THE CODEBREAKERS

by DAVID KAHN

  Alberti’s three remarkable firsts—the earliest Western exposition of cryptanalysis, the invention of polyalphabetic substitution, and the invention of enciphered code—make him the Father of Western Cryptology. But although his treatise was published in Italian in a collection of his works in 1568, and although his ideas were absorbed by the Argentis and so influenced the later development of cryptology, they never had the dynamic impact that such prodigious accomplishments ought to have produced. Symonds’ evaluation of his work in general may both explain why and summarize the modern view of his cryptological contributions: “This man of many-sided genius came into the world too soon for the perfect exercise of his singular faculties. Whether we regard him from the point of view of art, of science, or of literature, he occupies in each department the position of precursor, pioneer, and indicator. Always original and always fertile, he prophesied of lands he was not privileged to enter, leaving the memory of dim and varied greatness rather than any solid monument behind him.”

  Polyalphabeticity took another step forward in 1518, with the appearance of the first printed book on cryptology, written by one of the most famous intellectuals of his day. He was born February 2, 1462, in Trittenheim, Germany, where his father, a wealthy winegrower, was known only as Johannes of Heidenberg, his former village. The father died a year later, and the son, also named Johannes, was raised first by his mother and then by a rather stern stepfather, who ridiculed the boy’s passion for learning. At 17, Johannes left home and sought entry to the University of Heidelberg, where its chancellor, Johannes of Dalberg, was so impressed by the youth’s brilliance that he granted him a pauper’s certificate exonerating the tuition fees. Soon thereafter, Johannes of Dalberg, one Rodolphe Huesmann, and the young Johannes formed the Rhenish Literary Society, each taking, according to custom, a Latin and a Greek name. The young man chose “Trithemius,” which, while having a certain consonance with the name of his native village of Trittenheim, indicated that he was the third link of the group. He has been known as Johannes Trithemius ever since.

  In January, 1482, when the young Trithemius was on his way home from Heidelberg for a New Year’s visit, he sought shelter during a heavy snowstorm at the impoverished, 437-year-old Benedictine abbey of Saint Martin at Spanheim, Germany. He was very much attracted by the life of the monks and soon entered the novitiate. A year and a half later, only a little while after taking his final vows, he was elected abbot—either because the monks recognized his brilliance or because they thought that he would be too young to enforce discipline. He maintained his post, however, and at 24 published a book of sermons that gave him an instant fame. He was called upon to preach before princes and religious conventions. His reputation as a savant grew with his prolific writings—several histories, a biographical dictionary of famous Germans, one of famous Benedictines, a chronicle of the dukes of Bavaria and the Counts Palatine, a life of Saint Maximum and one of an archbishop of Mainz. Learned men corresponded with him. He knew the original Dr. Faustus well enough to consider him a charlatan. Powerful rulers like the Margrave of Brandenberg and the Holy Roman Emperor Maximilian I invited him to their castles. And posterity has honored him. His most important work, the Liber de scriptoribus ecclesiasticis, a chronological list of about 7,000 theological works by 963 authors that was published in 1494, earned him the title of Father of Bibliography. It was conferred by Theodore Besterman, compiler of the World Bibliography of Bibliographies, who said that Trithemius “was not the first to compile bibliographies, but he was certainly the first bibliographically-minded scholar to do so.”

  These were all solid works. But Trithemius’ other writings were darkened by his intense interest, not to say belief, in occult powers. (Like others of his day, he could reconcile this with his pious Christianity because the leading treatises on esoterism, thought to have been written by an Egyptian priest called Hermes Trismesgistus, had actually been compiled by Christians in the second century A.D. and so contained nothing monumentally offensive to the church.) Trithemius wrote on alchemy, classified witches into four carefully defined categories, explained the twelve angelic hierarchies ruled by emperors related to the chief winds and points of the compass. He analyzed history in terms of the 354-year cycles of the seven planetary angels, bearing names like Orifiel and Zachariel, and fixed the creation of the world at 5206 B.C. These writings made him one of the great figures of occult science, and today books on the subject venerate him as a superlative alchemist and as the mentor of two other almost legendary occultists, Paracelsus and Cornelius Agrippa.

  In 1499, Trithemius, who after long pondering had finally concluded that some things were unknowable, was said to have been visited in a dream by a spirit who taught him many of these very things. These he wrote down in a volume which he intended to comprise eight books and which he called “Steganographia,” from Greek words meaning “covered writing.” In the first two books he described some elementary reciprocal vowel-consonant substitutions and several variations on a system in which only certain letters of nonsense words signify the meaning, the other letters being nulls. For example, in the message beginning PARMESIEL OSHURMI DELMUSON THAFLOIN PEANO CHARUSTREA MELANY LYAMUNTO …, the decipherer extracts every other letter of every other word, beginning with the second word since the first indicates the specific system. The Latin plaintext begins Sum tali cautela ut…. But all this may have simply served as a cover for the magical operations described in the third book, which included no cryptography at all. Here Trithemius slipped again into the shadow world of spirits with names like Vathmiel, Choriel, and Sameron, and discussed methods that sound like telepathy. To convey a message to a desired recipient within 24 hours, for example, one needed simply to say it over an image of a planetary angel at a moment determined by complicated astrological calculations, wrap the image up with an image of the recipient, bury them under a threshold, say the proper incantations ending with “In nomine patris & filii & spiritus sancti, Amen,” and the message would arrive, Trithemius assured the reader, without words, writing, or messenger. Trithemius told how to use the network of angels for thought transference and for gaining knowledge of all things happening in the world. Involved is the Kabbalah-like computation of the numerical values of the angels’ names; Trithemius, like other hermeticists, regarded Moses as a kind of Jewish Hermes Trismesgistus.

  He showed the “Steganographia” in its incompleted state to a visitor, who was so horrified at its barbarous names of seraphim, its obscurantism, its impossible claims, that he denounced it as sorcery. A letter which Trithemius wrote to a friend arrived after the friend had died; the prior of the abbey opened it, was likewise shocked, and passed it around. Trithemius fell under a cloud of working in magic, which the church even then frowned upon. He abandoned the book, but probably did not mind the reputation he was gaining as a wonder-worker, for Trithemius was more than a bit of the braggart and publicity hound. He had concluded his ecclesiastical bibliography with some of his own books—inserted, he said, “at the solicitation of my friends.” To a visitor, he boasted that he had taught an illiterate German prince Latin in an hour, and then, before the prince departed, withdrew all his knowledge. He offered to make a thief return everything that he had stolen from the visitor if only the visitor would have faith; of course he did not have enough. Trithemius maintained that he comprehended nothing less than wisdom itself. This sort of thing naturally attracted crowds of the curious and hopeful and started the wild rumors about his magic powers that were circulating even during his life. According to one, the abbot, finding himself at an inn where supplies had run short, tapped on a window and called out in Latin, whereupon a spirit passed in to him a broiled pike and a bottle of wine.

  Believing sincerely that his own practices were devoutly Christian, Trithemius did not fight the legend, except to deny that there was anything demonic or un-Christian in his practices. His reputation for esoteric knowledge grew so great, in fact, that the “Steganographia” circulated in manuscri
pt for a hundred years, being copied by many persons eager to suck out the secrets that it was thought to hold. Parts were transcribed for Giordano Bruno, among others. It became famous, and controversy flamed about it. In 1599, for example, the Jesuit Martin Antoine Del Rio called it “full of peril and superstition.” Not until 1606 was it printed, and this exacerbated the dispute. The opponents scored a great victory when, on September 7, 1609, the Roman Catholic Church placed it on its Index of Prohibited Books. It stayed there for more than 200 years, throughout numerous reprintings, the last as late as 1721. Many scholars attacked it, and others wrote whole books defending it. But the larger controversy over magic faded as the Age of Reason gained sway, and the book lost its interest.

  Even during Trithemius’ lifetime, however, it had caused him trouble. In 1506, while he was away on a trip, the monks at Spanheim mutinied, apparently because his reputation as a magician, due in no small measure to the “Steganographia.” had brought odium to the monastery. He never returned, but obtained a transfer to the monastery of Saint Jacob in Wurzburg, where, on October 3, 1506, he was elected prior. Early in 1508, he addressed himself to a book carefully restricted to cryptology, as if to prove that that was what he meant all along. He called it the “Polygraphia” because of the multiplicity of ways of writing that it included. He perhaps began it on his 46th birthday, for he finished Book I on February 12, and he wrote each of its six books in an average of ten days. At that rate, he completed it quickly, probably by April 24, the date of its dedication to the Holy Roman Emperor Maximilian I. Like others of his writings, it was not published at once, and Trithemius turned to the composition of other texts. So he lived on quietly at Wurzburg, where he studied, wrote, corresponded, and received visitors, and where, on December 15, 1516, he died.

  A year and a half later, the descendants of his old preceptor, Johannes of Dalberg, paid for the publication of the “Polygraphia,” which thereby became the first printed book on cryptology. It bore the title Polygraphiae libri sex, Ioannis Trithemii abbatis Peapolitani, quondam Spanheimensis, ad Maximilianum Caesarem (“Six Books of Polygraphy, by Johannes Trithemius, Abbot at Wurzburg, formerly at Spanheim, for the Emperor Maximilian”). Johannes Haselberg of Aia completed its printing in July, 1518. It is a handsome small folio of 540 pages in red and black, with a woodcut title page borrowed from an earlier book by Trithemius. It ends with a “Clavis Polygraphiae” which repeats the original woodcut title page and gives a resume of the preceding six books. It was reprinted in 1550, 1571, 1600, and 1613, and a French translation (heavily edited and modified) by Gabriel de Collanges appeared in 1561 and was reprinted in 1625. This became the subject of one of the world’s most notorious plagiarisms when in 1620 a Frisian named Dominique de Hottinga published Collange’s work as his own and even complained of how hard it was to do!

  By far the bulk of the volume consists of the columns of words printed in large Gothic type that Trithemius used in his systems of cryptography. The first of the six books comprises 384 columns of Latin words, two columns per page, for Trithemius’ best-known invention, his Ave Maria. Each word represents the plaintext letter that stands opposite it. Trithemius so selected the words that, as the equivalents for the letters are taken from consecutive tables, they will make connected sense and will appear to be an innocent prayer. Thus abbot would be enciphered as DEUS CLEMENTISSIMUS REGENS AEVUM INFINIVET. Book II lists 284 similar alphabets. Book III has 1,056 numbered lines of three artificial words per line, arranged in columns. A typical column begins HUBA, HUBE, HUBI, HUBO, and so on down to the 24th word, HUBON. These were to be used like those of the Ave Maria—but just how this was to avoid suspicion is hard to see. Book IV lists 117 columns of artificial words whose second letter varied in each column from a to w (the last letter of the alphabet Trithemius used, following z): BALDACH, ABZACH, ECOZACH, ADONACH, … These served to construct a cover text in which only the second letters of each word would carry the secret message. Taking words from his first three alphabets in order, bad would become ABZACH HANASAR ADAMAI. Once again, this does not appear the height of innocence. Perhaps Trithemius just could not stay away from those incantatory words. Book VI gives supposed cipher alphabets of the Franks and Normans, as well as the first printed description of Tironian notes.

  The woodcut title page of the first printed book on cryptology. Though taken from an earlier book by the same author, Johannes Trithemius, the illustration was apparently appropriate to this book as well. It shows the author wearing his Benedictine habit and, with his abbot’s miter on the floor before him, kneeling to present his book—padlocked, as befits its secret character—to the dedicatee, the Holy Roman Emperor Maximilian I. Seated upon his throne in the imperial castle at Augsburg and wearing the imperial crown and mantle, Maximilian holds his scepter in one hand and blesses Trithemius with the other. Behind Trithemius, another person—either another monk or the publisher—extends towards Maximilian two keys to the book, these symbolizing Maximilian’s spiritual authority and temporal power. In the background Trithemius’ chaplain, a young monk, holds his abbot’s crozier. At bottom, Trithemius reclines with a fruit-laden branch representing the motto “Ye shall judge the tree by its fruits” and implying that Trithemius’ many works make him worthy of acclaim. At upper left, arms of the Holy Roman Empire; at upper right, arms of the engraver; at lower left, arms of Trithemius (the two bass back to back symbolizing his Christianity; the shells, his religious state; the grapes, his father, a winegrower); at lower right, arms of the then Bishop of Würzburg. At sides, philosophers hold an armillary sphere, a sextant, a compass, and a square rule; others hold the banner ends.

  The first page of Johannes Trithemius’ “Ave Maria” cipher

  It is Book V that contains Trithemius’ contributions to polyalphabeticity. Here appears, for the first time in cryptology, the square table, or tableau. This is the elemental form of polyalphabetic substitution, for it exhibits all at once all the cipher alphabets in a particular system. These are usually all the same sequence of letters, but shifted to different positions in relation to the plaintext alphabet, as in Alberti’s disk the inner alphabet assumed different positions in regard to the outer alphabet. The tableau sets them out in orderly fashion—the alphabets of the successive positions laid out in rows one below the other, each alphabet shifted one place to the left of the one above. Each row thus offers a different set of cipher substitutes to the letters of the plaintext alphabet at the top. Since there can be only as many rows as there are letters in the alphabet, the tableau is square.

  The simplest tableau is one that uses the normal alphabet in various positions as the cipher alphabets. Each cipher alphabet produces, in other words, a Caesar substitution. This is precisely Trithemius’ tableau, which he called his “tabula recta.” Its first and last few lines were:

  Trithemius used this tableau for his polyalphabetic encipherment, and in the simplest manner possible. He enciphered the first letter with the first alphabet, the second with the second, and so on. (He gave no separate plaintext alphabet, but the normal alphabet at the top can serve.) Thus a plaintext beginning Hunc caveto virum … became HXPF GFBMCZ FUEIB…. In this particular message, he switched to another alphabet after 24 letters, but in another example he followed the more normal procedure of repeating the alphabets over and over again in groups of 24.

  The great advantage of this procedure over Alberti’s is that a new alphabet is brought into play with each letter. Alberti shifted alphabets only after three or four words. Thus the ciphertext would mirror the obvious pattern of repeated letters of a word like Papa (“Pope”), or in English, attack, and the cryptanalyst could seize upon this reflection to break into the cryptogram. The letter-by-letter encipherment obliterates this clue.

  Trithemius’ system is also the first instance of a progressive key, in which all the available cipher alphabets are exhausted before any are repeated. Modern cipher machines very often embody such key progressions. Naturally, they avoid the chief d
efects of Trithemius’ primitive system: its paucity of alphabets and the rigid order of their use.

  Trithemius’ influence in cryptology was very great, owing in part to his reputation and in part to his having authored the first printed book on the subject. Letter-by-letter encipherment quickly became customary in polyalphabetic theorizing, and the tableau established itself as a standard item in cryptology. It formed the basis of innumerable ciphers, and so important did it become that some German authors attempted to enshrine their compatriot on this basis alone. But valuable as his contributions were, they do not justify that accolade.

  If the first two steps in polyalphabeticity were made by men who were giants in their time, the third was taken by a man who was so unexceptional that he left almost no traces. This is Giovan Batista Belaso; the sum total of knowledge about him consists of the facts that he came from Brescia of a noble family, served in the suite of one Cardinal Carpi, and, in 1553, brought out a little booklet entitled La cifra del. Sig. Giovan Batista Belaso. In this he proposed the use of a literal, easily remembered, and easily changed key—he called it a “countersign”—for a polyalphabetic cipher. Wrote Belaso: “This countersign may consist of some words in Italian or Latin or any other language, and the words may be few or many as desired. Then we take the words we wish to write, and put them on paper, writing them not too close together. Then over each of the letters we place a letter of our countersign in this form. Suppose, for example, our countersign is the little versetto VIRTUTI OMNIA PARENT. And suppose we wish to write these words: Larmata Turchesca partira a cinque di Luglio. We shall put them on paper in this manner:

  VIRTUTI OMNIA PARENT VIRTUTI OMNIA PARENT VI

  larmata turch escapa rtiraac inque dilugl io”