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Each letter in the English language has its own unique personality, which includes its frequency and its relation to other letters. It is this personality that allows us to establish the true ident.i.ty of a letter, even when it has been disguised by monoalphabetic subst.i.tution.

We have now confidently established four letters, O = e, X = a, Y = i and B = h, and we can begin to replace some of the letters in the ciphertext with their plaintext equivalents. I shall stick to the convention of keeping ciphertext letters in upper case, while putting plaintext letters in lower case. This will help to distinguish between those letters we still have to identify, and those that have already been established.

PCQ VMJiPD LhiK LiSe KhahJaWaV haV ZCJPe EiPD KhahJiUaJ LhJee KCPK. CP Lhe LhCMKaPV aPV IiJKL PiDhL, QheP Khe haV ePVeV Lhe LaRe CI Sa'aJMI, Khe JCKe aPV EiKKev Lhe DJCMPV ZeICJe h i S, KaUiPD: "DJeaL EiPD, ICJ a LhCMKaPV aPV CPe PiDhLK i haNe ZeeP JeACMPLiPD LC UCM Lhe IaZReK CI FaKL aDeK aPV Lhe ReDePVK CI aPAiePL EiPDK. SaU i SaEe KC ZCRV aK LC AJaNe a IaNCMJ CI UCMJ SaGeKLU?"

eFiRCDMe, LaReK IJCS Lhe LhCMKaPV aPV CPe PiDhLK This simple step helps us to identify several other letters, because we can guess some of the words in the ciphertext. For example, the most common three-letter words in English are the and and, and these are relatively easy to spot-Lhe, which appears six times, and aPV, which appears five times. Hence, L probably represents t, P probably represents n, and V probably represents d. We can now replace these letters in the ciphertext with their true values: nCQ dMJinD thiK tiSe KhahJaWad had ZCJne EinD KhahJiUaJ thJee KCnK. Cn the thCMKand and IiJKt niDht, Qhen Khe had ended the taRe CI Sa'aJMI, Khe JCKe and EiKKed the DJCMnd ZeICJe hiS, KaUinD: "DJeat EinD, ICJ a thCMKand and Cne niDhtK i haNe Zeen JeACMntinD tC UCM the IaZReK CI FaKt aDeK and the ReDendK CI anAient EinDK. SaU i SaEe KC ZCRd aK tC AJaNe a IaNCMJ CI UCMJ SaGeKtU?"

eFiRCDMe, taReK IJCS the thCMKand and Cne niDhtK Once a few letters have been established, crypta.n.a.lysis progresses very rapidly. For example, the word at the beginning of the second sentence is Cn. Every word has a vowel in it, so C must be a vowel. There are only two vowels that remain to be identified, u and o; u does not fit, so C must represent o. We also have the word Khe, which implies that K represents either t or s. But we already know that L = t, so it becomes clear that K = s. Having identified these two letters, we insert them into the ciphertext, and there appears the phrase thoMsand and one niDhts. A sensible guess for this would be thousand and one nights, and it seems likely that the final line is telling us that this is a pa.s.sage from Tales from the Thousand and One Nights Tales from the Thousand and One Nights. This implies that M = u, I = f, J = r, D = g, R = l, and S = m.

We could continue trying to establish other letters by guessing other words, but instead let us have a look at what we know about the plain alphabet and cipher alphabet. These two alphabets form the key, and they were used by the cryptographer in order to perform the subst.i.tution that scrambled the message. Already, by identifying the true values of letters in the ciphertext, we have effectively been working out the details of the cipher alphabet. A summary of our achievements, so far, is given in the plain and cipher alphabets below.

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By examining the partial cipher alphabet, we can complete the crypta.n.a.lysis. The sequence VOIDBY in the cipher alphabet suggests that the cryptographer has chosen a keyphrase as the basis for the key. Some guesswork is enough to suggest the keyphrase might be A VOID BY GEORGES PEREC, which is reduced to AVOID BY GERSPC after removing s.p.a.ces and repet.i.tions. Thereafter, the letters continue in alphabetical order, omitting any that have already appeared in the keyphrase. In this particular case, the cryptographer took the unusual step of not starting the keyphrase at the beginning of the cipher alphabet, but rather starting it three letters in. This is possibly because the keyphrase begins with the letter A, and the cryptographer wanted to avoid encrypting a as A. At last, having established the complete cipher alphabet, we can unscramble the entire ciphertext, and the crypta.n.a.lysis is complete.

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Now during this time Shahrazad had borne King Shahriyar three sons. On the thousand and first night, when she had ended the tale of Ma'aruf, she rose and kissed the ground before him, saying: "Great King, for a thousand and one nights I have been recounting to you the fables of past ages and the legends of ancient kings. May I make so bold as to crave a favor of your majesty?"

Epilogue, Tales from the Thousand and One Nights Tales from the Thousand and One Nights Renaissance in the West Between A.D A.D. 800 and 1200, Arab scholars enjoyed a vigorous period of intellectual achievement. At the same time, Europe was firmly stuck in the Dark Ages. While al-Kind was describing the invention of crypta.n.a.lysis, Europeans were still struggling with the basics of cryptography. The only European inst.i.tutions to encourage the study of secret writing were the monasteries, where monks would study the Bible in search of hidden meanings, a fascination that has persisted through to modern times (see Appendix C Appendix C).

Medieval monks were intrigued by the fact that the Old Testament contained deliberate and obvious examples of cryptography. For example, the Old Testament includes pieces of text encrypted with atbash atbash, a traditional form of Hebrew subst.i.tution cipher. Atbash involves taking each letter, noting the number of places it is from the beginning of the alphabet, and replacing it with a letter that is an equal number of places from the end of the alphabet. In English this would mean that a, at the beginning of the alphabet, is replaced by Z, at the end of the alphabet, b is replaced by Y, and so on. The term atbash itself hints at the subst.i.tution it describes, because it consists of the first letter of the Hebrew alphabet, aleph aleph, followed by the last letter taw taw, and then there is the second letter, beth beth, followed by the second to last letter shin shin. An example of atbash appears in Jeremiah 25: 26 and 51: 41, where "Babel" is replaced by the word "Sheshach"; the first letter of Babel is beth beth, the second letter of the Hebrew alphabet, and this is replaced by shin shin, the second-to-last letter; the second letter of Babel is also beth beth, and so it too is replaced by shin; shin; and the last letter of Babel is and the last letter of Babel is lamed lamed, the twelfth letter of the Hebrew alphabet, and this is replaced by kaph kaph, the twelfth-to-last letter.

Atbash and other similar biblical ciphers were probably intended only to add mystery, rather than to conceal meaning, but they were enough to spark an interest in serious cryptography. European monks began to rediscover old subst.i.tution ciphers, they invented new ones, and, in due course, they helped to reintroduce cryptography into Western civilization. The first known European book to describe the use of cryptography was written in the thirteenth century by the English Franciscan monk and polymath Roger Bacon. Epistle on the Secret Works of Epistle on the Secret Works of Art and the Nullity of Magic Art and the Nullity of Magic included seven methods for keeping messages secret, and cautioned: "A man is crazy who writes a secret in any other way than one which will conceal it from the vulgar." included seven methods for keeping messages secret, and cautioned: "A man is crazy who writes a secret in any other way than one which will conceal it from the vulgar."

By the fourteenth century the use of cryptography had become increasingly widespread, with alchemists and scientists using it to keep their discoveries secret. Although better known for his literary achievements, Geoffrey Chaucer was also an astronomer and a cryptographer, and he is responsible for one of the most famous examples of early European encryption. In his Treatise on the Astrolabe Treatise on the Astrolabe he provided some additional notes ent.i.tled "The Equatorie of the Planetis," which included several encrypted paragraphs. Chaucer's encryption replaced plaintext letters with symbols, for example b with he provided some additional notes ent.i.tled "The Equatorie of the Planetis," which included several encrypted paragraphs. Chaucer's encryption replaced plaintext letters with symbols, for example b with[image] . A ciphertext consisting of strange symbols rather than letters may at first sight seem more complicated, but it is essentially equivalent to the traditional letter-for-letter subst.i.tution. The process of encryption and the level of security are exactly the same. . A ciphertext consisting of strange symbols rather than letters may at first sight seem more complicated, but it is essentially equivalent to the traditional letter-for-letter subst.i.tution. The process of encryption and the level of security are exactly the same.

By the fifteenth century, European cryptography was a burgeoning industry. The revival in the arts, sciences and scholarship during the Renaissance nurtured the capacity for cryptography, while an explosion in political machinations offered ample motivation for secret communication. Italy, in particular, provided the ideal environment for cryptography. As well as being at the heart of the Renaissance, it consisted of independent city states, each trying to outmaneuver the others. Diplomacy flourished, and each state would send amba.s.sadors to the courts of the others. Each amba.s.sador received messages from his respective head of state, describing details of the foreign policy he was to implement. In response, each amba.s.sador would send back any information that he had gleaned. Clearly there was a great incentive to encrypt communications in both directions, so each state established a cipher office, and each amba.s.sador had a cipher secretary.

At the same time that cryptography was becoming a routine diplomatic tool, the science of crypta.n.a.lysis was beginning to emerge in the West. Diplomats had only just familiarized themselves with the skills required to establish secure communications, and already there were individuals attempting to destroy this security. It is quite probable that crypta.n.a.lysis was independently discovered in Europe, but there is also the possibility that it was introduced from the Arab world. Islamic discoveries in science and mathematics strongly influenced the rebirth of science in Europe, and crypta.n.a.lysis might have been among the imported knowledge. that it was introduced from the Arab world. Islamic discoveries in science and mathematics strongly influenced the rebirth of science in Europe, and crypta.n.a.lysis might have been among the imported knowledge.

Arguably the first great European crypta.n.a.lyst was Giovanni Soro, appointed as Venetian cipher secretary in 1506. Soro's reputation was known throughout Italy, and friendly states would send intercepted messages to Venice for crypta.n.a.lysis. Even the Vatican, probably the second most active center of crypta.n.a.lysis, would send Soro seemingly impenetrable messages that had fallen into its hands. In 1526, Pope Clement VII sent him two encrypted messages, and both were returned having been successfully crypta.n.a.lyzed. And when one of the Pope's own encrypted messages was captured by the Florentines, the Pope sent a copy to Soro in the hope that he would be rea.s.sured that it was unbreakable. Soro claimed that he could not break the Pope's cipher, implying that the Florentines would also be unable to decipher it. However, this may have been a ploy to lull the Vatican cryptographers into a false sense of security-Soro might have been reluctant to point out the weaknesses of the Papal cipher, because this would only have encouraged the Vatican to switch to a more secure cipher, one that Soro might not have been able to break.

Elsewhere in Europe, other courts were also beginning to employ skilled crypta.n.a.lysts, such as Philibert Babou, crypta.n.a.lyst to King Francis I of France. Babou gained a reputation for being incredibly persistent, working day and night and persevering for weeks on end in order to crack an intercepted message. Unfortunately for Babou, this gave the king ample opportunity to carry on a long-term affair with his wife. Toward the end of the sixteenth century the French consolidated their codebreaking prowess with the arrival of Francois Viete, who took particular pleasure in cracking Spanish ciphers. Spain's cryptographers, who appear to have been naive compared with their rivals elsewhere in Europe, could not believe it when they discovered that their messages were transparent to the French. King Philip II of Spain went as far as pet.i.tioning the Vatican, claiming that the only explanation for Viete's crypta.n.a.lysis was that he was an "archfiend in league with the devil." Philip argued that Viete should be tried before a Cardinal's Court for his demonic deeds; but the Pope, who was aware that his own crypta.n.a.lysts had been reading Spanish ciphers for years, rejected the Spanish pet.i.tion. News of the pet.i.tion soon reached cipher experts in various countries, and Spanish cryptographers became the laughingstock of Europe. had been reading Spanish ciphers for years, rejected the Spanish pet.i.tion. News of the pet.i.tion soon reached cipher experts in various countries, and Spanish cryptographers became the laughingstock of Europe.

The Spanish embarra.s.sment was symptomatic of the state of the battle between cryptographers and crypta.n.a.lysts. This was a period of transition, with cryptographers still relying on the monoalphabetic subst.i.tution cipher, while crypta.n.a.lysts were beginning to use frequency a.n.a.lysis to break it. Those yet to discover the power of frequency a.n.a.lysis continued to trust monoalphabetic subst.i.tution, ignorant of the extent to which crypta.n.a.lysts such as Soro, Babou and Viete were able to read their messages.

Meanwhile, countries that were alert to the weakness of the straightforward monoalphabetic subst.i.tution cipher were anxious to develop a better cipher, something that would protect their own nation's messages from being unscrambled by enemy crypta.n.a.lysts. One of the simplest improvements to the security of the monoalphabetic subst.i.tution cipher was the introduction of nulls nulls, symbols or letters that were not subst.i.tutes for actual letters, merely blanks that represented nothing. For example, one could subst.i.tute each plain letter with a number between 1 and 99, which would leave 73 numbers that represent nothing, and these could be randomly sprinkled throughout the ciphertext with varying frequencies. The nulls would pose no problem to the intended recipient, who would know that they were to be ignored. However, the nulls would baffle an enemy interceptor because they would confuse an attack by frequency a.n.a.lysis. An equally simple development was that cryptographers would sometimes deliberately misspell words before encrypting the message. Thys haz thi ifekkt off diztaughting thi ballans off frikwenseas-making it harder for the crypta.n.a.lyst to apply frequency a.n.a.lysis. However, the intended recipient, who knows the key, can unscramble the message and then deal with the bad, but not unintelligible, spelling.

Another attempt to sh.o.r.e up the monoalphabetic subst.i.tution cipher involved the introduction of codewords. The term code code has a very broad meaning in everyday language, and it is often used to describe any method for communicating in secret. However, as mentioned in the Introduction, it actually has a very specific meaning, and applies only to a certain form of subst.i.tution. So far we have concentrated on the idea of a subst.i.tution cipher, whereby each letter is replaced by a different letter, has a very broad meaning in everyday language, and it is often used to describe any method for communicating in secret. However, as mentioned in the Introduction, it actually has a very specific meaning, and applies only to a certain form of subst.i.tution. So far we have concentrated on the idea of a subst.i.tution cipher, whereby each letter is replaced by a different letter, number or symbol. However, it is also possible to have subst.i.tution at a much higher level, whereby each word is represented by another word or symbol-this would be a code. For example, number or symbol. However, it is also possible to have subst.i.tution at a much higher level, whereby each word is represented by another word or symbol-this would be a code. For example, [image]

Technically, a code code is defined as subst.i.tution at the level of words or phrases, whereas a is defined as subst.i.tution at the level of words or phrases, whereas a cipher cipher is defined as subst.i.tution at the level of letters. Hence the term is defined as subst.i.tution at the level of letters. Hence the term encipher encipher means to scramble a message using a cipher, while means to scramble a message using a cipher, while encode encode means to scramble a message using a code. Similarly, the term means to scramble a message using a code. Similarly, the term decipher decipher applies to unscrambling an enciphered message, and applies to unscrambling an enciphered message, and decode decode to unscrambling an encoded message. The terms to unscrambling an encoded message. The terms encrypt encrypt and and decrypt decrypt are more general, and cover scrambling and unscrambling with respect to both codes and ciphers. are more general, and cover scrambling and unscrambling with respect to both codes and ciphers. Figure 7 Figure 7 presents a brief summary of these definitions. In general, I shall keep to these definitions, but when the sense is clear, I might use a term such as "codebreaking" to describe a process that is really "cipher breaking"-the latter phrase might be technically accurate, but the former phrase is widely accepted. presents a brief summary of these definitions. In general, I shall keep to these definitions, but when the sense is clear, I might use a term such as "codebreaking" to describe a process that is really "cipher breaking"-the latter phrase might be technically accurate, but the former phrase is widely accepted.

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Figure 7 The science of secret writing and its main branches. The science of secret writing and its main branches.

At first sight, codes seem to offer more security than ciphers, because words are much less vulnerable to frequency a.n.a.lysis than letters. To decipher a monoalphabetic cipher you need only identify the true value of each of the 26 characters, whereas to decipher a code you need to identify the true value of hundreds or even thousands of codewords. However, if we examine codes in more detail, we see that they suffer from two major practical failings when compared with ciphers. First, once the sender and receiver have agreed upon the 26 letters in the cipher alphabet (the key), they can encipher any message, but to achieve the same level of flexibility using a code they would need to go through the painstaking task of defining a codeword for every one of the thousands of possible plaintext words. The codebook would consist of hundreds of pages, and would look something like a dictionary. In other words, compiling a codebook is a major task, and carrying it around is a major inconvenience.

Second, the consequences of having a codebook captured by the enemy are devastating. Immediately, all the encoded communications would become transparent to the enemy. The senders and receivers would have to go through the painstaking process of having to compile an entirely new codebook, and then this hefty new tome would have to be distributed to everyone in the communications network, which might mean securely transporting it to every amba.s.sador in every state. In comparison, if the enemy succeeds in capturing a cipher key, then it is relatively easy to compile a new cipher alphabet of 26 letters, which can be memorized and easily distributed.

Even in the sixteenth century, cryptographers appreciated the inherent weaknesses of codes, and instead relied largely on ciphers, or sometimes nomenclators nomenclators. A nomenclator is a system of encryption that relies on a cipher alphabet, which is used to encrypt the majority of a message, and a limited list of codewords. For example, a nomenclator book might consist of a front page containing the cipher alphabet, and then a second page containing a list of codewords. Despite the addition of codewords, a nomenclator is not much more secure than a straightforward cipher, because the bulk of a message can be deciphered using frequency a.n.a.lysis, and the remaining encoded words can be guessed from the context.

As well as coping with the introduction of the nomenclator, the best crypta.n.a.lysts were also capable of dealing with badly spelled messages and the presence of nulls. In short, they were able to break the majority of encrypted messages. Their skills provided a steady flow of uncovered secrets, which influenced the decisions of their masters and mistresses, thereby affecting Europe's history at critical moments. and the presence of nulls. In short, they were able to break the majority of encrypted messages. Their skills provided a steady flow of uncovered secrets, which influenced the decisions of their masters and mistresses, thereby affecting Europe's history at critical moments.

Nowhere is the impact of crypta.n.a.lysis more dramatically ill.u.s.trated than in the case of Mary Queen of Scots. The outcome of her trial depended wholly on the battle between her codemakers and Queen Elizabeth's codebreakers. Mary was one of the most significant figures of the sixteenth century-Queen of Scotland, Queen of France, pretender to the English throne-yet her fate would be decided by a slip of paper, the message it bore, and whether or not that message could be deciphered.

The Babington Plot On November 24, 1542, the English forces of Henry VIII demolished the Scottish army at the Battle of Solway Moss. It appeared that Henry was on the verge of conquering Scotland and stealing the crown of King James V. After the battle, the distraught Scottish king suffered a complete mental and physical breakdown, and withdrew to the palace at Falkland. Even the birth of a daughter, Mary, just two weeks later could not revive the ailing king. It was as if he had been waiting for news of an heir so that he could die in peace, safe in the knowledge that he had done his duty. Just a week after Mary's birth, King James V, still only thirty years old, died. The baby princess had become Mary Queen of Scots.

Mary was born prematurely, and initially there was considerable concern that she would not survive. Rumors in England suggested that the baby had died, but this was merely wishful thinking at the English court, which was keen to hear any news that might destabilize Scotland. In fact, Mary soon grew strong and healthy, and at the age of nine months, on September 9, 1543, she was crowned in the chapel of Stirling Castle, surrounded by three earls, bearing on her behalf the royal crown, scepter and sword.

The fact that Queen Mary was so young offered Scotland a respite from English incursions. It would have been deemed unchivalrous had Henry VIII attempted to invade the country of a recently dead king, now under the rule of an infant queen. Instead, the English king decided on a policy of wooing Mary in the hope of arranging a marriage between her and his son Edward, thereby uniting the two nations under a Tudor sovereign. He began his maneuvering by releasing the Scottish n.o.bles captured at Solway Moss, on the condition that they campaign in favor of a union with England. wooing Mary in the hope of arranging a marriage between her and his son Edward, thereby uniting the two nations under a Tudor sovereign. He began his maneuvering by releasing the Scottish n.o.bles captured at Solway Moss, on the condition that they campaign in favor of a union with England.

However, after considering Henry's offer, the Scottish court rejected it in favor of a marriage to Francis, the dauphin of France. Scotland was choosing to ally itself with a fellow Roman Catholic nation, a decision which pleased Mary's mother, Mary of Guise, whose own marriage with James V had been intended to cement the relationship between Scotland and France. Mary and Francis were still children, but the plan for the future was that they would eventually marry, and Francis would ascend the throne of France with Mary as his queen, thereby uniting Scotland and France. In the meantime, France would defend Scotland against any English onslaught.

The promise of protection was rea.s.suring, particularly as Henry VIII had switched from diplomacy to intimidation in order to persuade the Scots that his own son was a more worthy groom for Mary Queen of Scots. His forces committed acts of piracy, destroyed crops, burned villages and attacked towns and cities along the border. The "rough wooing," as it is known, continued even after Henry's death in 1547. Under the auspices of his son, King Edward VI (the would-be suitor), the attacks culminated in the Battle of Pinkie Cleugh, in which the Scottish army was routed. As a result of this slaughter it was decided that, for her own safety, Mary should leave for France, beyond the reach of the English threat, where she could prepare for her marriage to Francis. On August 7, 1548, at the age of six, she set sail for the port of Roscoff.

Mary's first few years in the French court would be the most idyllic time of her life. She was surrounded by luxury, protected from harm, and she grew to love her future husband, the dauphin. At the age of sixteen they married, and the following year Francis and Mary became King and Queen of France. Everything seemed set for her triumphant return to Scotland, until her husband, who had always suffered from poor health, fell gravely ill. An ear infection that he had nursed since a child had worsened, the inflammation spread toward his brain, and an abscess began to develop. In 1560, within a year of being crowned, Francis was dead and Mary was widowed.

From this point onward, Mary's life would be repeatedly struck by tragedy. She returned to Scotland in 1561, where she discovered a transformed nation. During her long absence Mary had confirmed her Catholic faith, while her Scottish subjects had increasingly moved toward the Protestant church. Mary tolerated the wishes of the majority and at first reigned with relative success, but in 1565 she married her cousin, Henry Stewart, the Earl of Darnley, an act that led to a spiral of decline. Darnley was a vicious and brutal man whose ruthless greed for power lost Mary the loyalty of the Scottish n.o.bles. The following year Mary witnessed for herself the full horror of her husband's barbaric nature when he murdered David Riccio, her secretary, in front of her. It became clear to everyone that for the sake of Scotland it was necessary to get rid of Darnley. Historians debate whether it was Mary or the Scottish n.o.bles who instigated the plot, but on the night of February 9, 1567, Darnley's house was blown up and, as he attempted to escape, he was strangled. The only good to come from the marriage was a son and heir, James.

Mary's next marriage, to James Hepburn, the Fourth Earl of Bothwell, was hardly more successful. By the summer of 1567 the Protestant Scottish n.o.bles had become completely disillusioned with their Catholic Queen, and they exiled Bothwell and imprisoned Mary, forcing her to abdicate in favor of her fourteen-month-old son, James VI, while her half-brother, the Earl of Moray, acted as regent. The next year, Mary escaped from her prison, gathered an army of six thousand royalists, and made a final attempt to regain her crown. Her soldiers confronted the regent's army at the small village of Langside, near Glasgow, and Mary witnessed the battle from a nearby hilltop. Although her troops were greater in number, they lacked discipline, and Mary watched as they were torn apart. When defeat was inevitable, she fled. Ideally she would have headed east to the coast, and then on to France, but this would have meant crossing territory loyal to her half-brother, and so instead she headed south to England, where she hoped that her cousin Queen Elizabeth I would provide refuge.

Mary had made a terrible misjudgment. Elizabeth offered Mary nothing more than another prison. The official reason for her arrest was in connection with the murder of Darnley, but the true reason was that Mary posed a threat to Elizabeth, because English Catholics considered Mary to be the true queen of England. Through her grandmother, Margaret Tudor, the elder sister of Henry VIII, Mary did indeed have a claim to the throne, but Henry's last surviving offspring, Elizabeth I, would seem to have a prior claim. However, according to Catholics, Elizabeth was illegitimate because she was the daughter of Anne Boleyn, Henry's second wife after he had divorced Catherine of Aragon in defiance of the Pope. English Catholics did not recognize Henry VIII's divorce, they did not acknowledge his ensuing marriage to Anne Boleyn, and they certainly did not accept their daughter Elizabeth as Queen. Catholics saw Elizabeth as a b.a.s.t.a.r.d usurper. Mary to be the true queen of England. Through her grandmother, Margaret Tudor, the elder sister of Henry VIII, Mary did indeed have a claim to the throne, but Henry's last surviving offspring, Elizabeth I, would seem to have a prior claim. However, according to Catholics, Elizabeth was illegitimate because she was the daughter of Anne Boleyn, Henry's second wife after he had divorced Catherine of Aragon in defiance of the Pope. English Catholics did not recognize Henry VIII's divorce, they did not acknowledge his ensuing marriage to Anne Boleyn, and they certainly did not accept their daughter Elizabeth as Queen. Catholics saw Elizabeth as a b.a.s.t.a.r.d usurper.

Mary was imprisoned in a series of castles and manors. Although Elizabeth thought of her as one of the most dangerous figures in England, many Englishmen admitted that they admired her gracious manner, her obvious intelligence and her great beauty. William Cecil, Elizabeth's Great Minister, commented on "her cunning and sugared entertainment of all men," and Nicholas White, Cecil's emissary, made a similar observation: "She hath withal an alluring grace, a pretty Scotch accent, and a searching wit, clouded with mildness." But, as each year pa.s.sed, her appearance waned, her health deteriorated and she began to lose hope. Her jailer, Sir Amyas Paulet, a Puritan, was immune to her charms, and treated her with increasing harshness.

By 1586, after 18 years of imprisonment, she had lost all her privileges. She was confined to Chartley Hall in Staffordshire, and was no longer allowed to take the waters at Buxton, which had previously helped to alleviate her frequent illnesses. On her last visit to Buxton she used a diamond to inscribe a message on a windowpane: "Buxton, whose warm waters have made thy name famous, perchance I shall visit thee no more-Farewell." It appears that she suspected that she was about to lose what little freedom she had. Mary's growing sorrow was compounded by the actions of her nineteen-year-old son, King James VI of Scotland. She had always hoped that one day she would escape and return to Scotland to share power with her son, whom she had not seen since he was one year old. However, James felt no such affection for his mother. He had been brought up by Mary's enemies, who had taught James that his mother had murdered his father in order to marry her lover. James despised her, and feared that if she returned then she might seize his crown. His hatred toward Mary was demonstrated by the fact that he had no qualms in seeking a marriage with Elizabeth I, the woman responsible for his mother's imprisonment (and who was also thirty years his senior). Elizabeth declined the offer. toward Mary was demonstrated by the fact that he had no qualms in seeking a marriage with Elizabeth I, the woman responsible for his mother's imprisonment (and who was also thirty years his senior). Elizabeth declined the offer.

Mary wrote to her son in an attempt to win him over, but her letters never reached the Scottish border. By this stage, Mary was more isolated then ever before: all her outgoing letters were confiscated, and any incoming correspondence was kept by her jailer. Mary's morale was at its lowest, and it seemed that all hope was lost. It was under these severe and desperate circ.u.mstances that, on January 6, 1586, she received an astonishing package of letters.

The letters were from Mary's supporters on the Continent, and they had been smuggled into her prison by Gilbert Gifford, a Catholic who had left England in 1577 and trained as a priest at the English College in Rome. Upon returning to England in 1585, apparently keen to serve Mary, he immediately approached the French Emba.s.sy in London, where a pile of correspondence had acc.u.mulated. The Emba.s.sy had known that if they forwarded the letters by the formal route, Mary would never see them. However Gifford claimed that he could smuggle the letters into Chartley Hall, and sure enough he lived up to his word. This delivery was the first of many, and Gifford began a career as a courier, not only pa.s.sing messages to Mary but also collecting her replies. He had a rather cunning way of sneaking letters into Chartley Hall. He took the messages to a local brewer, who wrapped them in a leather packet, which was then hidden inside a hollow bung used to seal a barrel of beer. The brewer would deliver the barrel to Chartley Hall, whereupon one of Mary's servants would open the bung and take the contents to the Queen of Scots. The process worked equally well for getting messages out of Chartley Hall.

Meanwhile, unknown to Mary, a plan to rescue her was being hatched in the taverns of London. At the center of the plot was Anthony Babington, aged just twenty-four but already well known in the city as a handsome, charming and witty bon viveur. What his many admiring contemporaries failed to appreciate was that Babington deeply resented the establishment, which had persecuted him, his family and his faith. The state's anti-Catholic policies had reached new heights of horror, with priests being accused of treason, and anybody caught harboring them punished by the rack, mutilation and disemboweling while still alive. The Catholic ma.s.s was officially banned, and families who remained loyal to the Pope were forced to pay crippling taxes. Babington's animosity was fueled by the death of Lord Darcy, his great-grandfather, who was beheaded for his involvement in the Pilgrimage of Grace, a Catholic uprising against Henry VIII. accused of treason, and anybody caught harboring them punished by the rack, mutilation and disemboweling while still alive. The Catholic ma.s.s was officially banned, and families who remained loyal to the Pope were forced to pay crippling taxes. Babington's animosity was fueled by the death of Lord Darcy, his great-grandfather, who was beheaded for his involvement in the Pilgrimage of Grace, a Catholic uprising against Henry VIII.

The conspiracy began one evening in March 1586, when Babington and six confidants gathered in The Plough, an inn outside Temple Bar. As the historian Philip Caraman observed, "He drew to himself by the force of his exceptional charm and personality many young Catholic gentlemen of his own standing, gallant, adventurous and daring in defense of the Catholic faith in its day of stress; and ready for any arduous enterprise whatsoever that might advance the common Catholic cause." Over the next few months an ambitious plan emerged to free Mary Queen of Scots, a.s.sa.s.sinate Queen Elizabeth and incite a rebellion supported by an invasion from abroad.

The conspirators were agreed that the Babington Plot, as it became known, could not proceed without the blessing of Mary, but there was no apparent way to communicate with her. Then, on July 6, 1586, Gifford arrived on Babington's doorstep. He delivered a letter from Mary, explaining that she had heard about Babington via her supporters in Paris, and looked forward to hearing from him. In reply, Babington compiled a detailed letter in which he outlined his scheme, including a reference to the excommunication of Elizabeth by Pope Pius V in 1570, which he believed legitimized her a.s.sa.s.sination.

Myself with ten gentlemen and a hundred of our followers will undertake the delivery of your royal person from the hands of your enemies. For the dispatch of the usurper, from the obedience of whom we are by the excommunication of her made free, there be six n.o.ble gentlemen, all my private friends, who for the zeal they bear to the Catholic cause and your Majesty's service will undertake that tragical execution.

As before, Gifford used his trick of putting the message in the bung of a beer barrel in order to sneak it past Mary's guards. This can be considered a form of steganography, because the letter was being hidden. As an extra precaution, Babington enciphered his letter so that even if it was intercepted by Mary's jailer, it would be indecipherable and the plot would not be uncovered. He used a cipher which was not a simple monoalphabetic subst.i.tution, but rather a nomenclator, as shown in intercepted by Mary's jailer, it would be indecipherable and the plot would not be uncovered. He used a cipher which was not a simple monoalphabetic subst.i.tution, but rather a nomenclator, as shown in Figure 8 Figure 8. It consisted of 23 symbols that were to be subst.i.tuted for the letters of the alphabet (excluding j, v and w), along with 35 symbols representing words or phrases. In addition, there were four nulls ([image]) and a symbol[image] which signified that the next symbol represents a double letter ("dowbleth"). which signified that the next symbol represents a double letter ("dowbleth").

Gifford was still a youth, even younger than Babington, and yet he conducted his deliveries with confidence and guile. His aliases, such as Mr. Colerdin, Pietro and Cornelys, enabled him to travel the country without suspicion, and his contacts within the Catholic community provided him with a series of safe houses between London and Chartley Hall. However, each time Gifford traveled to or from Chartley Hall, he would make a detour. Although Gifford was apparently acting as an agent for Mary, he was actually a double agent. Back in 1585, before his return to England, Gifford had written to Sir Francis Walsingham, Princ.i.p.al Secretary to Queen Elizabeth, offering his services. Gifford realized that his Catholic background would act as a perfect mask for infiltrating plots against Queen Elizabeth. In the letter to Walsingham, he wrote, "I have heard of the work you do and I want to serve you. I have no scruples and no fear of danger. Whatever you order me to do I will accomplish." against Queen Elizabeth. In the letter to Walsingham, he wrote, "I have heard of the work you do and I want to serve you. I have no scruples and no fear of danger. Whatever you order me to do I will accomplish."

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Figure 8 The nomenclator of Mary Queen of Scots, consisting of a cipher alphabet and codewords. The nomenclator of Mary Queen of Scots, consisting of a cipher alphabet and codewords.

Walsingham was Elizabeth's most ruthless minister. He was a Machiavellian figure, a spymaster who was responsible for the security of the monarch. He had inherited a small network of spies, which he rapidly expanded into the Continent, where many of the plots against Elizabeth were being hatched. After his death it was discovered that he had been receiving regular reports from twelve locations in France, nine in Germany, four in Italy, four in Spain and three in the Low Countries, as well as having informants in Constantinople, Algiers and Tripoli.

Walsingham recruited Gifford as a spy, and in fact it was Walsingham who ordered Gifford to approach the French Emba.s.sy and offer himself as a courier. Each time Gifford collected a message to or from Mary, he would first take it to Walsingham. The vigilant spymaster would then pa.s.s it to his counterfeiters, who would break the seal on each letter, make a copy, and then reseal the original letter with an identical stamp before handing it back to Gifford. The apparently untouched letter could then be delivered to Mary or her correspondents, who remained oblivious to what was going on.

When Gifford handed Walsingham a letter from Babington to Mary, the first objective was to decipher it. Walsingham had originally encountered codes and ciphers while reading a book written by the Italian mathematician and cryptographer Girolamo Cardano (who, incidentally, proposed a form of writing for the blind based on touch, a precursor of Braille). Cardano's book aroused Walsingham's interest, but it was a decipherment by the Flemish crypta.n.a.lyst Philip van Marnix that really convinced him of the power of having a codebreaker at his disposal. In 1577, Philip of Spain was using ciphers to correspond with his half-brother and fellow Catholic, Don John of Austria, who was in control of much of the Netherlands. Philip's letter described a plan to invade England, but it was intercepted by William of Orange, who pa.s.sed it to Marnix, his cipher secretary. Marnix deciphered the plan, and William pa.s.sed the information to Daniel Rogers, an English agent working on the Continent, who in turn warned Walsingham of the invasion. The English reinforced their defenses, which was enough to deter the invasion attempt.

Now fully aware of the value of crypta.n.a.lysis, Walsingham established a cipher school in London and employed Thomas Phelippes as his cipher secretary, a man "of low stature, slender every way, dark yellow haired on the head, and clear yellow bearded, eaten in the face with smallpox, of short sight, thirty years of age by appearance." Phelippes was a linguist who could speak French, Italian, Spanish, Latin and German, and, more importantly, he was one of Europe's finest crypta.n.a.lysts. a cipher school in London and employed Thomas Phelippes as his cipher secretary, a man "of low stature, slender every way, dark yellow haired on the head, and clear yellow bearded, eaten in the face with smallpox, of short sight, thirty years of age by appearance." Phelippes was a linguist who could speak French, Italian, Spanish, Latin and German, and, more importantly, he was one of Europe's finest crypta.n.a.lysts.

Upon receiving any message to or from Mary, Phelippes devoured it. He was a master of frequency a.n.a.lysis, and it would be merely a matter of time before he found a solution. He established the frequency of each character, and tentatively proposed values for those that appeared most often. When a particular approach hinted at absurdity, he would backtrack and try alternative subst.i.tutions. Gradually he would identify the nulls, the cryptographic red herrings, and put them to one side. Eventually all that remained were the handful of codewords, whose meaning could be guessed from the context.

When Phelippes deciphered Babington's message to Mary, which clearly proposed the a.s.sa.s.sination of Elizabeth, he immediately forwarded the d.a.m.ning text to his master. At this point Walsingham could have pounced on Babington, but he wanted more than the execution of a handful of rebels. He bided his time in the hope that Mary would reply and authorize the plot, thereby incriminating herself. Walsingham had long wished for the death of Mary Queen of Scots, but he was aware of Elizabeth's reluctance to execute her cousin. However, if he could prove that Mary was endorsing an attempt on the life of Elizabeth, then surely his queen would permit the execution of her Catholic rival. Walsingham's hopes were soon fulfilled.

On July 17, Mary replied to Babington, effectively signing her own death warrant. She explicitly wrote about the "design," showing particular concern that she should be released simultaneously with, or before, Elizabeth's a.s.sa.s.sination, otherwise news might reach her jailer, who might then murder her. Before reaching Babington, the letter made the usual detour to Phelippes. Having crypta.n.a.lyzed the earlier message, he deciphered this one with ease, read its contents, and marked it with a "[image]"-the sign of the gallows.

Walsingham had all the evidence he needed to arrest Mary and Babington, but still he was not satisfied. In order to destroy the conspiracy completely, he needed the names of all those involved. He asked Phelippes to forge a postscript to Mary's letter, which would entice Babington to name names. One of Phelippes's additional talents was as a forger, and it was said that he had the ability "to write any man's hand, if he had once seen it, as if the man himself had writ it." conspiracy completely, he needed the names of all those involved. He asked Phelippes to forge a postscript to Mary's letter, which would entice Babington to name names. One of Phelippes's additional talents was as a forger, and it was said that he had the ability "to write any man's hand, if he had once seen it, as if the man himself had writ it." Figure 9 Figure 9 shows the postscript that was added at the end of Mary's letter to Babington. It can be deciphered using Mary's nomenclator, as shown in shows the postscript that was added at the end of Mary's letter to Babington. It can be deciphered using Mary's nomenclator, as shown in Figure 8 Figure 8, to reveal the following plaintext: I would be glad to know the names and qualities of the six gentlemen which are to accomplish the designment; for it may be that I shall be able, upon knowledge of the parties, to give you some further advice necessary to be followed therein, as also from time to time particularly how you proceed: and as soon as you may, for the same purpose, who be already, and how far everyone is privy hereunto.

The cipher of Mary Queen of Scots clearly demonstrates that a weak encryption can be worse than no encryption at all. Both Mary and Babington wrote explicitly about their intentions because they believed that their communications were secure, whereas if they had been communicating openly they would have referred to their plan in a more discreet manner. Furthermore, their faith in their cipher made them particularly vulnerable to accepting Phelippes's forgery. Sender and receiver often have such confidence in the strength of their cipher that they consider it impossible for the enemy to mimic the cipher and insert forged text. The correct use of a strong cipher is a clear boon to sender and receiver, but the misuse of a weak cipher can generate a very false sense of security. they consider it impossible for the enemy to mimic the cipher and insert forged text. The correct use of a strong cipher is a clear boon to sender and receiver, but the misuse of a weak cipher can generate a very false sense of security.

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Figure 9 The forged postscript added by Thomas Phelippes to Mary's message. It can be deciphered by referring to Mary's nomenclator ( The forged postscript added by Thomas Phelippes to Mary's message. It can be deciphered by referring to Mary's nomenclator (Figure 8). (photo credit 1.3) Soon after receiving the message and its postscript, Babington needed to go abroad to organize the invasion, and had to register at Walsingham's department in order to acquire a pa.s.sport. This would have been an ideal time to capture the traitor, but the bureaucrat who was manning the office, John Scudamore, was not expecting the most wanted traitor in England to turn up at his door. Scudamore, with no support to hand, took the unsuspecting Babington to a nearby tavern, stalling for time while his a.s.sistant organized a group of soldiers. A short while later a note arrived at the tavern, informing Scudamore that it was time for the arrest. Babington, however, caught sight of it. He casually said that he would pay for the beer and meal and rose to his feet, leaving his sword and coat at the table, implying that he would return in an instant. Instead, he slipped out of the back door and escaped, first to St. John's Wood and then on to Harrow. He attempted to disguise himself, cutting his hair short and staining his skin with walnut juice to mask his aristocratic background. He managed to elude capture for ten days, but by August 15, Babington and his six colleagues were captured and brought to London. Church bells across the city rang out in triumph. Their executions were horrid in the extreme. In the words of the Elizabethan historian William Camden, "they were all cut down, their privities were cut off, bowelled alive and seeing, and quartered."

Meanwhile, on August 11, Mary Queen of Scots and her entourage had been allowed the exceptional privilege of riding in the grounds of Chartley Hall. As Mary crossed the moors she spied some hors.e.m.e.n approaching, and immediately thought that these must be Babington's men coming to rescue her. It soon became clear that these men had come to arrest her, not release her. Mary had been implicated in the Babington Plot, and was charged under the Act of a.s.sociation, an Act of Parliament pa.s.sed in 1584 specifically designed to convict anybody involved in a conspiracy against Elizabeth.

The trial was held in Fotheringhay Castle, a bleak, miserable place in the middle of the featureless fens of East Anglia. It began on Wednesday, October 15, in front of two chief justices, four other judges, the Lord Chancellor, the Lord Treasurer, Walsingham, and various earls, knights and barons. At the back of the courtroom there was s.p.a.ce for spectators, such as local villagers and the servants of the commissioners, all eager to see the humiliated Scottish queen beg forgiveness and plead for her life. However, Mary remained dignified and composed throughout the trial. Mary's main defense was to deny any connection with Babington. "Can I be responsible for the criminal projects of a few desperate men," she proclaimed, "which they planned without my knowledge or partic.i.p.ation?" Her statement had little impact in the face of the evidence against her. Chancellor, the Lord Treasurer, Walsingham, and various earls, knights and barons. At the back of the courtroom there was s.p.a.ce for spectators, such as local villagers and the servants of the commissioners, all eager to see the humiliated Scottish queen beg forgiveness and plead for her life. However, Mary remained dignified and composed throughout the trial. Mary's main defense was to deny any connection with Babington. "Can I be responsible for the criminal projects of a few desperate men," she proclaimed, "which they planned without my knowledge or partic.i.p.ation?" Her statement had little impact in the face of the evidence against her.

Mary and Babington had relied on a cipher to keep their plans secret, but they lived during a period when cryptography was being weakened by advances in crypta.n.a.lysis. Although their cipher would have been sufficient protection against the prying eyes of an amateur, it stood no chance against an expert in frequency a.n.a.lysis. In the spectators' gallery sat Phelippes, quietly watching the presentation of the evidence that he had conjured from the enciphered letters.

The trial went into a second day, and Mary continued to deny any knowledge of the Babington Plot. When the trial finished, she left the judges to decide her fate, pardoning them in advance for the inevitable decision. Ten days later, the Star Chamber met in Westminster and concluded that Mary had been guilty of "compa.s.sing and imagining since June 1st matters tending to the death and destruction of the Queen of England." They recommended the death penalty, and Elizabeth signed the death warrant. matters tending to the death and destruction of the Queen of England." They recommended the death penalty, and Elizabeth signed the death warrant.

On February 8, 1587, in the Great Hall of Fotheringhay Castle, an audience of three hundred gathered to watch the beheading. Walsingham was determined to minimize Mary's influence as a martyr, and he ordered that the block, Mary's clothing, and everything else relating to the execution be burned in order to avoid the creation of any holy relics. He also planned a lavish funeral procession for his son-in-law, Sir Philip Sidney, to take place the following week. Sidney, a popular and heroic figure, had died fighting Catholics in the Netherlands, and Walsingham believed that a magnificent parade in his honor would dampen sympathy for Mary. However, Mary was equally determined that her final appearance should be a defiant gesture, an opportunity to reaffirm her Catholic faith and inspire her followers.

While the Dean of Peterborough led the prayers, Mary spoke aloud her own prayers for the salvation of the English Catholic Church, for her son and for Elizabeth. With her family motto, "In my end is my beginning," in her mind, she composed herself and approached the block. The executioners requested her forgiveness, and she replied, "I forgive you with all my heart, for now I hope you shall make an end of all my troubles." Richard Wingfield, in his Narration of the Last Days of the Queen of Scots Narration of the Last Days of the Queen of Scots, describes her final moments: Then she laide herself upon the blocke most quietlie, & stretching out her armes & legges cryed out In ma.n.u.s tuas domine three or foure times, & at the laste while one of the executioners held her slightlie with one of his handes, the other gave two strokes with an axe before he cutt of her head, & yet lefte a little gristle behinde at which time she made verie small noyse & stirred not any parte of herself from the place where she laye...Her lipps stirred up & downe almost a quarter of an hower after her head was cutt of. Then one of her executioners plucking of her garters espied her little dogge which was crept under her clothes which could not be gotten forth but with force & afterwardes could not depart from her dead corpse, but came and laye betweene her head & shoulders a thing dilligently noted.

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Figure 10 The execution of Mary Queen of Scots. ( The execution of Mary Queen of Scots. (photo credit 1.4)

2 Le Chiffre Indechiffrable

For centuries, the simple monoalphabetic subst.i.tution cipher had been sufficient to ensure secrecy. The subsequent development of frequency a.n.a.lysis, first in the Arab world and then in Europe, destroyed its security. The tragic execution of Mary Queen of Scots was a dramatic ill.u.s.tration of the weaknesses of monoalphabetic subst.i.tution, and in the battle between cryptographers and crypta.n.a.lysts it was clear that the crypta.n.a.lysts had gained the upper hand. Anybody sending an encrypted message had to accept that an expert enemy codebreaker might intercept and decipher their most precious secrets.

The onus was clearly on the cryptographers to concoct a new, stronger cipher, something that could outwit the crypta.n.a.lysts. Although this cipher would not emerge until the end of the sixteenth century, its origins can be traced back to the fifteenth-century Florentine polymath Leon Battista Alberti. Born in 1404, Alberti was one of the leading figures of the Renaissance-a painter, composer, poet and philosopher, as well as the author of the first scientific a.n.a.lysis of perspective, a treatise on the housefly and a funeral oration for his dog. He is probably best known as an architect, having designed Rome's first Trevi Fountain and having written De re aedificatoria De re aedificatoria, the first printed book on architecture, which acted as a catalyst for the transition from Gothic to Renaissance design.

Sometime in the 1460s, Alberti was wandering through the gardens of the Vatican when he b.u.mped into his friend Leonardo Dato, the pontifical secretary, who began chatting to him about some of the finer points of cryptography. This casual conversation prompted Alberti to write an essay on the subject, outlining what he believed to be a new form of cipher. At the time, all subst.i.tution ciphers required a single cipher alphabet for encrypting each message. However, Alberti proposed using two or more cipher alphabets, switching between them during encipherment, thereby confusing potential crypta.n.a.lysts. two or more cipher alphabets, switching between them during encipherment, thereby confusing potential crypta.n.a.lysts.

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For example, here we have two possible cipher alphabets, and we could encrypt a message by alternating between them. To encrypt the message h.e.l.lo, we would encrypt the first letter according to the first cipher alphabet, so that h becomes A, but we would encrypt the second letter according to the second cipher alphabet, so that e becomes F. To encrypt the third letter we return to the first cipher alphabet, and to encrypt the fourth letter we return to the second alphabet. This means that the first l is enciphered as P, but the second l is enciphered as A. The final letter, o, is enciphered according to the first cipher alphabet and becomes D. The complete ciphertext reads AFPAD. The crucial advantage of Alberti's system is that the same letter in the plaintext does not necessarily appear as the same letter in the ciphertext, so the repeated l in h.e.l.lo is enciphered differently in each case. Similarly, the repeated A in the ciphertext represents a different plaintext letter in each case, first h and then l.

Although he had hit upon the most significant breakthrough in encryption for over a thousand years, Alberti failed to develop his concept into a fully formed system of encryption. That task fell to a diverse group of intellectuals, who built on his initial idea. First came Johannes Trithemius, a German abbot born in 1462, then Giovanni Porta, an Italian scientist born in 1535, and finally Blaise de Vigenere, a French diplomat born in 1523. Vigenere became acquainted with the writings of Alberti, Trithemius and Porta when, at the age of twenty-six, he was sent to Rome on a two-year diplomatic mission. To start with, his interest in cryptography was purely practical and was linked to his diplomatic work. Then, at the age of thirty-nine, Vigenere decided that he had acc.u.mulated enough money for him to be able to abandon his career and concentrate on a life of study. It was only then that he examined in detail the ideas of Alberti, Trithemius and Porta, weaving them into a coherent and powerful new cipher.

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Figure 11 Blaise de Vigenere. ( Blaise de Vigenere. (photo credit 2.1) Although Alberti, Trithemius and Porta all made vital contributions, the cipher is known as the Vigenere cipher in honor of the man who developed it into its final form. The strength of the Vigenere cipher lies in its using not one, but 26 distinct cipher alphabets to encrypt a message. The first step in encipherment is to draw up a so-called Vigenere square, as shown in Table 3 Table 3, a plaintext alphabet followed by 26 cipher alphabets, each shifted by one letter with respect to the previous alphabet. Hence, row 1 represents a cipher alphabet with a Caesar shift of 1, which means that it could be used to implement a Caesar shift cipher in which every letter of the plaintext is replaced by the letter one place further on in the alphabet. Similarly, row 2 represents a cipher alphabet with a Caesar shift of 2, and so on. The top row of the square, in lower case, represents the plaintext letters. You could encipher each plaintext letter according to any one of the 26 cipher alphabets. For example, if cipher alphabet number 2 is used, then the letter a is enciphered as C, but if cipher alphabet number 12 is used, then a is enciphered as M. of 2, and so on. The top row of the square, in lower case, represents the plaintext letters. You could encipher each plaintext letter according to any one of the 26 cipher alphabets. For example, if cipher alphabet number 2 is used, then the letter a is enciphered as C, but if cipher alphabet number 12 is used, then a is enciphered as M.

Table 3 A Vigenere square. A Vigenere square.

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If the sender were to use just one of the cipher alphabets to encipher an entire message, this would effectively be a simple Caesar cipher, which would be a very weak form of encryption, easily deciphered by an enemy interceptor. However, in the Vigenere cipher a different row of the Vigenere square (a different cipher alphabet) is used to encrypt different letters of the message. In other words, the sender might encrypt the first letter according to row 5, the second according to row 14, the third according to row 21, and so on.

To unscramble the message, the intended receiver needs to know which row of the Vigenere square has been used to encipher each letter, so there must be an agreed system of switching between rows. This is achieved by using a keyword. To ill.u.s.trate how a keyword is used with the Vigenere square to encrypt a short message, let us encipher divert troops to east ridge, using the keyword WHITE. First of all, the keyword is spelled out above the message, and repeated over and over again so that each letter in the message is a.s.sociated with a letter from the keyword. The ciphertext is then generated as follows. To encrypt the first letter, d, begin by identifying the key letter above it, W, which in turn defines a particular row in the Vigenere square. The row beginning with W, row 22, is the cipher alphabet that will be used to find the subst.i.tute letter for the plaintext d. We look to see where the column headed by d intersects the row beginning with W, which turns out to be at the letter Z. Consequently, the letter d in the plaintext is represented by Z in the ciphertext.

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To encipher the second letter of the message, i, the process is repeated. The key letter above i is H, so it is encrypted via a different row in the Vigenere square: the H row (row 7) which is a new cipher alphabet. To encrypt i, we look to see where the column headed by i intersects the row beginning with H, which turns out to be at the letter P. Consequently, the letter i in the plaintext is represented by P in the ciphertext. Each letter of the keyword indicates a particular cipher alphabet within the Vigenere square, and because the keyword contains five letters, the sender encrypts the message by cycling through five rows of the Vigenere square. The fifth letter of the message is enciphered according to the fifth letter of the keyword, E, but to encipher the sixth letter of the message we have to return encrypt i, we look to see where the column headed by i intersects the row beginning with H, which turns out to be at the letter P. Consequently, the letter i in the plaintext is represented by P in the ciphertext. Each letter of the keyword indicates a particular cipher alphabet within the Vigenere square, and because the keyword contains five letters, the sender encrypts the message by cycling through five rows of the Vigenere square. The fifth letter of the message is enciphered according to the fifth letter of the keyword, E, but to encipher the sixth letter of the message we have to return to the first letter of the keyword. A longer keyword, or perhaps a keyphrase, would bring more rows into the encryption process and increase the complexity of the cipher. to the first letter of the keyword. A longer keyword, or perhaps a keyphrase, would bring more rows into the encryption process and increase the complexity of the cipher. Table 4 Table 4 shows a Vigenere square, highlighting the five rows (i.e., the five cipher alphabets) defined by the keyword WHITE. shows a Vigenere square, highlighting the five rows (i.e., the five cipher alphabets) defined by the keyword WHITE.

Table 4 A Vigenere square with the rows defined by the keyword WHITE highlighted. Encryption is achieved by switching between the five highlighted cipher alphabets, defined by W, H, I, T and E. A Vigenere square with the rows defined by the keyword WHITE highlighted. Encryption is achieved by switching between the five highlighted cipher alphabets, defined by W, H, I, T and E.

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The great advantage of the Vigenere cipher is that it is impregnable to the frequency a.n.a.lysis described in Chapter 1 Chapter 1. For example, a crypta.n.a.lyst applying frequency a.n.a.lysis to a piece of ciphertext would usually begin by identifying the most common letter in the ciphertext, which in this case is Z, and then a.s.sume that this represents the most common letter in English, e. In fact, the letter Z represents three different letters, d, r and s, but not e. This is clearly a problem for the crypta.n.a.lyst. The fact that a letter which appears several times in the ciphertext can represent a diff