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.

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

Combinatorics

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

Turnovers

Clonking

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

Probability

The Friedman Test

The Kasiski Test

Cryptanalyis of Vigenere Keyword Ciphers

8. Hill Ciphers

Matrices

Hill Ciphers

Cryptanalyis of Hill Ciphers

9. RSA Ciphers

Introduction to Public-Key Ciphers

Introduction to RSA Ciphers

The Euclidean Algorithm

Modular Exponentiation

ASCII

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

Bibliography

Hints and Answers for Selected Exercises

Index