**Student Mathematical Library**

Volume: 18;
2002;
229 pp;
Softcover

MSC: Primary 94;
Secondary 11; 68

**Print ISBN: 978-0-8218-2986-8
Product Code: STML/18**

List Price: $51.00

Individual Price: $40.80

**Electronic ISBN: 978-1-4704-2132-8
Product Code: STML/18.E**

List Price: $48.00

Individual Price: $38.40

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# Cryptography: An Introduction

Share this page *Edited by *
*V. V. Yaschenko*

Learning about cryptography requires examining fundamental
issues about information security. Questions abound, ranging from
“From whom are we protecting ourselves?” and “How
can we measure levels of security?” to “What are our
opponent's capabilities?” and “What are their
goals?” Answering these questions requires an understanding of
basic cryptography. This book, written by Russian cryptographers,
explains those basics.

Chapters are independent and can be read in any order. The introduction
gives a general description of all the main notions of modern
cryptography: a cipher, a key, security, an electronic digital
signature, a cryptographic protocol, etc. Other chapters delve more
deeply into this material. The final chapter presents problems and
selected solutions from “Cryptography Olympiads for (Russian) High
School Students”.

This is an English translation of a Russian textbook. It is suitable for
advanced high school students and undergraduates studying information
security. It is also appropriate for a general mathematical audience
interested in cryptography.

Also on cryptography and available from the AMS is Codebreakers: Arne Beurling and the Swedish Crypto Program during World War II .

#### Readership

Undergraduates, graduate students, and research mathematicians interested in cryptography; general mathematical audience.

#### Reviews & Endorsements

It is a … book with a lot of useful information.

-- Cryptologia

Students and faculty alike will find this book to be an excellent guide/reference to cryptography … concepts are explained clearly … The book also contains some interesting examples of cryptography in literature … Each chapter is self-contained … This book is a smorgasbord of cryptography and covers all the major concepts. So read what you like to enjoy … Lando's Lectures on Generating Functions … is driven by very, very interesting problems and examples … he can hardly contain his enthusiasm (which is indeed quickly infectious) … author's particular choice of topics, it's really all an immense amount of fun … The book is very well suited to self study or use in a seminar for a hand-picked audience … beautifully written … a trip well worth taking.

-- MAA Online

#### Table of Contents

# Table of Contents

## Cryptography: An Introduction

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Preface vii8 free
- Chapter 1. Main Notions 112 free
- Chapter 2. Cryptography and Complexity Theory 2132
- Chapter 3. Cryptographic Protocols 3950
- §1. Introduction 3950
- §2. Integrity. Authentication and electronic signature protocols 4253
- §3. Untraceability. Electronic money 6071
- §4. Coin flipping by telephone protocols 6879
- §5. More about secret sharing 7485
- §6. Playing building blocks, or Election protocols 7788
- §7. Beyond standard assumptions. Confidential message transmission 8394
- §8. In place of a conclusion 8697

- Chapter 4. Algorithmic Problems of Number Theory 8798
- §1. Introduction 8798
- §2. The RSA cryptosystem 89100
- §3. Complexity of number-theoretic algorithms 93104
- §4. How to distinguish between a composite and a prime number 99110
- §5. How to construct large prime numbers 102113
- §6. How to test primality of a large number 105116
- §7. How to factorize a composite number 110121
- §8. Discrete logarithms 114125
- §9. Conclusion 120131

- Chapter 5. Mathematics of Secret Sharing 121132
- Chapter 6. Cryptography Olympiads for High School Students 135146
- Bibliography 225236
- Back Cover Back Cover1241