Series: **Discrete mathematics and its applications**

**Publisher : **
CRC Press - Boca Raton

**Bibliographic : **

- Hardcover Paperback
- ISBN: 0-8493-8521-0
- March 1995, © 1995
- 434 p. ; 24 cm
- Dewey No.: 005.8/2 20

- Coding theory. * Cryptography.

Cryptography is an outstanding new book that provides up-to-date treatments of all the major areas of cryptography in a readable, mathematically precise form. Several chapters deal with especially active areas of research and give the reader a quick introduction and overview of the basic results in the area.

Cryptography provides the mathematical theory that is necessary in order to understand how the various systems work. Most algorithms are presented in the form of pseudocode, together with examples and informal discussion of the underlying ideas. The book gives careful and comprehensive treatment of all the essential core areas of cryptography. Also, several chapters present recent topics that have not received thorough treatment in previous textbooks. Such topics include authentication codes, secret sharing schemes, identification schemes, and key distribution.

**FEATURES:**

- Pseudocode descriptions of all cryptosystems presented in the book
- Numerous worked examples and exercises
- Several figures for a visual representation of certain algorithms or procedures
- Accessible tutorial treatment of certain active research areas, i.e., authentication codes and key distribution
- Manuscript extensively class-tested
- Notes and references for each chapter

**SUPPLEMENTS:** Douglas Stinson's page of this book.

**CONTENTS : **

**Classical Cryptography **
* Introduction: Some Simple Cryptosystems
* Cryptanalysis
* Notes
* Exercises

**Shannon's Theory **
* Perfect Secrecy
* Entropy
* Properties of Entropy
* Spurious Keys and Unicity Distance
* Product Ciphers
* Notes
* Exercises

**The Data Encryption Standard **
* Introduction
* Description of DES
* The DES Controversy
* DES in Practice
* A Time-Memory Trade-Off
* Differential Cryptanalysis
* Notes and References
* Exercises

**The RSA System and Factoring **
* Introduction to Public-Key Cryptography
* More Number Theory
* The RSA Cryptosystem
* Implementing RSA
* Probabilistic Primality Testing
* Attacks on RSA
* The Rabin Cryptosystem
* Factoring Algorithms
* Notes and References
* Exercises

**Other Public-Key Cryptosystems **
* The ElGamal System and Discrete Logarithms
* Finite Field and Elliptic Curve Systems
* The Merckle-Hellman Knapsack System
* The McEliece System
* Notes and References
* Exercises

**Signature Schemes **
* Introduction
* The ElGamal Signature Scheme
* The Digital Signature Standard
* One-Time Signatures
* Undeniable Signatures
* Fail-Stop Signatures
* Notes and References
* Exercises

**Hash Functions **
* Signatures and Hash Functions
* Collision-Free Hash Functions
* The Birthday Attack
* A Hash Function Based on the Discrete Log Problem
* Extending Hash Functions
* Constructing Hash Functions from Private-Key Cryptosystems
* The MD4 Hash Function
* Timestamping
* Notes and References
* Exercises

**Key Distribution and Key Agreement **
* Introduction
* Key Predistribution
* On-Line Distribution by TA
* Certificate-Based Key Transfer
* Diffie-Hellman Key Exchange
* Notes and References

**Identification Schemes **
* Introduction
* The Schnorr Identification Scheme
* The Okamoto Identification Scheme
* The Guillou-Quisquater Identification Scheme
* Converting Identification to Signature Schemes
* Notes and References

**Authentication Codes **
* Introduction
* Computing Deception Probabilities
* Bounds on the Deception Probabilities
* Orthogonal Arrays
* Constructions and Bounds for OAs
* Entropy Bounds
* Notes and References
* Exercises

**Secret Sharing Schemes **
* Introduction: The Shamir Threshold Scheme
* Access Structures and General Secret Sharing
* The Monotone Circuit Construction
* Formal Definitions
* Information Rate
* The Brickell Vector Space Construction
* An Upper Bound on the Information Rate
* The Decomposition Construction
* Notes and References
* Exercises

**Pseudo-Random Number Generation **
* Introduction and Examples
* Indistinguishable Probability Distributions
* The Blum-Blum-Shub Generator
* Probabilistic Encryption
* Notes and References
* Exercises

**Zero-Knowledge Proofs **
* Interactive Proof Systems
* Perfect Zero-Knowledge Proofs
* Bit Commitments
* Computational Zero-Knowledge Proofs
* Notes and References
* Exercises

Includes bibliographical references (p. 413-427) and index.

**BOOK CATEGORY:**
This book can be used as a textbook by senior undergraduate and/or graduate students in
mathematics, computer science, or electrical engineering. It will also be of interest to researchers,
all data communication and security engineers, and practitioners. Students can use the book as an
introduction to the area. Researchers and practitioners will find treatments of specific topics to be
useful to them, for example, to obtain a quick introduction to an unfamiliar area.

Changed 22/01/1997. Comments: monika@cs.ioc.ee