Cryptology: Classical and Modern with Maplets

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ISBN 9781439872413
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  • Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine and Navajo code
  • Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Vigenère, and Hill
  • Gives straightforward explanations of the AES, public-key ciphers, and message authentication
  • Requires no prior programming knowledge or background in college-level mathematics
  • Integrates the easy-to-use technology of Maplets throughout
  • Offers material for teaching nonmathematical courses
  • Provides exercises in each chapter section, including some that can be used as projects
  • Presents all Maplet-based examples and exercises in separate sections
  • Supplies Maplet exercises and all of the Maplets used in the text online

Solutions manual available with qualifying course adoption

Watch Drs. Klima and Sigmon speak about the book.


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

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.

Table of Contents

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
ADFGX and ADFGVX Ciphers
A Maplet for ADFGX and ADFGVX Ciphers

The Enigma Machine and Navajo Code
The Enigma Cipher Machine
A Maplet for the Enigma Cipher Machine
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
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
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
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

The Advanced Encryption Standard
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


Hints or Answers to Selected Exercises


Author Bio(s)

Editorial 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