Introduction to Cryptography with Coding Theory / Edition 2

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Overview

With its conversational tone and practical focus, this text mixes applied and theoretical aspects for a solid introduction to cryptography and security, including the latest significant advancements in the field. Assumes a minimal background. The level of math sophistication is equivalent to a course in linear algebra. Presents applications and protocols where cryptographic primitives are used in practice, such as SET and SSL. Provides a detailed explanation of AES, which has replaced Feistel-based ciphers (DES) as the standard block cipher algorithm. Includes expanded discussions of block ciphers, hash functions, and multicollisions, plus additional attacks on RSA to make readers aware of the strengths and shortcomings of this popular scheme. For engineers interested in learning more about cryptography.

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Product Details

  • ISBN-13: 9780131862395
  • Publisher: Pearson
  • Publication date: 7/15/2005
  • Edition description: 2ND
  • Edition number: 2
  • Pages: 592
  • Sales rank: 643,782
  • Product dimensions: 7.20 (w) x 9.00 (h) x 1.40 (d)

Table of Contents

1 Overview

Secure Communications. Cryptographic Applications

2 Classical Cryptosystems.

Shift Ciphers. Affine Ciphers. The Vige&ngrave;ere Cipher. Substitution Ciphers. Sherlock Holmes. The Playfair and ADFGX Ciphers. Block Ciphers. Binary Numbers and ASCII. One-Time Pads. Pseudo-random Bit Generation. LFSR Sequences. Enigma. Exercises. Computer Problems.

3 Basic Number Theory.

Basic Notions. Solving ax + by = d. Congruences. The Chinese Remainder Theorem. Modular Exponentiation. Fermat and Euler. Primitive Roots. Inverting Matrices Mod n. Square Roots Mod n. Legendre and Jacobi Symbols. Finite Fields. Continued Fractions. Exercises. Computer Problems.

4 The Data Encryption Standard

Introduction. A Simplified DES-Type Algorithm. Differential Cryptanalysis. DES. Modes of Operation. Breaking DES. Meet-in-the-Middle Attacks. Password Security. Exercises.

5 AES: Rijndael

The Basic Algorithm. The Layers. Decryption. Design Considerations.

6 The RSA Algorithm

The RSA Algorithm. Attacks on RSA. Primality Testing. Factoring. The RSA Challenge. An Application to Treaty Verification. The Public Key Concept. Exercises. Computer Problems

7 Discrete Logarithms

Discrete Logarithms. Computing Discrete Logs. Bit Commitment Diffie-Hellman Key Exchange. ElGamal Public Key Cryptosystems. Exercises. Computer Problems.

8 Hash Functions

Hash Functions. A Simple Hash Example. The Secure Hash Algorithm. Birthday Attacks. Multicollisions. The Random Oracle Model. Using Hash Functions to Encrypt.

9 Digital Signatures

RSA Signatures. The ElGamal Signature Scheme. Hashing and Signing. Birthday Attacks on Signatures. The Digital Signature Algorithm. Exercises. Computer Problems.

10 Security Protocols

Intruders-in-the-Middle and Impostors. Key Distribution. Kerberos

Public Key Infrastructures (PKI). X.509 Certificates. Pretty Good Privacy. SSL and TLS. Secure Electronic Transaction. Exercises.

11 Digital Cash

Digital Cash. Exercises.

12 Secret Sharing Schemes

Secret Splitting. Threshold Schemes. Exercises. Computer Problems.

13 Games

Flipping Coins over the Telephone. Poker over the Telephone. Exercises.

14 Zero-Knowledge Techniques

The Basic Setup. The Feige-Fiat-Shamir Identification Scheme. Exercises.

15 Information Theory

Probability Review. Entropy. Huffman Codes. Perfect Secrecy. The Entropy of English. Exercises.

16 Elliptic Curves

The Addition Law. Elliptic Curves Mod n. Factoring with Elliptic Curves. Elliptic Curves in Characteristic 2. Elliptic Curve Cryptosystems. Identity-Based Encryption. Exercises. Computer Problems.

17 Lattice Methods

Lattices. Lattice Reduction. An Attack on RSA. NTRU. Exercises

18 Error Correcting Codes

Introduction. Error Correcting Codes. Bounds on General Codes. Linear Codes. Hamming Codes. Golay Codes. Cyclic Codes. BCH Codes. Reed-Solomon Codes. The McEliece Cryptosystem. Other Topics. Exercises. Computer Problems.

19 Quantum Techniques in Cryptography

A Quantum Experiment. Quantum Key Distribution. Shor’s Algorithm. 4 Exercises.

Mathematica Examples

Maple Examples

MATLAB Examples

Further Reading

Bibliography

Index

Engineers

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Preface

This book is based on a course in cryptography at the upper level undergraduate and beginning graduate level that has been given at the University of Maryland since 1997. When designing the course, we decided on the following requirements.

  • The course should be up-to-date and cover a broad selection of topics from a mathematical point of view.
  • The material should be accessible to mathematically mature students having little background in number theory and computer programming.
  • There should be examples involving numbers large enough to demonstrate how the algorithms really work.

We wanted to avoid concentrating solely on RSA and discrete logarithms, which would have made the course mostly a number theory course. We also did not want to teach a course on protocols and how to hack into friends' computers. That would have made the course less mathematical than desired.

There are numerous topics in cryptology that can be discussed in an introductory course. We have tried to include many of them. The chapters represent, for the most part, topics that were covered during the different semesters we taught the course. There is certainly more material here than could be treated in most one-semester courses. The first eight chapters represent the core of the material. The choice of which of the remaining chapters are used depends on the level of the students.

The chapters are numbered, thus giving them an ordering. However, except for Chapter 3 on number theory, which pervades the subject, the chapters are fairly independent of each other and can be covered in almost any reasonable order. Although we don't recommend doing so, adaring reader could possibly read Chapters 4 through 17 in reverse order, with only having to look ahead/behind a few times.

The chapters on Information Theory, Elliptic Curves, (quantum Methods, and Error Correcting Codes are somewhat more mathematical than the others. The chapter on Error Correcting Codes was included, at the suggestion of several reviewers, because courses that include introductions to both cryptology and coding theory are fairly common.

Computer examples. Suppose you want to give an example for RSA. You could choose two one-digit primes and pretend to be working with fifty-digit primes, or you could use your favorite software package to do an actual example with large primes. Or perhaps you are working with shift ciphers and are trying to decrypt a message by trying all 26 shifts of the ciphertext. This should also be done on a computer. At the end of the book are appendices containing Computer Examples written in each of Mathematica®, Maple®, and MATLAB® that show how to do such calculations. These languages were chosen because they are user friendly and do not require prior programming experience. Although the course has been taught successfully without computers, these examples are an integral part of the book and should be studied, if at all possible. Not only do they contain numerical examples of how to do certain computations but also they demonstrate important ideas and issues that arise. They were placed at the end of the book because of the logistic and aesthetic problems of including extensive computer examples in three languages at the ends of chapters.

Programs available in each of the three languages can be downloaded from the Web site
www.prenhall.com/washington

In a classroom, all that is needed is a computer (with one of the languages installed) and a projector in order to produce meaningful examples as the lecture is being given. Homework problems (the Computer Problems in various chapters) based on the software allow students to play with examples individually. Of course, students having more programming background could write their own programs instead.

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  • Anonymous

    Posted February 16, 2008

    Excellent Book

    I highly, highly recommend this book to anyone who either is taking a course in cryptography in school or wants to learn about it. It is a very well written book which clarifies a lot of basic concepts. I bought it as it was recommended by my professor in school and managed to get an A in the course. It is a good book and I think it helped me come back after a lecture and find all the matter that I needed. Good reference material.

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  • Anonymous

    Posted June 22, 2006

    digital cash and quantum cryptography

    Trappe and Washington give us a very up to date education in cryptography, circa 2005. The discourse is for a sophisticated maths student who, however, need never have encountered cryptography before. The level of mathematical treatment is good and rigourous. With theorems stated and proved at a level that should satisfy even a picky mathematician. The recent nature of the book is reflected in several places. Notably where it explains the Advanced Encryption Standard, or Rijndael. This is significant because it is endorsed by the US National Institute of Standards and Technology as the replacement for DES, in such contexts as electronic commerce. (DES is also covered by the book.) Interestingly, the authors offer a short chapter on digital cash. A fascinating look at a possible future direction of a (physically) cashless society. Other texts on cryptography rarely cover the topic, so it's good to see it here. Yes, the first implementations of digital cash largely died in the dot com crash. But the idea lives on, and may yet take fruit. It has solid intellectual foundations, as shown by the book. Then there is an even more speculative chapter on quantum cryptography. Radically different from the symmetric and public key cryptosystems described in the rest of the book. Who knows how quantum cryptography will turn out? Some very hard physical problems need to be solved.

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