Cryptology : Classical and Modern book cover
2nd Edition

Classical and Modern

ISBN 9781138047624
Published December 3, 2018 by Chapman and Hall/CRC
496 Pages 43 B/W Illustrations

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Book Description

Cryptology: Classical and Modern, Second Edition proficiently introduces readers to the fascinating field of cryptology. The book covers classical methods including substitution, transposition, Alberti, Vigenère, and Hill ciphers. It also includes coverage of the Enigma machine, Turing bombe, and Navajo code. Additionally, the book presents modern methods like RSA, ElGamal, and stream ciphers, as well as the Diffie-Hellman key exchange and Advanced Encryption Standard. When possible, the book details methods for breaking both classical and modern methods.

The new edition expands upon the material from the first edition which was oriented for students in non-technical fields. At the same time, the second edition supplements this material with new content that serves students in more technical fields as well. Thus, the second edition can be fully utilized by both technical and non-technical students at all levels of study. The authors include a wealth of material for a one-semester cryptology course, and research exercises that can be used for supplemental projects. Hints and answers to selected exercises are found at the end of the book.


  • Requires no prior programming knowledge or background in college-level mathematics
  • Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine, Turing bombe, and Navajo code
  • Gives straightforward explanations of the Advanced Encryption Standard, public-key ciphers, and message authentication
  • Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Alberti, Vigenère, and Hill

Table of Contents

1. Introduction to Cryptology

Basic Terminology

Cryptology in Practive

Why Study Cryptology?

2. Substitution Ciphers

Keyword Substitution Ciphers

Cryptanalysis of Substitution Cipher

Playrair Ciphers

The Navajo Code

3. Transposition Ciphers

Columnar Transposition Ciphers

Cryptanalysis of Transposition Ciphers

ADFGX and ADFGVX Ciphers

4. The Enigma Machine

The Enigma Cipher Machine


Security of the Enigma Machine

5. The Turing Bombe

Cribs and Menus

Loops and Logical Inconsistencies

Searching for the Correct Configuration

The Diagonal Board

The Checking Machine



Final Observations

6. Shift and Affine Ciphers

Modular Arithmetic

Shift Ciphers

Cryptanalysis of Shift Ciphers

Affine Ciphers

Cryptanalysis of Affine Ciphers

7. Alberti and Vigenere Ciphers

Alberti Ciphers

Vigenere Ciphers


The Friedman Test

The Kasiski Test

Cryptanalyis of Vigenere Keyword Ciphers

8. Hill Ciphers


Hill Ciphers

Cryptanalyis of Hill Ciphers

9. RSA Ciphers

Introduction to Public-Key Ciphers

Introduction to RSA Ciphers

The Euclidean Algorithm

Modular Exponentiation


RSA Ciphers

Cryptanalyis of RSA Ciphers

Primality Testing

Integer Factorization

The RSA Factoring Challenges

10. ElGamal Ciphers

The Diffie-Hellman Key Exchange

Discrete Logarithms

ElGamal Ciphers

Cryptanalyis of ElGamal Ciphers

11. The Advanced Encryption Standard

Representations of Numbers

Sream Ciphers

AES Preliminaries

AES Encryption

AES Decryption

AES Security

12. Message Authentication

RSA Signatures

Hash Functions

RSA Signatures with Hashing

The Man-in-the-Middle Attack

Public-Key Infrastructures


Hints and Answers for Selected Exercises




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Richard E. Klima is a professor in the Department of Mathematical Sciences at Appalachian State University. Prior to Appalachian State, Dr. Klima was a cryptologic mathematician at the National Security Agency. He earned a Ph.D. in applied mathematics from North Carolina State University. His research interests include cryptology, error-correcting codes, applications of linear and abstract algebra, and election theory. Neil P. Sigmon is a professor in the Department of Mathematics and Statistics at Radford University. Dr. Sigmon earned a Ph.D. in applied mathematics from North Carolina State University. His research interests include cryptology, the use of technology to illustrate mathematical concepts, and applications of linear and abstract algebra.