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`PRAISE FOR SIMON SINGH AND The Code Book
`
`“Singh spins tales of cryptic intrigue in every chapter.”
`
`—The Wall Street Journal
`“Brings together … the geniuses who have secured communications, saved lives, and influenced
`the fate of nations. A pleasure to read.”
`
`—Chicago Tribune
`“Singh pursues the fascinating story [of codes] through the centuries, always providing plenty of
`detailed examples of ciphers for those who appreciate the intricacies of the medium.”
`—Los Angeles Times
`“Especially effective at putting the reader in the codebreaker’s shoes, facing each new,
`apparently unbreakable code.… Singh does a fine job.”
`
`—The New York Times Book Review
`
`“Entertaining.… Singh has a flair for narrative.”
`
`—San Francisco Chronicle
`“Singh is an interesting mix of scientist and storyteller, and this subject is the perfect mix of true
`fact and tall tales.”
`
`—The San Diego Union-Tribune
`“Where would we Information Age ignoramuses be without smart guys like Stephen Jay Gould,
`the late Carl Sagan, or Simon Singh? They are the troubadours of our time, making complicated
`subjects understandable and entertaining.”
`
`—The Plain Dealer
`“In this entertaining survey, the evolution of cryptography is driven by the ongoing struggle
`between code-makers and codebreakers.”
`
`—The New Yorker
`“[Singh] is well-equipped to describe all the arcane mathematics in layman’s language.”
`
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`—Forbes
`“Wonderful stories.… Close reading is rewarded with the flash of logical insight that the
`codebreakers must enjoy.”
`
`—Hartford Advocate
`“An illuminating and entertaining account.… From the first page, Singh shows his knack both for
`explaining complex areas of science and telling rip-roaring stories.”
`
`—New York Law Journal
`“My only regret is that this great book has come far too late. If only someone had given it to me
`when I was 10, my secret plans for world playground domination might never have been foiled.”
`—James Flint, The Observer (London)
`“Full of fascinating case histories covering the development and practical use of cryptography.”
`—Mail on Sunday (London)
`“Singh has created an authoritative and engrossing read which both explains and humanizes the
`subject.… This intelligent, exciting book takes its drive from a simple premise-that nothing is as
`exciting as a secret.”
`
`—Scotland on Sunday
`
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`SIMON SINGH
`The Code Book
`
`Simon Singh received his Ph.D. in physics from Cambridge
`University. A former BBC producer, he directed an award-
`winning documentary film on Fermat’s Last Theorem that aired
`on PBS’s Nova series and wrote the bestselling book, Fermat’s
`Enigma. He lives in London, England.
`
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`Also by Simon Singh
` Fermat’s Enigma
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`FIRST ANCHOR BOOKS EDITION, SEPTEMBER 2000
`Copyright © 1999 by Simon Singh
`All rights reserved under International and Pan-American Copyright Conventions. Published in
`the United States by Anchor Books, a division of Random House, Inc., New York, and
`simultaneously in Canada by Random House of Canada Limited, Toronto. Originally published in
`hardcover in the United States by Doubleday, a division of Random House, Inc., New York, and
`in the United Kingdom by the Fourth Estate, London, in 1999.
`Anchor Books and colophon are registered trademarks of Random House, Inc.
`The Library of Congress has cataloged the Doubleday edition as follows:
`Singh, Simon.
`The code book : the evolution of secrecy from Mary Queen of Scots to quantum cryptography /
`Simon Singh. –1st ed.
`p. cm.
`1. Cryptography–History. 2. Data encryption (Computer science)–History. I. Title.
`Z103.S56 1999
`652′.8′09–dc21 99-35261
`eISBN: 978-0-30778784-2
`Author photo © Nigel Spalding
`www.anchorbooks.com
`
`v3.1_r2
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`For my mother and father,
`
`Sawaran Kaur and Mehnga Singh
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`The urge to discover secrets is deeply ingrained in human
`nature; even the least curious mind is roused by the promise of
`sharing knowledge withheld from others. Some are fortunate
`enough to find a job which consists in the solution of mysteries,
`but most of us are driven to sublimate this urge by the solving
`of artificial puzzles devised for our entertainment. Detective
`stories or crossword puzzles cater for the majority; the solution
`of secret codes may be the pursuit of a few.
`
`
`John Chadwick
`The Decipherment of Linear B
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`Contents
`
`Cover
`About the Author
`Other Books by This Author
`Title Page
`Copyright
`Dedication
`Epigraph
`Introduction
`1 The Cipher of Mary Queen of Scots
`2 Le Chiffre Indéchiffrable
`3 The Mechanization of Secrecy
`4 Cracking the Enigma
`5 The Language Barrier
`6 Alice and Bob Go Public
`7 Pretty Good Privacy
`8 A Quantum Leap into the Future
`The Cipher Challenge
`Appendices
`Glossary
`Acknowledgments
`Further Reading
`Picture Credits
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`FI
`
`ntroduction
`
`or thousands of years, kings, queens and generals have relied on
`efficient communication in order to govern their countries and
`command their armies. At the same time, they have all been aware of
`the consequences of their messages falling into the wrong hands,
`revealing precious secrets to rival nations and betraying vital
`information to opposing forces. It was the threat of enemy interception
`that motivated the development of codes and ciphers: techniques for
`disguising a message so that only the intended recipient can read it.
`The desire for secrecy has meant that nations have operated
`codemaking departments, responsible for ensuring the security of
`communications by inventing and implementing the best possible codes.
`At the same time, enemy codebreakers have attempted to break these
`codes, and steal secrets. Codebreakers are linguistic alchemists, a
`mystical tribe attempting to conjure sensible words out of meaningless
`symbols. The history of codes and ciphers is the story of the centuries-
`old battle between codemakers and codebreakers, an intellectual arms
`race that has had a dramatic impact on the course of history.
`In writing The Code Book, I have had two main objectives. The first is
`to chart the evolution of codes. Evolution is a wholly appropriate term,
`because the development of codes can be viewed as an evolutionary
`struggle. A code is constantly under attack from codebreakers. When the
`codebreakers have developed a new weapon that reveals a code’s
`weakness, then the code is no longer useful. It either becomes extinct or
`it evolves into a new, stronger code. In turn, this new code thrives only
`until the codebreakers identify its weakness, and so on. This is analogous
`to the situation facing, for example, a strain of infectious bacteria. The
`bacteria live, thrive and survive until doctors discover an antibiotic that
`exposes a weakness in the bacteria and kills them. The bacteria are
`forced to evolve and outwit the antibiotic, and, if successful, they will
`thrive once again and reestablish themselves. The bacteria are
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`continually forced to evolve in order to survive the onslaught of new
`antibiotics.
`The ongoing battle between codemakers and codebreakers has
`inspired a whole series of remarkable scientific breakthroughs. The
`codemakers have continually striven to construct ever-stronger codes for
`defending communications, while codebreakers have continually
`invented more powerful methods for attacking them. In their efforts to
`destroy and preserve secrecy, both sides have drawn upon a diverse
`range of disciplines and technologies, from mathematics to linguistics,
`from information theory to quantum theory. In return, codemakers and
`codebreakers have enriched these subjects, and their work has
`accelerated technological development, most notably in the case of the
`modern computer.
`History is punctuated with codes. They have decided the outcomes of
`battles and led to the deaths of kings and queens. I have therefore been
`able to call upon stories of political intrigue and tales of life and death to
`illustrate the key turning points in the evolutionary development of
`codes. The history of codes is so inordinately rich that I have been forced
`to leave out many fascinating stories, which in turn means that my
`account is not definitive. If you would like to find out more about your
`favorite tale or your favorite codebreaker then I would refer you to the
`list of further reading, which should help those readers who would like
`to study the subject in more detail.
`Having discussed the evolution of codes and their impact on history,
`the book’s second objective is to demonstrate how the subject is more
`relevant today than ever before. As information becomes an increasingly
`valuable commodity, and as the communications revolution changes
`society, so the process of encoding messages, known as encryption, will
`play an increasing role in everyday life. Nowadays our phone calls
`bounce off satellites and our e-mails pass through various computers,
`and both forms of communication can be intercepted with ease, so
`jeopardizing our privacy. Similarly, as more and more business is
`conducted over the Internet, safeguards must be put in place to protect
`companies and their clients. Encryption is the only way to protect our
`privacy and guarantee the success of the digital marketplace. The art of
`secret communication, otherwise known as cryptography, will provide
`the locks and keys of the Information Age.
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`However, the public’s growing demand for cryptography conflicts with
`the needs of law enforcement and national security. For decades, the
`police and the intelligence services have used wire-taps to gather
`evidence against terrorists and organized crime syndicates, but the
`recent development of ultra-strong codes threatens to undermine the
`value of wire-taps. As we enter the twenty-first century, civil libertarians
`are pressing for the widespread use of cryptography in order to protect
`the privacy of the individual. Arguing alongside them are businesses,
`who require strong cryptography in order to guarantee the security of
`transactions within the fast-growing world of Internet commerce. At the
`same time, the forces of law and order are lobbying governments to
`restrict the use of cryptography. The question is, which do we value
`more—our privacy or an effective police force? Or is there a
`compromise?
`Although cryptography is now having a major impact on civilian
`activities, it should be noted that military cryptography remains an
`important subject. It has been said that the First World War was the
`chemists’ war, because mustard gas and chlorine were employed for the
`first time, and that the Second World War was the physicists’ war,
`because the atom bomb was detonated. Similarly, it has been argued
`that the Third World War would be the mathematicians’ war, because
`mathematicians will have control over the next great weapon of war—
`information. Mathematicians have been responsible for developing the
`codes that are currently used to protect military information. Not
`surprisingly, mathematicians are also at the forefront of the battle to
`break these codes.
`While describing the evolution of codes and their impact on history, I
`have allowed myself a minor detour. Chapter 5 describes the
`decipherment of various ancient scripts, including Linear B and Egyptian
`hieroglyphics. Technically, cryptography concerns communications that
`are deliberately designed to keep secrets from an enemy, whereas the
`writings of ancient civilizations were not intended to be indecipherable:
`it is merely that we have lost the ability to interpret them. However, the
`skills required to uncover the meaning of archaeological texts are closely
`related to the art of codebreaking. Ever since reading The Decipherment
`of Linear B, John Chadwick’s description of how an ancient
`Mediterranean text was unraveled, I have been struck by the astounding
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`intellectual achievements of those men and women who have been able
`to decipher the scripts of our ancestors, thereby allowing us to read
`about their civilizations, religions and everyday lives.
`Turning to the purists, I should apologize for the title of this book. The
`Code Book is about more than just codes. The word “code” refers to a
`very particular type of secret communication, one that has declined in
`use over the centuries. In a code, a word or phrase is replaced with a
`word, number or symbol. For example, secret agents have codenames,
`words that are used instead of their real names in order to mask their
`identities. Similarly, the phrase Attack at dawn could be replaced by
`the codeword Jupiter, and this word could be sent to a commander in
`the battlefield as a way of baffling the enemy. If headquarters and the
`commander have previously agreed on the code, then the meaning of
`Jupiter will be clear to the intended recipient, but it will mean nothing
`to an enemy who intercepts it. The alternative to a code is a cipher, a
`technique that acts at a more fundamental level, by replacing letters
`rather than whole words. For example, each letter in a phrase could be
`replaced by the next letter in the alphabet, so that A is replaced by B, B
`by C, and so on. Attack at dawn thus becomes Buubdl bu ebxo.
`Ciphers play an integral role in cryptography, and so this book should
`really have been called The Code and Cipher Book. I have, however,
`forsaken accuracy for snappiness.
`As the need arises, I have defined the various technical terms used
`within cryptography. Although I have generally adhered to these
`definitions, there will be occasions when I use a term that is perhaps not
`technically accurate, but which I feel is more familiar to the non-
`specialist. For example, when describing a person attempting to break a
`cipher, I have often used codebreaker rather than the more accurate
`cipherbreaker. I have done this only when the meaning of the word is
`obvious from the context. There is a glossary of terms at the end of the
`book. More often than not, though, crypto-jargon is quite transparent:
`for example, plaintext is the message before encryption, and ciphertext is
`the message after encryption.
`Before concluding this introduction, I must mention a problem that
`faces any author who tackles the subject of cryptography: the science of
`secrecy is largely a secret science. Many of the heroes in this book never
`gained recognition for their work during their lifetimes because their
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`contribution could not be publicly acknowledged while their invention
`was still of diplomatic or military value. While researching this book, I
`was able to talk to experts at Britain’s Government Communications
`Headquarters (GCHQ), who revealed details of extraordinary research
`done in the 1970s which has only just been declassified. As a result of
`this declassification, three of the world’s greatest cryptographers can
`now receive the credit they deserve. However, this recent revelation has
`merely served to remind me that there is a great deal more going on, of
`which neither I nor any other science writer is aware. Organizations
`such as GCHQ and America’s National Security Agency continue to
`conduct classified research into cryptography, which means that their
`breakthroughs remain secret and the individuals who make them remain
`anonymous.
`Despite the problems of government secrecy and classified research, I
`have spent the final chapter of this book speculating about the future of
`codes and ciphers. Ultimately, this chapter is an attempt to see if we can
`predict who will win the evolutionary struggle between codemaker and
`codebreaker. Will codemakers ever design a truly unbreakable code and
`succeed in their quest for absolute secrecy? Or will codebreakers build a
`machine that can decipher any message? Bearing in mind that some of
`the greatest minds work in classified laboratories, and that they receive
`the bulk of research funds, it is clear that some of the statements in my
`final chapter may be inaccurate. For example, I state that quantum
`computers—machines potentially capable of breaking all today’s ciphers
`—are at a very primitive stage, but it is possible that somebody has
`already built one. The only people who are in a position to point out my
`errors are also those who are not at liberty to reveal them.
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`O1
`
` The Cipher of Mary Queen of Scots
`
`n the morning of Saturday, October 15, 1586, Queen Mary entered
`the crowded courtroom at Fotheringhay Castle. Years of
`imprisonment and the onset of rheumatism had taken their toll, yet she
`remained dignified, composed and indisputably regal. Assisted by her
`physician, she made her way past the judges, officials and spectators,
`and approached the throne that stood halfway along the long, narrow
`chamber. Mary had assumed that the throne was a gesture of respect
`toward her, but she was mistaken. The throne symbolized the absent
`Queen Elizabeth, Mary’s enemy and prosecutor. Mary was gently guided
`away from the throne and toward the opposite side of the room, to the
`defendant’s seat, a crimson velvet chair.
`Mary Queen of Scots was on trial for treason. She had been accused of
`plotting to assassinate Queen Elizabeth in order to take the English
`crown for herself. Sir Francis Walsingham, Elizabeth’s Principal
`Secretary, had already arrested the other conspirators, extracted
`confessions, and executed them. Now he planned to prove that Mary was
`at the heart of the plot, and was therefore equally culpable and equally
`deserving of death.
`Walsingham knew that before he could have Mary executed, he would
`have to convince Queen Elizabeth of her guilt. Although Elizabeth
`despised Mary, she had several reasons for being reluctant to see her put
`to death. First, Mary was a Scottish queen, and many questioned
`whether an English court had the authority to execute a foreign head of
`state. Second, executing Mary might establish an awkward precedent—if
`the state is allowed to kill one queen, then perhaps rebels might have
`fewer reservations about killing another, namely Elizabeth. Third,
`Elizabeth and Mary were cousins, and their blood tie made Elizabeth all
`the more squeamish about ordering her execution. In short, Elizabeth
`would sanction Mary’s execution only if Walsingham could prove
`beyond any hint of doubt that she had been part of the assassination
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`plot.
`
`Figure 1 Mary Queen of Scots.(photo credit 1.1)
`
`The conspirators were a group of young English Catholic noblemen
`intent on removing Elizabeth, a Protestant, and replacing her with Mary,
`a fellow Catholic. It was apparent to the court that Mary was a
`figurehead for the conspirators, but it was not clear that she had actually
`given her blessing to the conspiracy. In fact, Mary had authorized the
`plot. The challenge for Walsingham was to demonstrate a palpable link
`between Mary and the plotters.
`On the morning of her trial, Mary sat alone in the dock, dressed in
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`sorrowful black velvet. In cases of treason, the accused was forbidden
`counsel and was not permitted to call witnesses. Mary was not even
`allowed secretaries to help her prepare her case. However, her plight
`was not hopeless because she had been careful to ensure that all her
`correspondence with the conspirators had been written in cipher. The
`cipher turned her words into a meaningless series of symbols, and Mary
`believed that even if Walsingham had captured the letters, then he could
`have no idea of the meaning of the words within them. If their contents
`were a mystery, then the letters could not be used as evidence against
`her. However, this all depended on the assumption that her cipher had
`not been broken.
`Unfortunately for Mary, Walsingham was not merely Principal
`Secretary, he was also England’s spymaster. He had intercepted Mary’s
`letters to the plotters, and he knew exactly who might be capable of
`deciphering them. Thomas Phelippes was the nation’s foremost expert on
`breaking codes, and for years he had been deciphering the messages of
`those who plotted against Queen Elizabeth, thereby providing the
`evidence needed to condemn them.
`If he could decipher the
`incriminating letters between Mary and the conspirators, then her death
`would be inevitable. On the other hand, if Mary’s cipher was strong
`enough to conceal her secrets, then there was a chance that she might
`survive. Not for the first time, a life hung on the strength of a cipher.
`
`The Evolution of Secret Writing
`Some of the earliest accounts of secret writing date back to Herodotus,
`“the father of history” according to the Roman philosopher and
`statesman Cicero. In The Histories, Herodotus chronicled the conflicts
`between Greece and Persia in the fifth century B.C., which he viewed as a
`confrontation between freedom and slavery, between the independent
`Greek states and the oppressive Persians. According to Herodotus, it was
`the art of secret writing that saved Greece from being conquered by
`Xerxes, King of Kings, the despotic leader of the Persians.
`The long-running feud between Greece and Persia reached a crisis
`soon after Xerxes began constructing a city at Persepolis, the new capital
`for his kingdom. Tributes and gifts arrived from all over the empire and
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`neighboring states, with the notable exceptions of Athens and Sparta.
`Determined to avenge this insolence, Xerxes began mobilizing a force,
`declaring that “we shall extend the empire of Persia such that its
`boundaries will be God’s own sky, so the sun will not look down upon
`any land beyond the boundaries of what is our own.” He spent the next
`five years secretly assembling the greatest fighting force in history, and
`then, in 480 B.C., he was ready to launch a surprise attack.
`However, the Persian military buildup had been witnessed by
`Demaratus, a Greek who had been expelled from his homeland and who
`lived in the Persian city of Susa. Despite being exiled he still felt some
`loyalty to Greece, so he decided to send a message to warn the Spartans
`of Xerxes’ invasion plan. The challenge was how to dispatch the message
`without it being intercepted by the Persian guards. Herodotus wrote:
`As the danger of discovery was great, there was only one way in which he could contrive to
`get the message through: this was by scraping the wax off a pair of wooden folding tablets,
`writing on the wood underneath what Xerxes intended to do, and then covering the
`message over with wax again. In this way the tablets, being apparently blank, would cause
`no trouble with the guards along the road. When the message reached its destination, no
`one was able to guess the secret, until, as I understand, Cleomenes’ daughter Gorgo, who
`was the wife of Leonidas, divined and told the others that if they scraped the wax off, they
`would find something written on the wood underneath. This was done; the message was
`revealed and read, and afterward passed on to the other Greeks.
`As a result of this warning, the hitherto defenseless Greeks began to arm
`themselves. Profits from the state-owned silver mines, which were
`usually shared among the citizens, were instead diverted to the navy for
`the construction of two hundred warships.
`Xerxes had lost the vital element of surprise and, on September 23,
`480 B.C., when the Persian fleet approached the Bay of Salamis near
`Athens, the Greeks were prepared. Although Xerxes believed he had
`trapped the Greek navy, the Greeks were deliberately enticing the
`Persian ships to enter the bay. The Greeks knew that their ships, smaller
`and fewer in number, would have been destroyed in the open sea, but
`they realized that within the confines of the bay they might
`outmaneuver the Persians. As the wind changed direction the Persians
`found themselves being blown into the bay, forced into an engagement
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`on Greek terms. The Persian princess Artemisia became surrounded on
`three sides and attempted to head back out to sea, only to ram one of
`her own ships. Panic ensued, more Persian ships collided and the Greeks
`launched a full-blooded onslaught. Within a day, the formidable forces
`of Persia had been humbled.
`Demaratus’ strategy for secret communication relied on simply hiding
`the message. Herodotus also recounted another incident in which
`concealment was sufficient to secure the safe passage of a message. He
`chronicled the story of Histaiaeus, who wanted to encourage Aristagoras
`of Miletus to revolt against the Persian king. To convey his instructions
`securely, Histaiaeus shaved the head of his messenger, wrote the
`message on his scalp, and then waited for the hair to regrow. This was
`clearly a period of history that tolerated a certain lack of urgency. The
`messenger, apparently carrying nothing contentious, could travel
`without being harassed. Upon arriving at his destination he then shaved
`his head and pointed it at the intended recipient.
`Secret communication achieved by hiding the existence of a message
`is known as steganography, derived from the Greek words steganos,
`meaning “covered,” and graphein, meaning “to write.” In the two
`thousand years since Herodotus, various forms of steganography have
`been used throughout the world. For example, the ancient Chinese wrote
`messages on fine silk, which was then scrunched into a tiny ball and
`covered in wax. The messenger would then swallow the ball of wax. In
`the sixteenth century, the Italian scientist Giovanni Porta described how
`to conceal a message within a hard-boiled egg by making an ink from a
`mixture of one ounce of alum and a pint of vinegar, and then using it to
`write on the shell. The solution penetrates the porous shell, and leaves a
`message on the surface of the hardened egg albumen, which can be read
`only when the shell is removed. Steganography also includes the practice
`of writing in invisible ink. As far back as the first century A.D., Pliny the
`Elder explained how the “milk” of the thithymallus plant could be used
`as an invisible ink. Although transparent after drying, gentle heating
`chars the ink and turns it brown. Many organic fluids behave in a similar
`way, because they are rich in carbon and therefore char easily. Indeed, it
`is not unknown for modern spies who have run out of standard-issue
`invisible ink to improvise by using their own urine.
`The longevity of steganography illustrates that it certainly offers a
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`modicum of security, but it suffers from a fundamental weakness. If the
`messenger is searched and the message is discovered, then the contents
`of the secret communication are revealed at once. Interception of the
`message immediately compromises all security. A thorough guard might
`routinely search any person crossing a border, scraping any wax tablets,
`heating blank sheets of paper, shelling boiled eggs, shaving people’s
`heads, and so on, and inevitably there will be occasions when the
`message is uncovered.
`Hence, in parallel with the development of steganography, there was
`the evolution of cryptography, derived from the Greek word kryptos,
`meaning “hidden.” The aim of cryptography is not to hide the existence
`of a message, but rather to hide its meaning, a process known as
`encryption. To render a message unintelligible, it is scrambled according
`to a particular protocol which is agreed beforehand between the sender
`and the intended recipient. Thus the recipient can reverse the scrambling
`protocol and make the message comprehensible. The advantage of
`cryptography is that if the enemy intercepts an encrypted message, then
`the message is unreadable. Without knowing the scrambling protocol,
`the enemy should find it difficult, if not impossible, to recreate the
`original message from the encrypted text.
`Although cryptography and steganography are independent, it is
`possible to both scramble and hide a message to maximize security. For
`example, the microdot is a form of steganography that became popular
`during the Second World War. German agents in Latin America would
`photographically shrink a page of text down to a dot less than 1
`millimeter in diameter, and then hide this microdot on top of a full stop
`in an apparently innocuous letter. The first microdot to be spotted by the
`FBI was in 1941, following a tip-off that the Americans should look for a
`tiny gleam from the surface of a letter, indicative of smooth film.
`Thereafter, the Americans could read the contents of most intercepted
`microdots, except when the German agents had taken the extra
`precaution of scrambling their message before reducing it. In such cases
`of cryptography combined with steganography, the Americans were
`sometimes able to intercept and block communications, but they were
`prevented from gaining any new information about German spying
`activity. Of the two branches of secret communication, cryptography is
`the more powerful because of this ability to prevent information from
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`Zoom Video Commc’ns, Inc. - Ex. 1039, Page 21
`Zoom Video Commc’ns, Inc. v. Cyph, Inc. (IPR2023-00142)
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`falling into enemy hands.
`In turn, cryptography itself can be divided into two branches, known
`as transposition and substitution. In transposition, the letters of the
`message are simply rearranged, effectively generating an anagram. For
`very short messages, such as a single word, this method is relatively
`insecure because there are only a limited number of ways of rearranging
`a handful of letters. For example, three letters can be arranged in only
`six different ways, e.g., cow, cwo, ocw, owc, wco, woc. However, as the
`number of
`letters gradually
`increases, the number of possible
`arrangements rapidly explodes, making it impossible to get back to the
`original message unless the exact scrambling process is known. For
`example, consider this short sentence. It contains just 35 letters,