codes - the guide to secrecy from ancient to modern times

Codes
The Guide to Secrecy
from Ancient
to Modern Times
Juergen Bierbrauer
, Introduction to Coding Theory
Kun-Mao Chao and Bang Ye Wu,
Spanning Trees and Optimization Problems
Charalambos A. Charalambides,
Enumerative Combinatorics
Charles J. Colbourn and Jeffrey H. Dinitz,
The CRC Handbook of Combinatorial Designs
Steven Furino, Ying Miao, and Jianxing Yin,
Frames and Resolvable Designs: Uses,
Constructions, and Existence
Randy Goldberg and Lance Riek,
A Practical Handbook of Speech Coders
Jacob E. Goodman and Joseph O’Rourke,
Handbook of Discrete and Computational Geometry,
Second Edition
Jonathan Gross and Jay Yellen,
Graph Theory and Its Applications
Jonathan Gross and Jay Yellen,
Handbook of Graph Theory
Darrel R. Hankerson, Greg A. Harris, and Peter D. Johnson,
Introduction to Information
Theory and Data Compression, Second Edition
Daryl D. Harms, Miroslav Kraetzl, Charles J. Colbourn, and John S. Devitt,
Network Reliability:
Experiments with a Symbolic Algebra Environment

Derek F. Holt with Bettina Eick and Eamonn A. O’Brien
, Handbook of Computational Group Theory
David M. Jackson and Terry I. Visentin,
An Atlas of Smaller Maps in Orientable and
Nonorientable Surfaces
Richard E. Klima, Ernest Stitzinger, and Neil P. Sigmon,
Abstract Algebra Applications
with Maple
Patrick Knupp and Kambiz Salari,
Verification of Computer Codes in Computational Science
and Engineering
William Kocay and Donald L. Kreher
, Graphs, Algorithms, and Optimization
Donald L. Kreher and Douglas R. Stinson,
Combinatorial Algorithms: Generation Enumeration
and Search
Charles C. Lindner and Christopher A. Rodgers,
Design Theory
Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone,
Handbook of Applied
Cryptography
Series Editor
Kenneth H. Rosen, Ph.D.
and
DISCRETE
MATHEMATICS
ITS APPLICATIONS
Continued Titles
Richard A. Mollin,
Algebraic Number Theory

Richard A. Mollin
, Codes: The Guide to Secrecy from Ancient to Modern Times
Richard A. Mollin,
Fundamental Number Theory with Applications
Richard A. Mollin,
An Introduction to Cryptography
Richard A. Mollin,
Quadratics
Richard A. Mollin,
RSA and Public-Key Cryptography
Kenneth H. Rosen,
Handbook of Discrete and Combinatorial Mathematics
Douglas R. Shier and K.T. Wallenius,
Applied Mathematical Modeling: A Multidisciplinary
Approach
Jörn Steuding
, Diophantine Analysis
Douglas R. Stinson,
Cryptography: Theory and Practice, Second Edition
Roberto Togneri and Christopher J. deSilva,
Fundamentals of Information Theory and
Coding Design
Lawrence C. Washington,
Elliptic Curves: Number Theory and Cryptography

Series Editor KENNETH H. ROSEN
DISCRETE MATHEMATICS AND ITS APPLICATIONS
Boca Raton London New York Singapore
Richard A. Mollin
Codes

The Guide to Secrecy
from Ancient
to Modern Times
Published in 2005 by
Chapman & Hall/CRC
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2005 by Taylor & Francis Group, LLC
Chapman & Hall/CRC is an imprint of Taylor & Francis Group
No claim to original U.S. Government works
Printed in the United States of America on acid-free paper
10987654321
International Standard Book Number-10: 1-58488-470-3 (Hardcover)
International Standard Book Number-13: 978-1-58488-470-5 (Hardcover)
Library of Congress Card Number 2005041403
This book contains information obtained from authentic and highly regarded sources. Reprinted material is
quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts
have been made to publish reliable data and information, but the author and the publisher cannot assume
responsibility for the validity of all materials or for the consequences of their use.
No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic,
mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and
recording, or in any information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com
( or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive,
Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration
for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate
system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only
for identification and explanation without intent to infringe.

Library of Congress Cataloging-in-Publication Data
Mollin, Richard A., 1947-
Codes: the guide to secrecy from ancient to modern times / Richard A. Mollin.
p. cm.
Includes bibliographical references and index.
ISBN 1-58488-470-3 (alk. paper)
1. Computer security. 2. Data encryption (Computer science) I. Title.
QA76.9.A25M67 2005
005.8'2 dc22 2005041403
Visit the Taylor & Francis Web site at

and the CRC Press Web site at

Taylor & Francis Group
is the Academic Division of T&F Informa plc.
C4703_Discl.fm Page 1 Friday, April 8, 2005 1:36 PM
Preface
This book has been written with a broad spectrum of readers in mind, which
includes anyone interested in secrecy and related issues. Thus, this is a tome
for the merely curious, as well as history-minded readers, amateur mathemati-
cians, engineers, bankers, academics, students, those practitioners working in
cryptography, specialists in the field, and instructors wanting to use the book
for a text in a course on a variety of topics related to codes. We will look at
this topic from all aspects including not only those related to cryptography (the
study of methods for sending messages in secret), but also the notion of codes
as removal of noise from telephone channels, satellite signals, CDs and the like.
The uninitiated reader may consider the following. Imagine a world where
you can send a secret message to someone, and describe to anyone listening
in precise detail how you disguised the message. Yet that person could not
remove the disguise from that message no matter how much time or how many

resources are available. Well, that world exists in the here and now, and the
methodology is called public-key cryptography. It permeates our lives, from the
use of a bank card at an automated teller machine ATM to the buying of items
or bank transactions over the Internet. You can even purchase items over the
Internet and do so anonymously, as you would using hard cash. In this book,
you will find out how this is done.
Do you ever wonder how secure your private conversation is over a cell phone?
In general, they are not secure at all. In this book, you will find out how they
can be made secure. And those transactions over the Internet, just how secure
are they? Can these methods be trusted? In this text, you will learn which
methodologies are secure and which are not. Here is an excerpt from the end
of Chapter 2 that is apt. “What made all of the above not just possible, but
rather a necessity — that good old mother of invention — was the advent of
the Internet. While information secrecy, as we have seen throughout history,
was strictly the purview of governments and their agents, the Internet, and its
associated e-mail and e-commerce activities, demanded a mechanism for the
ordinary citizen to have their privacy concerns addressed. Few of us actually
understand the mechanisms behind all of these protocols that we use every
day (although this book will foster that understanding), yet cryptography has
become everybody’s business, hence everybody’s concern. Therefore it is almost
a personal duty that each of us learn as much as possible about the underlying
mechanisms that affect our security, our privacy, and therefore our well-being.”
What are smart cards and how do they affect your life? This book reveals
the answers. What are biometrics and how do they affect you? Several of your
identity characteristics such as fingerprints, retinal data, voice prints, and facial
geometry, to mention a few, can be embedded in smart cards to identify you
to a bank, for instance. Perhaps you have allergies to some medicines, such as
penicillin, and this information can be embedded in a medical smart card so
that in the event of an accident, appropriate measures can be taken that may
save your life. Read this book to find out how this is done.

vii
viii
How did all this begin and where is it headed? Read Chapter 1 to learn
about the rumblings of the art of secrecy carved in stone almost four millennia
ago and how it evolved to the present where it permeates nearly every aspect
of your life.
◆ Features of This Text
• The text is accessible to virtually anyone who wishes to learn the issues
surrounding secrecy. To this end, Appendix A contains all necessary mathe-
matical facts for the novice, or as a fingertip reference for the initiated. Other
appendices, such as Appendix E, contain the requisite probability theory for
background needed to understand Information and Coding Theory in Chapter
11, for instance. Moreover, the main text is geared to gently introduce the
necessary concepts as they arise. The more difficult or advanced topics are
marked with the pointing hand symbol ☞ for the more advanced (or adventur-
ous) reader.
• There are nearly 200 examples, diagrams, figures, and tables throughout
the text to illustrate the history and concepts presented.
• More than 200 footnotes pepper the text as further routes for information-
gathering. Think of these as analogues of hyperlinks in the Internet (see page
328), where you can click on a highlighted portion to get further information
about a given topic, or ignore it if you already have this knowledge or are not
interested. These links provide avenues to pursue information about related
topics that might be of separate interest to a wide variety of readers.
• There are more than 80 mini bibliographies throughout the text of those
who helped to develop the concepts surrounding codes, as well as historical data
in general to provide the human side of the concepts introduced.
• There are just under 300 references for further reading in the bibliography.
This provides further pointers for the reader interested in pursuing topics of
interest related to what is presented herein. Moreover, it provides the foundation

for the facts presented.
• The index has nearly 5000 entries, and has been devised in such a way to
ensure that there is maximum ease in getting information from the text.
• To the instructor who wishes to give a course from this text: There are
more than 370 exercises in Appendix G separated according to chapter and even
the appendices A–F. (Some are marked with a ✰ symbol for those particularly
challenging problems.) The wealth of material in this book allows for more
than one course to be given on various aspects of secrecy and even a mini-
course in coding and information theory (see Chapter 11). With nearly 50
Theorems, Propositions, and related material, and more than 60 equations, the
background is amply covered. Moreover, this text is self-contained so that no
other reference is needed since the aforementioned appendices have all possible
background and advanced material covered in detail (see the Table of Contents
for the information covered in each appendix).
• The webpage cited below will contain a file for updates. Furthermore,
comments via the e-mail address below are also welcome.
ix
◆ Acknowledgments: The author is grateful to various people for their
time in proofreading various aspects of this project. Thanks go to Professor John
Brillhart, who received portions pertaining to his expertise, and as a pioneer
in computational number theory with his seminal work in primality testing
and factoring, it is an honour to have had him on board. I am grateful to
my American colleague Jacek Fabrykowski, a mathematician who devoted his
time to looking at the material. A special thanks to my former student (now
working cryptographer), Thomas Zaplachinski, whose invaluable expertise in
the field helped to keep the material current and accurate. A nonspecialist,
Michael Kozielec, assisted greatly in giving me the valuable perspective of the
uninitiated for this project which was highly beneficial in setting the proper
tone for the book. Thanks go to Ken Rosen, the series editor, who always
works diligently to promote the books in the series, and another special thanks

to Bob Stern, my senior editor, who makes the transition from copy to finished
product a seamless task. For specific information, especially on fine-tuning of
details on MULTICS, and related information, thanks go to Brian Kernighan
for providing background data.
Richard Mollin, Calgary
website: />e-mail:
x
xi
About the Author
Richard Anthony Mollin received his Ph.D. in mathematics (1975) from
Queen’s University, Kingston, Ontario, Canada. He is now a full professor in
the Mathematics Department at the University of Calgary, Alberta, Canada. He
has to his credit over 170 publications in algebra, number theory, computational
mathematics, and cryptology. This book is his eighth, with [164]–[170] being
the other seven.
xii
xiii
Dedicated to the memory of Pope John Paul II
— God’s shepherd of the people.
xiv
Contents
List of Figures xix
1 From the Riddles of Ancient Egypt to Cryptography in the
Renaissance — 3500 Years in the Making 1
1.1 Antiquity — From Phaistos 1
1.2 Cryptography in Classical Literature 22
1.3 The Middle Ages 39
1.4 Cryptology and the Arabs 44
1.5 Rise of the West 47
2 From Sixteenth-Century Cryptography to the New Millennium

— The Last 500 Years 59
2.1 Three Post-Renaissance Centuries 59
2.2 The American Colonies 65
2.3 Nineteenth-Century Cryptography 74
2.4 Two World Wars 78
2.5 The Postwar Era and the Future 97
3 Symmetric-Key Cryptography 107
3.1 Block Ciphers and DES 107
3.2 S-DES and DES 116
3.3 Modes of Operation 133
3.4 Blowfish 138
3.5 ☞ The Advanced Encryption Standard 143
3.6 Stream Ciphers 151
3.7 RC4 159
4 Public-Key Cryptography 161
4.1 The Ideas behind PKC 161
4.2 RSA 172
4.3 Digital Signatures 180
4.4 ElGamal 185
xv
xvi
5 Cryptographic Protocols 191
5.1 Introduction 191
5.2 Keys 195
5.3 Identification 202
5.4 Commitment 208
5.5 Secret Sharing 212
5.6 Electronic Voting 216
5.7 Protocol Layers and SSL 218
5.8 Digital Cash Schemes 227

6 Key Management 233
6.1 Authentication, Exchange, and Distribution 233
6.2 Public-Key Infrastructure (PKI) 237
6.3 Secure Electronic Transaction (SET) 243
7 Message Authentication 251
7.1 Authentication Functions 251
7.2 Message Authentication Codes 260
7.3 Encryption Functions 265
7.4 Authentication Applications 268
8 Electronic Mail and Internet Security 271
8.1 Pretty Good Privacy (PGP) 271
8.2 S/MIME and PGP 287
8.3 ☞ IPSec 294
8.4 Internetworking and Security — Firewalls 313
8.5 Client–Server Model and Cookies 322
8.6 History of the Internet and the WWW 326
9 Applications and the Future 329
9.1 Login and Network Security 329
9.2 Wireless Security 340
9.3 Smart Cards 354
9.4 Biometrics 362
9.5 Quantum Cryptography 366
9.6 Nuclear Test Ban Treaty Compliance 372
10 Noncryptographic Security Issues 375
10.1 Cybercrime 375
10.2 Hackers 384
10.3 Viruses and Other Infections 397
10.4 Legal Matters and Controversy 410
xvii
11 Information Theory and Coding 425

11.1 Shannon 425
11.2 Entropy 428
11.3 Huffman Codes 433
11.4 Information Theory of Cryptosystems 435
11.5 Error-Correcting Codes 441
Appendix A: Mathematical Facts 466
A.1 Sets, Relations, and Functions 466
A.2 Basic Arithmetic 469
A.3 Modular Arithmetic 475
A.4 Groups, Fields, Modules, and Rings 483
A.5 Vector Spaces 490
A.6 Basic Matrix Theory 491
A.7 Continued Fractions 496
A.8 Elliptic Curves 498
A.9 Complexity 500
Appendix B: Pseudorandom Number Generation 506
B.1 ANSI X9.17 506
B.2 The Blum-Blum-Shub-(BBS) PRNG 508
Appendix C: Factoring Large Integers 509
C.1 Classical Factorization Methods 509
C.2 The Continued Fraction Algorithm 512
C.3 Pollard’s p − 1 Algorithm 514
C.4 Pollard’s Rho Method 515
C.5 The Quadratic Sieve (QS) 517
C.6 Multipolynomial Quadratic Sieve (MPQS) 519
C.7 The Elliptic Curve Method (ECM) 522
C.8 ☞ The General Number Field Sieve 524
Appendix D: Technical and Advanced Details 527
D.1 AES 527
D.2 Silver-Pohlig-Hellman 530

D.3 Baby-Step Giant-Step Algorithm 533
D.4 Index-Calculus Algorithm 534
D.5 ☞ Brands’ Digital Cash Scheme 536
D.6 Radix-64 Encoding 541
Appendix E: Probability Theory 543
E.1 Basic Probability 543
E.2 Randomness, Expectation, and Variance 546
E.3 Binomial Distribution 547
E.4 The Law of Large Numbers 548
E.5 Probability and Error Detection 548
xviii
Appendix F: Recognizing Primes 550
F.1 Primality and Compositeness Tests 550
F.2 Miller-Selfridge-Rabin 552
F.3 Primes is in P 555
F.4 Generation of Random Primes 558
F.5 Decision Problem or Primality Test? 560
Appendix G: Exercises 561
G.1 Chapter 1 Exercises 561
G.2 Chapter 2 Exercises 563
G.3 Chapter 3 Exercises 567
G.4 Chapter 4 Exercises 573
G.5 Chapter 5 Exercises 581
G.6 Chapter 6 Exercises 585
G.7 Chapter 7 Exercises 586
G.8 Chapter 8 Exercises 588
G.9 Chapter 9 Exercises 589
G.10 Chapter 10 Exercises 591
G.11 Chapter 11 Exercises 592
G.12 Appendices Exercises 599

Bibliography 605
List of Symbols 627
Index 629
List of Figures
1.1 View of hills and valley to the west from Phaistos. . . . . . . . . 2
1.2 Phaistos disk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Phaistos royal apartments. . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Phaistos krater, Kamares style. . . . . . . . . . . . . . . . . . . . 4
1.5 R¨ok stone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 The Kylver stone. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 An Ogham stone. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.8 Paris Codex zodiac 1. . . . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Paris Codex zodiac 2. . . . . . . . . . . . . . . . . . . . . . . . . 18
1.10 Pyramid of the Magician. . . . . . . . . . . . . . . . . . . . . . . 19
1.11 Easter Island Moais. . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.12 Rongorongo tablet. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.13 Santiago Staff Segment. . . . . . . . . . . . . . . . . . . . . . . . 21
1.14 An artist’s rendition of life at Knossos. . . . . . . . . . . . . . . . 28
1.15 Knossos Linear B Tablet . . . . . . . . . . . . . . . . . . . . . . . 29
1.16 A Knossos symbol: double axe. . . . . . . . . . . . . . . . . . . . 30
1.17 Knossos fresco: blue dolphins. . . . . . . . . . . . . . . . . . . . . 31
1.18 Palace ruines at Knossos. . . . . . . . . . . . . . . . . . . . . . . 32
1.19 Prince of Knossos. . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.20 Edgar Allan Poe. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.21 A modern-day steganographic device. . . . . . . . . . . . . . . . 43
1.22 Alberti disk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.23 Leon Battista Alberti. . . . . . . . . . . . . . . . . . . . . . . . . 50
1.24 Polygraphia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.25 Natural Magic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.1 Fran¸cois Vi`ete. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2.2 John Wallis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.3 George Washington. . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.4 Thomas Jefferson. . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.5 Wheel cypher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.6 Samuel Morse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.7 Abraham Lincoln. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.8 Confederate cipher. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.9 Confederate cipher disk. . . . . . . . . . . . . . . . . . . . . . . . 72
xix
xx
2.10 Codebook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.11 Guglielmo Marconi. . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.12 Georges Painvin. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.13 William Friedman. . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.14 Elizabeth S. Friedman. . . . . . . . . . . . . . . . . . . . . . . . . 86
2.15 Herbert Yardley. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.16 Purple machine replica. . . . . . . . . . . . . . . . . . . . . . . . 89
2.17 Frank Rowlett. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.18 Midway exhibit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.19 SIGABA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.20 Purple cipher switch. . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.21 BOMBE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
2.22 Enigma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.23 The Cray XMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.1 Phil Zimmermann. . . . . . . . . . . . . . . . . . . . . . . . . . . 272
8.2 Phil Zimmermann, after the charges. . . . . . . . . . . . . . . . . 273
8.3 Phil Zimmermann in Red Square. . . . . . . . . . . . . . . . . . . 286
10.1 Cybercrime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
10.2 Richard Stallman. . . . . . . . . . . . . . . . . . . . . . . . . . . 386
10.3 Jim Gosling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

10.4 Brian Kernighan. . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
10.5 Steve Jobs (with a blue box) and Steve Wozniak in 1975. . . . . 392
10.6 The NSA’s 50th Anniversary Exhibit. . . . . . . . . . . . . . . . 418
10.7 The NSA’s Cryptologic Memorial. . . . . . . . . . . . . . . . . . 419
11.1 Claude Shannon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
A.1 Hierarchy of Problems in Complexity Theory. . . . . . . . . . . . 505
Chapter 1
From the Riddles of
Ancient Egypt to
Cryptography in the
Renaissance — 3500 Years
in the Making
It was the secrets of heaven and earth that I desired to learn.
Mary Shelly (1797–1851), English novelist
— from Frankenstein (1818), Chapter 4
1.1 Antiquity — From Phaistos
Imagine an inscription created some 3600 years ago that nobody, to this
day, has been able to decode! It exists and is carved on a clay disk, called
the Phaistos (pronounced feye-stos) disk, roughly 16 centimeters (6.3 inches) in
diameter, unearthed from the (old) palace of Phaistos, one of the most important
locations of Minoan culture on the island of Crete, now part of Greece.
The Messara Plain is the most sizable and fertile on Crete. Only five kilo-
meters (3.1 miles) from the coast, it ascends to form a chain of hills on the most
eastern of which sits Phaistos, which was, according to Greek mythology, the
residence of Rhadamanthys, one of Zeus’ sons. Another son of Zeus was Minos,
from which the name for the Minoan civilization derives. This civilization flour-
ished from approximately 3000 BC to 1100 BC. Crete was the principal location
of Bronze Age culture and centre of the eminent civilization in the Aegean Sea.
When this author visited Crete on a lecture tour in August of 2003, the
first sight of Phaistos was a phenomenal experience, but perhaps more subdued

1
21.From the Riddles of Ancient Egypt
than that of Henry Miller, the famed American author who spent a few hours
there in 1939 during his five-month trip to Greece. He is purported to have
said: “God, it’s incredible! I turned my eyes away, it was too much to try to
accept at once I had reached the apogee, I wanted to give, prodigally and
indiscriminately of all I possessed I wanted to stay forever, turn my back
on the world, renounce everything.” These anecdotes serve to give the well-
deserved impression that Greece, in general, and Crete with the Phaistos site, in
particular, are cradles of civilization — deserve to be praised in the highest terms
— and a trip there is highly recommended. Now back to the Phaistos Disk itself.
Figure 1.1: View of hills and valley to
the west from Phaistos.
Figures 1.1–1.4 were photographed by
and courtesy of Bridget Mollin.
Sometime in the evening of July 3,
1908, an excavator was the first person
to unearth and view the the Phaistos
Disk. At the center of the (so-called)
A side or front side of the disk is an
eight-petalled rosette, whereas on the
B side there is a helmet sign. On both
sides are inscriptions, consisting of a
total of 242 symbols, 123 on the front
and 119 on the back, and they spiral
away from the center on the front and
toward it on the back. The problem
with finding the meaning of the sym-
bols is that the disk is unique in that
there are no other known texts written

in the script of the Phaistos Disk, and the shortness of the existing text means
that we do not have enough clues to achieve results with statistical methods.
(Later, we shall learn more about statistical analysis of disguised texts such as
these, called ciphertexts, in order to achieve the undisguised text, called plain-
text.) The uniqueness of the disk means that there are no deductions that can
be drawn from other objects in the Minoan culture as a means to begin deci-
phering, meaning the removal of the disguise to achieve the plaintext. Similarly,
enciphering (also called encrypting), means disguising, the turning of plaintext
into ciphertext. Later we will learn more about the difficulty of deciphering
when there is very little ciphertext available. There are those who believe it is
possible to decipher the disk, and several authors have published their versions
of what they believe the plaintext to be. These range from a methodology for
the execution of sexual rites at the palace of Phaistos to offerings to appease the
gods. However, there appears to be no general agreement. No doubt there will
be even more interpretations in the future. For the reader interested in more
detail on this fascinating story, see Ballister’s excellent and very readable, de-
tailed, and entertaining book [12], where he concludes with: “How much longer
the charming bearer of secrets and its potential solvers compete with one an-
other, and who in the end will win, only the future will show. Until then, I
recommend to everyone to visit the archeological museum in Heraklion to enjoy
the beauty and the (as yet) mysterious aura of the Phaistos Disk.”
1.1. Antiquity 3
Figure 1.2: Phaistos disk.
(In the above figure, the A side is on the left, and the B side on the right.)
Earlier we made some references to Greek mythology. There are other
references in this type of myth to cryptography: the study of methods for
sending messages in secret, which we now understand to mean the study of
methods for transforming of plaintext into ciphertext. (The word “cryptog-
raphy” comes from the Greek krypt´os meaning hidden and gr´aphein, mean-
ing to write.) We will learn a lot more about the cryptographic anecdotes

in Greek mythology in Section 1.2. For now, this is a convenient juncture
to introduce some terms related to cryptography, and discuss their origins.
Cryptanalysis is the study of methods for defeating cryptography. The ety-
Figure 1.3: Phaistos royal apartments.
41.From the Riddles of Ancient Egypt
mology of the word is from the Greek krypt´os, as above, and anal´yein, to untie.
Figure 1.4: Phaistos krater, Kamares style.
Therefore, to say someone crypt-
analyzed a text, means they deci-
phered it. (Later in the text, we
will learn a great deal about crypt-
analytic techniques.) The term
cryptology is used to encompass
the study of both cryptography
and cryptanalysis. The (English)
term “cryptography” was coined in
1658 by Thomas Browne, a British
physician and writer, whereas the
term “cryptology” was coined by
James Howell in 1645. Yet, the
modern usage of the word “cryp-
tology” is probably due to the ad-
vent of David Kahn’s encyclope-
dic book [131], The Codebreakers,
published in 1967, after which the
word became synonymous with the
embodiment of the studies of both
cryptography and cryptanalysis. Of course, cryptographers, cryptanalysts, and
cryptologists are those practicing cryptography, cryptanalysis, and cryptology,
respectively. Lastly, the term cipher (which we will use interchangeably with

the term cryptosystem) is a method for enciphering and deciphering. Later,
when we have developed more maturity in our cryptographic travels, we will be
more precise, but this will serve us for the current path we are traversing. Now
we continue with our discussion of antiquity and carry a new concrete set of
terms to help pave our way.
Not only do the Greeks of antiquity have stories about cryptography, but
also ancient Egypt has some fascinating history in the cryptographic arena. In
fact, the oldest text known to employ a deliberate disguise of writing occurred
almost 4000 years ago in Egypt. This is our next story.
Ancient Egypt
A nobleman, Khumhotep II, was responsible for the erection of several mon-
uments for the Pharaoh Amenemhet II. In around 1900 BC, a scribe used hi-
eroglyphic symbol substitution (which, in this case meant the replacing of some
ordinary hieroglyphic symbols with some more exceptional ones) in his writing
on the tomb of the nobleman to tell stories of his deeds. (The term hieroglyph
means secret carving and is actually a Greek translation of the Egyptian phrase,
the god’s words. Hieroglyphs are actually characters used in a system of picto-
rial writing, usually, but not always, standing for sounds.) The scribe was not
actually trying to disguise the inscription, but rather intended to impart some
prestige and authority to his writing. Think of this as resembling the use of