THE CODEBREAKERS

by DAVID KAHN

  * This may be why Rochefort did not simply request the keys from Washington via COPEK.

  * The correct plaintexts were simply and, with the extra nd probably an inadvertent repetition, and China, it must, with the LYL probably a codeword for comma.

  The Pageant of Cryptology

  2

  THE FIRST 3,000 YEARS

  ON A DAY nearly 4,000 years ago, in a town called Menet Khufu bordering the thin ribbon of the Nile, a master scribe sketched out the hieroglyphs that told the story of his lord’s life—and in so doing he opened the recorded history of cryptology.

  His was not a system of secret writing as the modern world knows it; he used no fully developed code of hieroglyphic symbol substitutions. His inscription, carved about 1900 B.C. into the living rock in the main chamber of the tomb of the nobleman Khnumhotep II, merely uses some unusual hieroglyphic symbols here and there in place of the more ordinary ones. Most occur in the last 20 columns of the inscription’s 222, in a section recording the monuments that Khnumhotep had erected in the service of the pharaoh Amenemhet II. The intention was not to make it hard to read the text. It was to impart a dignity and authority to it, perhaps in the same way that a government proclamation will spell out “In the year of Our Lord One thousand eight hundred and sixty three” instead of just writing “1863.” The anonymous scribe may also have been demonstrating his knowledge for posterity. Thus the inscription was not secret writing, but it incorporated one of the essential elements of cryptography: a deliberate transformation of the writing. It is the oldest text known to do so.

  As Egyptian civilization waxed, as the writing developed and the tombs of the venerated dead multiplied, these transformations grew more complicated, more contrived, and more common. Eventually the scribes were replacing the usual hieroglyphic form of a letter, like the full-face mouth representing /r/, by a different form, like a profiled mouth. Sometimes they used new hieroglyphs whose first sound represented the letter desired, as a picture of a pig, “rer,” would mean /r/. Sometimes the sounds of the two hieroglyphs differed but their images resembled one another. The horned asp, representing /f/, was replaced by the serpent, representing /z/. And sometimes the scribes used a hieroglyph on the rebus principle, as in English a picture of a bee might represent b; thus a sailboat, “khentey,” stands for another Egyptian word khentey, which means “who presides at”—this latter being part of a title of the god Amon, “he who presides at Karnak.” These procedures of acrophony and the rebus are essentially those of ordinary Egyptian writing; it was through them that the hieroglyphics originally acquired their sound values. The Egyptian transformations merely carry them further, elaborate them, and make them more artificial.

  The transformations occur in funerary formulas, in a hymn to Thoth, in a chapter of the Book of the Dead, on the sarcophagus of the pharaoh Seti I, in royal titles displayed in Luxor, on the architrave of the Temple of Luxor, on stele, in laudatory biographic inscriptions. There is nothing meant to be concealed in all this; indeed, many of the statements are repeated in ordinary form right next to the altered ones. Why, then, the transformations? Sometimes for essentially the same reason as in Khnumhotep’s tomb: to impress the reader. Occasionally for a calligraphic or decorative effect; rarely, to indicate a contemporary pronunciation; perhaps even for a deliberate archaism as a reaction against foreign influence.

  But many inscriptions are tinctured, for the first time, with the second essential for cryptology—secrecy. In a few cases, the secrecy was intended to increase the mystery and hence the arcane magical powers of certain religious texts. But the secrecy in many more cases resulted from the understandable desire of the Egyptians to have passersby read their epitaphs and so confer upon the departed the blessings written therein. In Egypt, with its concentration upon the afterlife, the number of these inscriptions soon proliferated to such an extent that the attention and the goodwill of visitors flagged. To revive their interest, the scribes deliberately made the inscriptions a bit obscure. They introduced the cryptographic signs to catch the reader’s eye, make him wonder, and tempt him into unriddling them—and so into reading the blessings. It was a sort of Madison Avenue technique in the Valley of the Kings. But the technique failed utterly. Instead of interesting the readers, it evidently destroyed even the slightest desire to read the epitaphs, for soon after the funerary cryptography was begun, it was abandoned.

  The addition of secrecy to the transformations produced cryptography. True, it was more of a game than anything else—it sought to delay comprehension for only the shortest possible time, not the longest—and the cryptanalysis was, likewise, just a puzzle. Egypt’s was thus a quasi cryptology in contrast to the deadly serious science of today. Yet great things have small beginnings, and these hieroglyphs did include, though in an imperfect fashion, the two elements of secrecy and transformation that comprise the essential attributes of the science. And so cryptology was born.

  In its first 3,000 years, it did not grow steadily. Cryptology arose independently in many places, and in most of them it died the deaths of its civilizations. In other places, it survived, embedded in a literature, and from this the next generation could climb to higher levels. But progress was slow and-jerky. More was lost than retained. Much of the history of cryptology of this time is a patchwork, a crazy quilt of unrelated items, sprouting, flourishing, withering. Only toward the Western Renaissance does the accreting knowledge begin to build up a momentum. The story of cryptology during these years is, in other words, exactly the story of mankind.

  China, the only high civilization of antiquity to use ideographic writing, seems never to have developed much real cryptography—perhaps for that reason. Diplomats and military authorities relied mainly on oral statements, memorized and delivered by messenger. For written messages, the Chinese would often write on exceedingly thin silk or paper, which they rolled into a ball and covered with wax. The messenger hid the wax ball, or “la wan,” somewhere about his person, or in his rectum, or he sometimes swallowed it. This, of course, was a form of steganography.

  Actual cryptography often involved open codes. If a man’s name included the ideogram for “chrysanthemum,” the correspondents would refer to him as“the yellow flower.” But for military purposes, the 11th-century compilation, Wu-ching tsung-yao (“Essentials from Military Classics”), recommended a true if small code. To a list of 40 plaintext items, ranging from requests for bows and arrows to the report of a victory, the correspondents would assign the first 40 ideograms of a poem. Then, when a lieutenant wished, for example, to request more arrows, he was to write the corresponding ideogram at a specified place on an ordinary dispatch and stamp his seal on it. The general could put down the same character with his own seal to indicate approval, or his seal without the character to indicate disapproval. Even if the message were intercepted, the code portion would remain secret.

  Hieroglyphic encipherments of proper names and titles, with cipher hieroglyphs at left, plain equivalents at right

  It is questionable, however, whether such methods were much used. The greatest conqueror of them all, Genghis Khan, seems never to have made use of cryptography. Nor do ciphers seem possible. The ideographic nature of the language precludes them. The cipher-like technique of altering the form of the ideograms by shifting lines or elements from one place to another in the pattern would be, one authority has said, neither practical nor effective. In fact, one of the apparently few cryptologic episodes in the history of China involves a Western alphabet.

  In 1722, Yin-t’ang, ninth son of the late Emperor Shêng-tsu, lost out to his elder brother, Yin-chên, in a struggle for the throne. He was banished to Sining. With him went his supporter, a Portuguese missionary named João Mourão, who had taught him the Latin alphabet. Yin-t’ang used it for a code with his son. Early in 1726, a letter from the son in this alphabet was intercepted by agents of Emperor Yin-chên. Ever alert for such an opportunity, the emperor used it as evidence to condemn his brother’s acti
vities as treasonable, expel him from the Imperial Clan, and remove him from Sining to Paoting, Chihli. Here Yin-t’ang was confined in a small house surrounded by high walls; he received his food by pulleys. Within a few months he was dead of dysentery. The emperor announced that his brother had been called to justice by the netherworld. Mourão himself died in confinement at about the same time.

  Why did China, so far ahead of other civilizations in so many things, not develop cryptography? An astute comment by Professor Owen Lattimore of the University of Leeds may give the reason. “Although writing is extremely old in the Chinese culture, literacy was always restricted to such a small minority that the mere act of putting something into writing was to a certain extent equivalent to putting it into code.”

  In China’s great neighbor to the west, India, whose civilization likewise developed early and to high estate, several forms of secret communications were known and, apparently, practiced. The Artha-śāstra, a classic work on statecraft attributed to Kautilya, in describing the espionage service of India as practically riddling the country with spies, recommended that the officers of the institutes of espionage give their spies their assignments by secret writing. The Lalita-Vistara, a work that extols the career and excellencies of the Buddha, tells how Buddha astounded the tutor who was to teach him writing by enumerating 64 different kinds. Some of these, such as the perpendicular writing, or the disordered writing, or the scattered writing, or the cross writing, are sometimes regarded as cryptographic, though many are fanciful and probably never existed.

  Perhaps most interesting to cryptologists, amateur or professional, is that Vātsyāyana’s famous textbook of erotics, the Kāma-sūtra, lists secret writing as one of the 64 arts, or yogas, that women should know and practice. It is 45th in a list that begins with vocal music and runs through prestidigitation, solution of verbal puzzles, and exercises in enigmatic poetry. The yoga is called “mlecchita-vikalpā.” In his commentary on the Kāma-sūtra, Yaśod-hara describes two kinds of mlecchita-vikalpā. One is called “kautiliyam,” in which the letter substitutions are based upon phonetic relations—the vowels become consonants, for example. A simplification of this form is called “dur-bodha.” Another kind of secret writing is “mūladevīya.” Its cipher alphabet consists merely of the reciprocal one with all other letters remaining unchanged. Mūladevīya existed in both a spoken form—as such it figures in Indian literature and is used by traders, with geographical variations—and a written form, in which case it is called “gūdhalekhya.”

  Beyond these unquestioned types of cryptography, ancient India made use of allusive language, a sort of impromptu open code called “sābhāsa,” and a finger communication, “nirābhāsa,” in which the phalanges stand for the consonants and the joints for the vowels. Deaf and dumb people still use it, as do traders and moneylenders.

  Whether India owes this profusion of mentions of cryptography to actual use or to her great interest in grammar and language in general—the world’s first grammarian, Pānini, was an Indian—remains in question. That cryptology is not mentioned in the classic drama of political intrigue, the MudrāRāksasa, suggests that it was not widely used. On the other hand, the Arthaśāstra, which was written sometime between 321 and 300 B.C., recommended that ambassadors use cryptanalysis to obtain intelligence: “If there is no possibility of carrying on any such conversation (conversation with the people regarding their loyalty), he [the envoy] may try to gather such information by observing the talk of beggars, intoxicated and insane persons, or of persons babbling in sleep, or by observing the signs made in places of pilgrimage and temples, or by deciphering paintings or secret writings.” (One begins to wonder whether Kautilya, by putting cryptanalysis in the company of such sources, meant to praise or damn it.) Nevertheless, though he gives no suggestions on how to solve either paintings or secret writings, the fact that he knows that solution is possible bespeaks some cryptologic sophistication. His is, moreover, the first reference in history to cryptanalysis for political purposes.

  The fourth great civilization of antiquity, the Mesopotamian, rather paralleled Egypt early in its cryptographic evolution, but then surpassed it, attaining a surprisingly modern level of cryptography. Its oldest encipherment appears in a tiny cuneiform tablet only about 3 by 2 inches, dating from about 1500 B.C. and found on the site of ancient Seleucia on the banks of the Tigris. It contains the earliest known formula for the making of glazes for pottery. The scribe, jealously guarding his professional secret, used cuneiform signs—which could have several different syllabic values—in their least common values. His method resembles George Bernard Shaw’s way of using the /f/ sound of GH in “tough,” the /i/ sound of o in “women,” and the /sh/ sound of TI in “nation” to write fish as GHOTI. The scribe also truncated sounds by ignoring the final consonant of several syllabic signs, and spelled the same word with different signs at different places. Interestingly, as knowledge of glaze-making spread, the need for secrecy evaporated, and later texts were written in straightforward language.

  The Babylonian and Assyrian scribes sometimes used rare or unusual cuneiform signs in signing and dating their clay tablets. These ending formulas, called “colophons,” were short and stereotyped, and the substitution of the unusual signs for the usual were not intended to conceal but simply to show off the scribe’s knowledge of cuneiform to later copyists. Nothing precisely like this exists in the modern world, because literacy is so widespread and spelling so standardized. But comparable might be a businessman’s writing “We beg to acknowledge receipt of your communication of the 25th ult.” instead of “Thank you for your letter of May 25,” or a schoolboy’s using long words where short would do—both seeking to impress their readers with their learning.

  In the final period of cuneiform writing, in colophons written at Uruk (in present-day Iraq) under the Seleucid kings in the last few score years before the Christian era, occasional scribes converted their names into numbers. The encipherment—if such it be—may have been only for amusement or to show off. Because colophons are so stereotyped, and because several of the enciphered ones have only one or two number signs among many plaintext, Assyriologists have been able to “cryptanalyze” them. For example, a tablet giving lunar eclipses for from 130 to 113 B. C. includes in its colophon “palih 21 50 10 40 la….” Comparing this with the identical formula in plaintext in another tablet, Otto Neugebauer determined that 21 = Anu, 50 = u, 10 40 = An-tu. The formula reads: “He who worships Anu and Antu shall not remove it [the tablet].” With the help of these equivalencies, Erie Leichty attacked the signature at the foot of a large tablet reciting a myth of the goddess Ishtar that might be an indirect source of the biblical story of Esther, whose name might be another version of “Ishtar.” The signature reads “tuppi ¹21 35 35 26 44 apil ¹21 11 20 42,” or “tablet of Mr. 21 35 35 26 44, son of Mr. 21 11 20 42.” Leichty suggested that the solution was “tablet of Mr. Anu-aba-uttirri, son of Mr. Anu-bel-su-nu,” whose father-son relationship is well known.

  Other tablets employ the same numbers with the same values. No simple relationship between the equivalencies appears. “A check of the various lexical series shows that the numbers are not based on a counting of signs either forward from the beginning of the series, nor backward from the end,” wrote Leichty. “It is of course possible that a tablet of equations between numbers and signs existed.” He suggested that two little tablet-fragments from Susa (in present-day Iran) might comprise such a codebook, but added that they were too short to be certain. The broken pieces of clay list cuneiform numbers in order in a vertical column; opposite them stand cuneiform signs. Unfortunately, none of the numbers used in the cryptograms occur on these fragments (except for 35, whose cuneiform sign is blurred to illegibility), and so it is not possible to determine whether these tablets served as the codebook for the colophon cryptography. But if they are indeed codebooks, they are the oldest in the world.

  The Holy Scriptures themselves have not escaped a touch of cry
ptography—or protocryptography, to be precise, for the element of secrecy is lacking. As with the hieroglyphics in the tomb of Khnumhotep or the colophons of the Mesopotamian scribes, the transformations are present without any apparent desire to conceal. Probably the main motives in the biblical transformations, as with the others, were the human ones of pride and a longing for immortality, attained here by making a textual alteration which, as later scribes faithfully copied it, would transmit a bit of one’s self down through the centuries. If this was in fact the idea, it most certainly succeeded.

  Hebrew tradition lists three different transformations in the Old Testament (none are recorded for the New). In Jeremiah 25:26 and 51:41, the form SHESHACH appears in place of Babel (“Babylon”). The second occurrence strikingly demonstrates the lack of a secrecy motive, since the phrase with SHESHACH is immediately followed by one using “Babylon”:

  A cuneiform tablet from Susa lists the numbers from 1 to 8 and from 32 to 35 opposite parallel columns of cuneiform signs in what might be the oldest codebook in the world

  How is Sheshach taken!

  And the praise of the whole earth seized!

  How is Babylon become an astonishment

  Among the nations!

  Confirmation that SHESHACH is really a substitute for Babel and not a wholly separate place comes from the Septuagint and the Targums, the Aramaic paraphrases of the Bible, which simply use “Babel” where the Old Testament version has SHESHACH. The second transformation, at Jeremiah 51:1, puts LEB KAMAI (“heart of my enemy”) for Kashdim (“Chaldeans”).