ciphers 127136
- Chapter 21. RSA Cipher 131140
- Chapter 22. Signatures 133142
- Chapter 23. Security and Implementation of the RSA Cipher 143152
- Chapter 24. Computer Programs 149158
- Chapter 25. Further Reading 151160
- Chapter 26. Answers to Selected Exercises 153162
- Index 157166
- Back Cover Back Cover1169