THE CODEBREAKERS

by DAVID KAHN

  He apparently became interested in cryptology about the mid-1880s. He devised some of the first cipher machines to integrate a printing mechanism:* after enciphering, the cryptographer pressed a button which imprinted the cipher letter on a paper tape. He published for the first time in cryptology what he called “cryptographic equations.” (Babbage had employed such equations in his own work, but had never described them publicly.)

  In articles in the scientific journal Le Génie Civil for May 12 and 19, 1888 (the first two parts of a series that was later collected into a book), de Viaris proposed that the Greek letter chi (χ) stand for any ciphertext letter, gamma (γ) for any keyletter and the lower-case c for any cleartext letter. He then proved that the algebraic formula c + γ = χ would produce a Vigenère en-cipherment no different from the standard manipulations of tableau, slide, or disk. If the letters of the alphabet be numbered from zero to 25,

  the Vigenère may be duplicated mathematically by adding the values for plain and key together and then turning the sum (less 26 if it is 26 or above) back into letter form. For example, a standard tableau encipherment of plaintext d with key G yields cipher J. With the formula, these same letters give 3 + 6 = 9, or J. A different cipher will naturally have a different formula. Those for the Big Three of normal-alphabet polyalphabetics are (using the modern notation of P for plain, K for key and C for cipher):

  Plan of the Marquis de Viaris’ printing cipher device

  The symmetry of these formulas clearly shows almost graphically that Beaufort is a reciprocal substitution and that Variant and Vigenère are inverse operations. It is a striking demonstration of how mathematics floodlights the architecture of ciphers, revealing their framework in a glare of illumination.

  Mathematics was just de Viaris’ bright idea in the 1880s. Nobody paid much attention to his formulas, and even he did not pursue the matter. But they testify to his originality. In 1893, he published another book that, like Kerckhoffs’, stressed the cryptanalytic. It included a fine solution of a difficult cipher proposed by a fellow cryptologist. During this time he had reorganized the Bureau du Chiffre of the Ministry of Foreign Affairs, instituting a new method of communication—probably his Dictionnaire ABC, published in 1898, which used a flexible band with numbers printed on it to facilitate superencipherment. De Viaris died on February 18, 1901.

  The work of Paul Louis Eugène Valério, a captain of artillery, began appearing in the Journal des Sciences militaires in December, 1892, almost exactly ten years after Kerckhoffs’ first article. But where Kerckhoffs was concise, Valério was exhaustive. The last often installments was not published until May of 1895, by which time the work totaled 214 pages. More than two thirds was taken up by an exhaustive study of the phonological characteristics of the main European languages; Valério, who felt the drift of the times, concentrated heavily on German. The rest of the work—later assembled into book form as De la cryptographice—detailed the solutions of cipher systems and, for perhaps the first time in cryptology, of codes. Except for his exposition on code cryptanalysis, Valério added little that was new to the science, but his comprehensiveness filled in areas merely outlined by his predecessors and gave French cryptology a feeling of completion and solidity that it had lacked.

  Félix Marie Delastelle was the only major writer on cryptology of the time who was not in the military. He was born January 2, 1840, at the Brittany seaport of Saint-Malo to a long line of seafaring ancestors—his father, master of an oceangoing vessel, was apparently lost at sea when Félix was three. After graduating from the College of Saint-Malo, Delastelle got a job as inspector with the government’s Tobacco Administration, with duties involving warehousing in cities as large as Marseilles, a post he held for forty years. After his retirement in 1900, the quiet bachelor moved into Ker Kador, an apartment hotel in Paramé, near Saint-Malo, where he devoted full time to writing a book on cryptology that would improve on the short one he had written seven years earlier. He signed the foreword at Paramé on May 25, and the book, Traité Élémentaire de Cryptographie, was published the following year by the respected house of Gauthier-Villars. But on April 2, 1902, while he was about to go to the home of his elder brother, Auguste Michel, who had just died, he was stricken with a heart attack, and died the same day.

  His book’s 156 pages deal mostly with systems of encipherment. Delastelle accused most previous books with considerable justice of being “only catalogues, more or less complete and detailed, of various systems, of which none is studied in depth, even several that differ only in appearance. I therefore believe,” he wrote in his foreword, “that I have done something useful in classifying all these systems and in discussing how principles may be deduced from them.”

  But while the individuality of cipher systems balked this plan, Delastelle’s good intentions rewarded him. While searching for a method of bigraphic encipherment that did not require cumbersome 26-by-26 enciphering tables (during which he reasoned his way to an independent invention of the Play-fair), Delastelle invented a fractionating system of considerable importance in cryptology. It differed from those of Pliny Earle Chase, who had subjected the letter fractions to substitution before recombining them. Delastelle transposed them. His cipher, the bifid, requires the fundamental bipartite substitution, which he somehow never wrote in checkerboard form:

  The plaintext is written in groups of a specified length, say five letters, and the coordinates are written vertically beneath each letter. Delastelle set up his own plaintext, Attendez des ordres (“Wait for orders”), like this:

  To form the ciphertext, the coordinates are paired horizontally group by group and reconverted into letters: 43 = Y, 33 = P, 12 = N, 55 = O, and so on. The complete ciphertext: YPNOA PYDZV FHIRB DJ. If a different alphabet serves for the recomposition, the system is called a bifid with conjugated matrices. If tripartite coordinates (a = 111, b = 112, c = 113, etc.) are decomposed, the elements shuffled and then recomposed in different combinations, the system is called a trifid.

  Delastelle experimented to nullify Kerckhoffs’ symmetry of position by shifting the positions of key, plain, cipher, and index letters in St.-Cyr slides. The traditional arrangement regards the first letter of the stator alphabet as the index letter; the key is set under this; the plaintext is then located in the stator alphabet and the ciphertext on the slide beneath it. Delastelle burst the bonds and showed that other dispositions would serve as well. For example, the keyletter may be located in the stator alphabet and the plaintext set under it; then the letter designated as the index letter may be located on the slide and the ciphertext found on the stator above it. Because Delastelle did not move the index letter, he found only eight such dispositions. But there are actually twelve, and, despite Delastelle’s attempt, all show some kind of symmetry, whether latent or patent, vertical or horizontal, in the plain or in the cipher component.

  Étienne Bazeries is the great pragmatist of cryptology. His theoretical contributions are negligible, but he was one of the greatest natural crypt-analysts the science has seen. Ciphers melted under the fierce intensity of his mental processes. Historical cryptograms, new inventions, official systems, the clandestine communications of plotters—all receded, abandoned their ramparts, and finally succumbed to his blazing onslaught. He was also the most opinionated cryptanalyst the science has known. His barbed pronunciamentos, hurled like Jovian thunderbolts, enraged his contemporaries and lashed the usually unruffled waters of cryptology into unwonted tempests.

  He was born August 21, 1846, the son of a mounted policeman, in the little Mediterranean fishing village of Port-Vendres, which lies in the shadow of the mighty Pyrenees. Raised there, étienne learned Catalan at the same time he learned French. Five days after he turned seventeen, he enlisted in the Army’s 4th Supply Squadron to avoid the agricultural career his family had planned for him. He fought in the Franco-Prussian War and was taken prisoner of war when Metz fell, but escaped, disguised as a bricklayer. Promotions came slowly but steadily, de
spite a strong-willed individualism that refused to accept things as they are simply because they are: as a lieutenant, he nervily told a general that the regimental harness injured the squadron’s horses. He had been given his lieutenancy in 1874, and the next year was sent to Algeria on the first of three tours of duty there. On his return in 1876, he married Marie-Louise-Elodie Berthon, by whom he had three daughters.

  He seems to have become interested in cryptology by solving the cryptograms in the newspapers’ personal columns, some of them setting up adulterous assignations, with whose sordid details he regaled his messmates. One day in 1890, while stationed at Nantes, he said aloud to his brother officers at the headquarters of the 11th Corps that the official French military cipher, a complicated form of transposition, could be read without the key. There was a general roar of laughter—but one who did not join the chorus was the corps commander, General Charles Alexandre Fay, one of the best-known officers of the time. He took Bazeries up on the implied challenge and sent him several cryptograms in the system. Bazeries solved them; his comrades and Fay were impressed; even the War Ministry took note, and readied a new system. Then Bazeries topped his own feat by reading the test messages in the new system before it even went into service.

  Word of his ability had evidently spread beyond the parade ground, for early the next year a gentleman from Nantes, one Bord, who had invented a printing cryptograph that, Bazeries conceded, was “a jewel of an instrument,” submitted eight cryptograms enciphered with it to Bazeries. This was on January 8, 1891; by the 31st, Bord, attempting to salvage the system, was sending him five messages in a more complicated arrangement of the device. Bazeries read two more sets, of increasing complication if not difficulty, until, wanting to halt what had become for him a tedious repetition, he had Bord compose one in his ultimate system. Bazeries easily discovered that it read, “I want to be hanged if you decipher this,” hastily implored the inventor not to do anything rash, and observed later that if all those whose ciphers had been solved were to be hanged, the penalty would lose all meaning.

  By now his reputation had reached the Quai d’Orsay in Paris, for in August of 1891 the Army placed him temporarily at the disposition of the Bureau du Chiffre of the Ministry of Foreign Affairs. He was promoted in 1892 to the command of his own supply squadron, and served again with the Foreign Ministry in 1894.

  These years in and around Paris were his most active, cryptologically. As fast as new ciphers appeared, he smashed them. Among those he solved were the systems of La Feuillade, Hermann, and d’Ocagne, and the devices of Gavrelle and de Viaris—the latter feat one that was soon to boomerang. He became interested in historical ciphers when a commandant on the general staff asked him for help in reading some ciphered dispatches for a study of Louis XIV’s military campaigns. Bazeries solved that system, and then rifled the archives for others, succeeding in breaking down nomenclators of Francis I, Francis II, Henry IV, Mirabeau, and Napoleon. He found the campaign ciphers of the great military genius so feeble that he contemptuously put the word “ciphers” in quotation marks in the title of his monograph on them.

  He bloodied his knuckles in the arena of real-life cryptanalysis, too. In 1892, French authorities arrested a group of anarchists and brought them to trial. Included in the evidence was a number of cryptograms that had been solved by Bazeries. They used a system called the Gronsfeld, a kind of truncated Vigenère named for the Count of Gronsfeld, who described it to the 17th-century author Gaspar Schott while they went together from Mainz to Frankfort. Its key consists of numbers, each of which indicates the number of letters forward in the normal alphabet that the encipherer is to count from the plaintext letter to the ciphertext letter. For example, with the anarchist key of 456327, the first word of the message of April 30, Demande, would be enciphered to HJSDPKI in this manner: counting four letters beyond d gives E, F, G, H—and H is the ciphertext letter; five letters beyond e stands J, and so on. Bazeries was not up to his usual standard here, however: the mere use of six nulls at the head and the tail of the cryptograms incomprehensibly delayed his solution for an entire fortnight. For some reason, he always considered this solution, which should have been his least distinguished, as his best.

  After he retired from the Army in 1899, the Foreign Ministry hired him as a cryptanalyst. He worked partly at home, partly in the office, living much of the time at Versailles. That same year, the ministry recommended him to the police as the man who might solve a series of dispatches captured, with a numerical Beaufort table, in the quarters of one Chevilly, a supporter of the Duke of Orléans, pretender to the throne of France. The messages consisted of groups of four digits, none of which was smaller than 1111 or larger than 3737. This indicated to Bazeries that each pair of numbers stood for a letter, 11 representing A; 12, B; and so on up to 36 for Z and 37 again for A. He was put off for a good while by that rare but extraordinarily bewildering cryptologic mischance: long repetitions in a polyalphabetic cryptogram that result purely from chance and not, as Bazeries long thought, from the interaction of a periodic key with a repeated plaintext. For example, in a telegram of February 17, 1898, the digits 30 24 14 12 repeated at a distance of 21, indicating a period of 3 or of 7; when the cryptogram was solved, the first repetition proved to be the plaintext lesd enciphered by ERVE, and the second plaintext prou with key IERV. In another telegram, a false trigraphic repetition indicated a period of 8. Bazeries eventually broke the messages down by a series of inspired guesses as to probable words, and found them to fall into two sets, one enciphered with successive lines of the famous poem Nuit de décembre by Alfred de Musset, the other with the day and date on which the message was sent. Each message thus had its own key, which would have made it necessary for each to be attacked individually—except that Bazeries, after solving a few, deduced the key to the keys.

  Thus he had the satisfaction of solving a message that could not be deciphered by the duke because it was loaded with errors—and of reading the duke’s short and pointed reply. The duke’s dispatch—3733 3737 1514 1224 2920 2524—was sent at 9:35 a.m. on Tuesday, December 13, 1898, after a long and fruitless night of trying to decipher the incoming message. Bazeries translated it with the key MARDI TREIZE D[ECEMBRE] and discovered one of the most heartfelt expressions of disgust ever vented by a cipherer who has received a garbled wire. Seven null q’s gave the message bulk, but the meaningful portion was monosyllabic: Merde. “The word,” the cryptanalyst remarked with uncharacteristic understatement, “is vigorous.” Bazeries later testified to these solutions at the trial of the conspirators in the High Court of Justice.

  In 1913, Bazeries bought a house in Céret, a small town not far from his birthplace, in search of health for one of his daughters. Neighbors did not know that the bearded, gray-haired gentleman with the wide forehead and the piercing gaze was known as the Lynx of the Quai d’Orsay, the Napoleon of Ciphers, the Magician. They seldom saw him, for he came down from Versailles only when he had a major solution to prepare, and then he shut himself up in his house on the Place des Neuf Jets, where he would hire only illiterate servants, and, fortified with his pipes and pots of coffee, assailed the cryptograms that the Foreign Ministry sent down from Paris. Only when exhausted by a long bout would he emerge and head for a day of picnicking in the nearby mountains. His wife and three daughters, Césarine, Fernande, and Paule, dressed in the long, rustling skirts that were then the height of fashion, trailed their cane-swinging father through the village to an upland farm, where he would interrogate the farmers in Catalan and try to convince his daughters to like the local Roussillon wine that his wife could not stand. When World War I came, he assisted in solving German military cryptograms. He did not retire until 1924, when he was 78. He died at Noyon on November 7, 1931, aged 85.

  But if he was continually successful in cryptanalysis, he was continually rebuffed in his years-long cryptographic battle to have the military establishment adopt the ciphers he proposed instead of the official ones which, he said, “of
fer little resistance to solution.” He had little trouble in demonstrating their frangibility: in addition to the Nantes solutions, he was given a test cryptogram in the army cipher by a general of artillery during one of his Algerian tours, and he solved it during a 250-mile train ride from Constantine to Philippeville. But, as he himself said, “to prove that a cipher that is being used is worthless is one thing, but it is another to propose something better in its place.”

  His disdain for the official ciphers stung him into firing off two polyalphabetic systems of his own, both of which the general staff rejected on the ground that they were too complicated. A friendly officer at Nantes—perhaps General Fay—then suggested that he might have greater success if he devised an apparatus that a cipher clerk could use “without knocking his brains out.” Bazeries reworked one of his systems, which employed 20 different cipher alphabets, and came up with his “cylindrical cryptograph.” It was practically the same as Jefferson’s wheel cypher, except that it had 20 disks with 25 letters on their circumferences instead of 36 disks with a full alphabet. He offered it to the Ministry of War on February 12, 1891, backed by a recommendation from Fay, and described it on September 19 of that same year at a convention of the French Association for the Advancement of Sciences in Marseilles. The Army turned it down as too complicated. Bazeries simplified it, and resubmitted it at a meeting of the Military Cryptography Commission on February 9, 1893. Present, Bazeries relates, was the captain who had invented the system then in use, which Bazeries had solved. “We knew,” Bazeries wrote later, “that, as a foregone conclusion, he would be hostile to all inventors of cryptologic systems.” In fact the Bazeries cylinder—as it is commonly called—was not adopted, but the Marquis de Viaris, perhaps piqued by Bazeries’ shattering of his cipher device, exerted himself to solve a series of three messages sent him by Bazeries and thus rationalized the Army’s decision.