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Publisher:

Chapman & Hall/CRC

Publication Date:

2013

Number of Pages:

594

Format:

Hardcover

Series:

Discrete Mathematics and Its Applications

Price:

69.95

ISBN:

9781466561861

Category:

Monograph

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by , on ]

Ellen Ziliak

08/4/2014

Cryptology is the study of the science of creating cipher systems and the art of breaking ciphers. This topic is of increasing interest and relevance in our modern world of online banking, online shopping, email, and the cloud. It is now safe to say that cryptology impacts our daily lives on a regular basis. What’s more, this topic illustrates the beauty of pure mathematics. Many of the results used by cryptologists today stemmed from discoveries in pure mathematics with no intended applications. For example, using Fermat’s Little Theorem from the 17th century, cryptologist have developed schemes in public key cryptography which have allowed us to communicate securely without ever meeting our intended receiver. This invention has dramatically transformed life as we know it.

In *Secret History: The Story of Cryptology* the history and development of this field is presented. The book presents a wonderful story of the development of this field. It is written more like a novel than like your traditional textbook, but it contains all the necessary material to also serve as a textbook. In fact, the author has created a companion website that provides sample syllabi and problems if the book is to be used in the classroom. The syllabi will be especially helpful, as the book contains too many topics to cover in a single semester, so that these recommendations can help an instructor pick a series of topics that make up a meaningful course. The book also serves as a comprehensive reference on the topic of cryptology, from the ancient roots to ciphers of increasing complexity, to a discussion on how machines such as the Enigma were used to transform communication during times of war. Finally the book concludes with a complete discussion of the modern topics of cryptography, including public key cryptography, digital signatures and hashing.

In the classroom I could envision using the book as a resource for class projects. The author does not assume a deep mathematical background; a student in a basic 100 level college math course could understand much of the mathematics presented in this book. Each topic is self-contained, so it would be easy enough to assign a student or a group of students a chapter to study and research further. In addition, each chapter ends with references and further reading which could aid in further investigations.

This book is enjoyable. I would recommend it to anyone interested in learning more about the topic of cryptology. It is especially interesting to someone like me, an algebraist who uses cryptology as a meaningful response to why topics in pure mathematics that do not seem to have obvious applications are still very important to study.

Ellen Ziliak is an Assistant Professor of mathematics at Benedictine University in Lisle IL. Her training is in computational group theory. More recently she has become interested in ways to introduce undergraduate students to research in abstract algebra through applications.

**CLASSICAL CRYPTOLOGY
Ancient Roots**

Caveman Crypto

Greek Cryptography

Viking Cryptography

Early Steganography

**Monalphabetic Substitution Ciphers, or MASCs: Disguises for Messages**

Caesar Cipher

Other MASC Systems

Edgar Allen Poe

Arthur Conan Doyle

Frequency Analysis

Biblical Cryptology

More Frequencies and Pattern Words

Vowel Recognition Algorithms

More MASCs

Cryptanalysis of a MASC

Unsolved Ciphers by a Killer and a Composer

Affine Ciphers

Morse Code and Huffman Coding

MASC Miscellanea

Nomenclators

Cryptanalysis of Nomenclators

Book Codes

**Simple Progression to an Unbreakable Cipher**

Vigenère Cipher

History of the Vigenère Cipher

Cryptanalysis of the Vigenère Cipher

Kryptos

Autokeys

Running Key Cipher and Its Cryptoanalysis

One-Time Pad or Vernam Cipher

Breaking the Unbreakable

Faking Randomness

Unsolved Cipher from 1915

OTPs and the SOE

History Rewritten!

**Transposition Ciphers**

Simple Rearrangements and Columnar Transposition

Cryptanalysis of Columnar Transposition

Historic Uses

Anagrams

Double Transposition

Word Transposition

Transposition Devices

**Shakespeare, Jefferson, and JFK**

Shakespeare vs. Bacon

Thomas Jefferson: President, Cryptographer

Cipher Wheel Cryptanalysis

Playfair Cipher

Playfair Cryptanalysis

**World War I and Herbert O. Yardley**

Zimmermann Telegram

ADFGX: A New Kind of Cipher

Cryptanalysis of ADFGX

Herbert O. Yardley

Peacetime Victory and a Tell-All Book

Case of the Seized Manuscript

Cashing in, Again

Herbert O. Yardley: Traitor

Censorship

**Matrix Encryption**

Levine and Hill

How Matrix Encryption Works

Levine’s Attacks

Bauer and Millward’s Attack

More Stories Left to Tell

**World War II: The Enigma of Germany**

Rise of the Machines

How Enigma Works

Calculating the Keyspace

Cryptanalysis Part 1. Recovering the Rotor Wirings

Cryptanalysis Part 2. Recovering the Daily Keys

After the Break

Alan Turing and Bletchley Park

Lorenz Cipher and Colossus

What If Enigma Had Never Been Broken?

Endings and New Beginnings

**Cryptologic War against Japan**

Forewarning of Pearl Harbor?

Friedman’s Team Assembles

Cryptanalysis of Red, a Japanese Diplomatic Cipher

Purple: How It Works

Purple Cryptanalysis

Practical Magic

Code Talkers

Code Talkers in Hollywood

Use of Languages as Oral Codes

**MODERN CRYPTOLOGY
Claude Shannon**

About Claude Shannon

Entropy

One More Time

Unicity Points

Dazed and Confused

**National Security Agency**

Origins of NSA

TEMPEST

Size and Budget

The *Liberty *and the *Pueblo*

Church Committee Investigations

Post Cold War Downsizing

Some Speculation

2000 and Beyond

Interviewing with NSA

BRUSA, UKUSA, and Echelon

**Data Encryption Standard**

How DES Works

Reactions to and Cryptanalysis of DES

EFF vs. DES

Second Chance

Interesting Feature

Modes of Encryption

**Birth of Public Key Cryptography**

Revolutionary Cryptologist

Diffie-Hellman Key Exchange

RSA: Solution from MIT

Government Control of Cryptologic Research

RSA Patented, Alice and Bob Born Free

**Attacking RSA**

Eleven Non-Factoring Attacks

Factoring Challenge

Trial Division and the Sieve of Eratosthenes (ca. 284–204 BCE)

Fermat’s Factorization Method

Euler’s Factorization Method

Pollard’s *p *– 1 Algorithm

Dixon’s Algorithm

Pollard’s Number Field Sieve

**Primality Testing and Complexity Theory**

Some Facts about Primes

Fermat Test (1640)

Miller-Rabin Test

Deterministic Tests for Primality

Complexity Classes, **P **vs. **NP**, Probabilistic vs. Deterministic

Ralph Merkle’s Public Key Systems

Knapsack Encryption

ElGamal Encryption

**Authenticity**

Problem from World War II

Digital Signatures (and Some Attacks)

Hash Functions: Speeding Things Up

Digital Signature Algorithm

**Pretty Good Privacy**

Best of Both Worlds

Birth of PGP

In Zimmermann’s Own Words

Impact of PGP

Implementation Issues

**Stream Ciphers**

Congruential Generators

Linear Feedback Shift Registers

LFSR Attack

The Cellphone Stream Cipher A5/1

RC4

**Suite B All-Stars**

Elliptic Curve Cryptography (ECC)

Personalities behind ECC

Advanced Encryption Standard (AES)

AES Attacks

**Possible Futures**

Quantum Cryptography: How It Works

Quantum Cryptography: Historical Background

DNA Computing

**Index**

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