# Cryptology

## Classical and Modern with Maplets

© 2012 – Chapman and Hall/CRC

548 pages | 163 B/W Illus.

Hardback: 9781439872413
pub: 2012-06-20
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Easily Accessible to Students with Nontechnical Backgrounds

In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used.

Technology Resource

By using the Maplets, students can complete complicated tasks with relative ease. They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator. The Maplets are available for download at www.radford.edu/~npsigmon/cryptobook.html.

A Gentle, Hands-On Introduction to Cryptology

After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers. With a focus on public-key cryptography, the book describes RSA ciphers, the Diffie–Hellman key exchange, and ElGamal ciphers. It also explores current U.S. federal cryptographic standards, such as the AES, and explains how to authenticate messages via digital signatures, hash functions, and certificates.

### Reviews

All told, the authors have done an admirable job of balancing the competing goals of producing a text that can be read by people with limited mathematics background, but at the same time is maintained at a college level. This is not "cryptology for dummies", watered down to the point of uselessness, but is instead a book that, though accessible, requires an appropriate amount of effort and thought on the part of the reader. … This is a book that not only meets but exceeds its goal of being a suitable text for a course in cryptology for non-majors. It is highly recommended for anybody teaching such a course, and it certainly belongs in any good university library.

—Mark Hunacek, MAA Reviews, September 2012

Introduction to Cryptology

Basic Terminology

Cryptology in Practice

Why Study Cryptology?

Substitution Ciphers

Keyword Substitution Ciphers

A Maplet for Substitution Ciphers

Cryptanalysis of Substitution Ciphers

A Maplet for Cryptanalysis of Substitution Ciphers

Playfair Ciphers

A Maplet for Playfair Ciphers

Transposition Ciphers

Columnar Transposition Ciphers

A Maplet for Transposition Ciphers

Cryptanalysis of Transposition Ciphers

Maplets for Cryptanalysis of Transposition Ciphers

The Enigma Machine and Navajo Code

The Enigma Cipher Machine

A Maplet for the Enigma Cipher Machine

Combinatorics

Cryptanalysis of the Enigma Cipher Machine

The Navajo Code

A Maplet for the Navajo Code

Shift and Affine Ciphers

Modular Arithmetic

A Maplet for Modular Reduction

Shift Ciphers

A Maplet for Shift Ciphers

Cryptanalysis of Shift Ciphers

A Maplet for Cryptanalysis of Shift Ciphers

Affine Ciphers

A Maplet for Affine Ciphers

Cryptanalysis of Affine Ciphers

A Maplet for Cryptanalysis of Affine Ciphers

Alberti and Vigenère Ciphers

Alberti Ciphers

A Maplet for Alberti Ciphers

Vigenère Ciphers

A Maplet for Vigenère Keyword Ciphers

Probability

The Friedman Test

A Maplet for the Friedman Test

The Kasiski Test

A Maplet for the Kasiski Test

Cryptanalysis of Vigenère Keyword Ciphers

A Maplet for Cryptanalysis of Vigenère Keyword Ciphers

Hill Ciphers

Matrices

A Maplet for Matrix Multiplication

Hill Ciphers

A Maplet for Hill Ciphers

Cryptanalysis of Hill Ciphers

A Maplet for Cryptanalysis of Hill Ciphers

RSA Ciphers

Introduction to Public-Key Ciphers

Introduction to RSA Ciphers

The Euclidean Algorithm

Maplets for the Euclidean Algorithm

Modular Exponentiation

A Maplet for Modular Exponentiation

ASCII

RSA Ciphers

Maplets for RSA Ciphers

Cryptanalysis of RSA Ciphers

A Maplet for Cryptanalysis of RSA Ciphers

Primality Testing

Integer Factorization

The RSA Factoring Challenges

ElGamal Ciphers

The Diffie–Hellman Key Exchange

Maplets for the Diffie–Hellman Key Exchange

Discrete Logarithms

A Maplet for Discrete Logarithms

ElGamal Ciphers

Maplets for ElGamal Ciphers

Cryptanalysis of ElGamal Ciphers

A Maplet for Cryptanalysis of ElGamal Ciphers

Representations of Numbers

A Maplet for Base Conversions

Stream Ciphers

A Maplet for Stream Ciphers

AES Preliminaries

AES Encryption

AES Decryption

A Maplet for AES Ciphers

AES Security

Message Authentication

RSA Signatures

Hash Functions

RSA Signatures with Hashing

Maplets for RSA Signatures

The Man-in-the-Middle Attack

A Maplet for the Man-in-the-Middle Attack

Public-Key Infrastructures

Maplets for X.509 Certificates

Bibliography

Hints or Answers to Selected Exercises

Index

#### Rick Klima

Boone, North Carolina, USA

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 an associate 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.