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Secret History

The Story of Cryptology

By Craig P. Bauer

Chapman and Hall/CRC – 2013 – 620 pages

Series: Discrete Mathematics and Its Applications

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    March 25th 2013


Winner of an Outstanding Academic Title Award from CHOICE Magazine

Most available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment of both the mathematics and history of cryptology. Requiring minimal mathematical prerequisites, the book presents the mathematics in sufficient detail and weaves the history throughout the chapters. In addition to the fascinating historical and political sides of cryptology, the author—a former Scholar-in-Residence at the U.S. National Security Agency (NSA) Center for Cryptologic History—includes interesting instances of codes and ciphers in crime, literature, music, and art.

Following a mainly chronological development of concepts, the book focuses on classical cryptology in the first part. It covers Greek and Viking cryptography, the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson’s cipher wheel, the Playfair cipher, ADFGX, matrix encryption, World War II cipher systems (including a detailed examination of Enigma), and many other classical methods introduced before World War II.

The second part of the book examines modern cryptology. The author looks at the work of Claude Shannon and the origin and current status of the NSA, including some of its Suite B algorithms such as elliptic curve cryptography and the Advanced Encryption Standard. He also details the controversy that surrounded the Data Encryption Standard and the early years of public key cryptography. The book not only provides the how-to of the Diffie-Hellman key exchange and RSA algorithm, but also covers many attacks on the latter. Additionally, it discusses Elgamal, digital signatures, PGP, and stream ciphers and explores future directions such as quantum cryptography and DNA computing.

With numerous real-world examples and extensive references, this book skillfully balances the historical aspects of cryptology with its mathematical details. It provides readers with a sound foundation in this dynamic field.


"Every once and a while a book appears that has a significant impact on the field of cryptologic history. David Kahn’s The Codebreakers and F.L. Bauer’s Decrypted Secrets are two such books. Secret History now joins that collection. … Secret History could be used as a textbook for a general education class that explores the history of cryptology (and ignores many of the mathematical sections) or for an upper-division class for mathematics or computer science majors that follows the historical evolution of cryptology (and pays attention to the mathematical sections). … What would appeal to a general audience is the engaging writing that reflects Bauer’s interest in and enthusiasm for all aspects of cryptology. … Bauer has merged cryptologic history with the mathematical foundations of cryptology in a correct, understandable, and enthusiastic presentation. Secret History is an excellent choice for a historian of cryptology, a teacher of cryptology, or anyone who wants to get a glimpse of cryptology."

—Chris Christensen, Cryptologia

"… one of the most engaging storytelling adventures on the evolution of secret keeping. In the first part of the book, Bauer (York College of Pennsylvania; formerly, scholar-in-residence, National Security Agency) discusses the inception of secret codes in Viking messages and substitution ciphers in the era of Caesar, as well as cryptography in works of fiction such as Edgar Allen Poe’s short story "The Gold Bug." Of course, Bauer also covers the famous Bletchley Park and its enigmatic star, Alan Turing. The second part focuses on current uses of cryptography and ends with a discussion of quantum cryptography. The book will challenge anyone with even a passing interest in cryptography to try to resist developing an intense passion for it. The math behind the systems described, while present, is never obscured by the fascinating setting in which it was developed. This is the way in which cryptography, one of the most difficult applications of discrete mathematics, was meant to be learned, with real-life cloak-and-dagger intrigue. Summing Up: Highly recommended. All levels/libraries."

—T.D. Richardson, CHOICE, Vol. 51, 2013

"… looking at the table of contents it appears EXCELLENT. The field is covered thoroughly and comprehensively and in a very up-to-date manner. It is by far the clearest and most comprehensive of the books dealing with the new cryptology, including of course the classic ciphers and some of the important historical ones such as Enigma and Purple, but also the newer systems such as DES and public-key cryptography. The history seems accurate and the book provides what I was unable to give cryptology—a mathematical underpinning to it all. … All of us in the cryptology community are grateful to you for it."

—David Kahn, historian, and author of The Codebreakers

"There have been plenty of 'light reading' books covering the history and mechanics of cryptology - this isn't one of them. Most focus on light math concepts and/or history - this isn't one of them. Instead, it covers both but provides much more depth and detail, surveying the political side of cryptology's developments, the use of codes in crime, music and literature, and considering how classical cryptology grew from Greek to modern times. It provides close examination of the groundbreaking works of cryptologists and considers specific algorithms and their functions, and it provides charts, graphs and calculations to show exactly how cryptology works. Any with more than a casual interest in the topic will find this a solid reference."

—California Bookwatch, January 2014



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


Cryptanalysis of Nomenclators

Book Codes

Simple Progression to an Unbreakable Cipher

Vigenère Cipher

History of the Vigenère Cipher

Cryptanalysis of the Vigenère Cipher



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


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


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


Claude Shannon

About Claude Shannon


One More Time

Unicity Points

Dazed and Confused

National Security Agency

Origins of NSA


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


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


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


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


References and Further Reading appear at the end of each chapter.

Author Bio

Craig P. Bauer is an associate professor of mathematics at York College of Pennsylvania and the editor-in-chief of Cryptologia. He was the 2011-2012 Scholar-in-Residence at the National Security Agency (NSA) Center for Cryptologic History, where he wrote several papers for NSA journals, gave a large number of lectures, and made substantial progress on a second book focused on unsolved codes and ciphers. He earned a Ph.D. in mathematics from North Carolina State University.

Related Subjects

  1. Cryptology
  2. Combinatorics

Name: Secret History: The Story of Cryptology (Hardback)Chapman and Hall/CRC 
Description: By Craig P. Bauer. Winner of an Outstanding Academic Title Award from CHOICE Magazine Most available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment of...
Categories: Cryptology, Combinatorics