by DAVID KAHN
Both transformations resulted from the application of a traditional substitution of letters called “atbash,” in which the last letter of the Hebrew alphabet replaces the first, and vice versa; the next-to-last replaces the second, and vice versa; and so on. It is the Hebrew equivalent of a = z, b = Y, C = x, … Z = A.
Consequently, in Babel, the repeated b, or beth, the second letter of the Hebrew alphabet, became the repeated SH, or SHIN, the next-to-last letter, in SHESHACH. Similarly, the I, or lamed, became the hard CH, or KAPH. The kaph of Kashdim reciprocally became the LAMED of LEB KAMAI. In this determination, the Hebrew letters sin and shin, which differ only by where a dot is placed, are regarded as the same letter. The only letters in Hebrew are consonants and two silent letters, aleph and ayin; vowels are represented by dots or lines, usually below the letters. What is a final i in the English LEB KAMAI is a letter YOD in Hebrew, whose atbash reciprocal is mem. The word “atbash,” incidentally, derives from the very procedure it denotes, since it is composed of aleph, taw, beth, and shin—the first, last, second, and next-to-last letters of the Hebrew alphabet.
Both SHESHACH and LEB KAMAI have considerably embarrassed biblical commentators. They have devised numerous ingenious explanations for why so odd a result as LEB KAMAI would be desired, or why secrecy was wanted. Some have even thought Sheshach the name of a Babylonian district. But the idea of simple scribal manipulation, which would mean that such desires never even existed, and which is advanced by modern authorities and bolstered by the similar examples from other cultures and by the predilection of scribes for amusing themselves with word and alphabet games, seems the best explanation.
The two transformations by atbash are straightforward and universally recognized. The third transformation in the Old Testament, which resulted from a different substitution system, is disputed. The system is called “albam.” It splits the Hebrew alphabet in half and equates the two halves. Thus, the first letter of the first half, aleph, substitutes for the first letter of the second half, lamed, and vice versa; the second of the first half, beth, for the second of the second half, mem, and vice versa; and so on. The term “albam” derives from the first four letters of this arrangement. According to the Midrash Rabbah (Numbers 18:21), the name TABEEL in Isaiah 7:6 is an albam transformation for Remala, or “Remaliah,” who figures in verses 1 and 4. But while the albam works for the first two letters (the third, lamed, retains its identity because it would otherwise be transformed into a silent aleph), the “solution” does not clarify the text. The Midrash Rabbah does not give any reasons for thinking it albam. Most authorities seem to regard “Tabeel” as a corruption or some form of contemptuous epithet, and not as albam. In this connection it might be noted that many authorities also think that the meaningless names Shadrach, Meshach, and Abed-nego represent distortions, deliberate or accidental, of the names of real kings or countries. Shadrach, for example, may stand for Marduk—Hebrew samekh and mem look alike, and the transposition of consonants is not an uncommon linguistic phenomenon.
Hebrew literature records a third traditional form of letter substitution. It is called “atbah,” and, like atbash and albam, its name stems from its system. This is based on Hebrew numbers, which, like Roman numbers, were written with the letters of the Hebrew alphabet. Within the first nine letters of the alphabet, the substitutes were chosen so that their numerical value would add up to 10. Thus, aleph, the first letter, would be replaced by teth, the ninth, and vice versa; beth, the second, by heth, the eighth, and vice versa. The remaining letters were paired on a similar system that would total to the Hebrew digital version of 100. In decimal notation, this means that the two letters will add up to 28. Thus mem, the 13th letter, and samekh, the 15th, replace one another. What happens to the 19th letter and those beyond is not clear. The 5th letter, he, and the 14th, nun, which under the system would represent themselves, are made to replace each other. This rather confusing system of atbah is not used in the Bible, though there is at least one use in the Babylonian Talmud (Seder Mo’ed, Sukkah, 52b). This example plays on the word “witness” and its atbah substitution “master” to make a moral point.
These three substitutes are used here and there throughout Hebrew writing, particularly atbash, which is the most common. Their importance consists, however, in that the use of atbash in the Bible sensitized the monks and scribes of the Middle Ages to the idea of letter substitution. And from them flowed the modern use of ciphers—as distinct from codes—as a means of secret communication.
While SHESHACH and LEB KAMAI are an imperfect cryptography because, although they are transformations, they lack the element of secrecy, another “cryptogram” in the Bible—perhaps the most famous in the world—is imperfect for the opposite reason. It was shrouded in secrecy, but it apparently involved no transformation!
This is the message of the handwriting on the wall. It appeared ominously at Belshazzar’s feast: MENE MENE TEKEL UPHARSIN. The real mystery is not what the words meant but why the king’s wise men could not read it. The Bible says nothing about secret or unusual writing, and the words themselves are ordinary roots in Aramaic (the language, related to Hebrew, in which the book of Daniel is written) meaning “numbered,” “weighed,” and “divided.” When Belshazzar summoned Daniel, the latter had no difficulty in reading the handwriting and interpreting the three words: “MENE, God hath numbered thy kingdom, and brought it to an end. TEKEL, thou art weighed in the balances, and art found wanting, PERES, thy kingdom is divided [perisa] and given to the Medes and Persians [paras],” with the extra play on PERES, which, in Aramaic, would be identical with UPHARSIN. The message may also reflect a series of pieces of money whose names stem from the Aramaic roots: a mina, a tekel (the Aramaic equivalent for shekel, which is 1/60 th of a mina), and a peres, which is a half-mina. Though the order is illogical, the series might symbolize the breaking up of the Babylonian empire and its wealth. Dr. Cyrus Gordon has devised an ingenious American equivalent that makes this clear: “You will be quartered, halved, and cent to perdition.”
With all these interpretations possible, it seems strange that the Babylonian priests could not read what was essentially a plain-language message. Perhaps they feared to give the bad news to Belshazzar, or perhaps God blinded them and opened the eyes of Daniel. Whatever the reason, Daniel alone penetrated the enigma and became, in consequence, the first known cryptanalyst. And just as there were giants in the earth in those days, so the biblical reward for cryptanalysis far exceeded any that has been given ever since: “They clothed Daniel with purple, and put a chain of gold around his neck, and made proclamation concerning him that he should rule as one of three in the kingdom.”
“Queen Anteia, Proetus’s wife, had fallen in love with the handsome youth,” the “incomparable Bellerophon … who was endowed with every manly grace, and begged him to satisfy her passion in secret.” So Homer begins the story in the Iliad that includes the world’s first conscious reference to—as distinct from use of—secret writing.
“But Bellerophon was a man of sound principles and refused. So Anteia went to King Proetus with a lying tale. ‘Proetus,’ she said, ‘Bellerophon has tried to ravish me. Kill him—or die yourself.’ The king was enraged when he heard this infamous tale. He stopped short of putting Bellerophon to death—it was a thing he dared not do—but he packed him off to Lycia with sinister credentials from himself. He gave him a folded tablet on which he had traced a number of devices with a deadly meaning, and told him to hand this to his father-in-law, the Lycian king, and thus ensure his own death.”
The Lycian king feasted Bellerophon for nine days. “But the tenth day came, and then, in the first rosy light of Dawn, he examined him and asked to see what credentials he had brought him from his son-in-law Proetus. When he had deciphered the fatal message from his son-in-law, the king’s first step was to order Bellerophon to kill the Chimera,” a fire-breathing monster with a lion’s head, a goat’s body, and a serpent’s tail. Bellerophon did. The Lyc
ian king then tried one ruse after another to carry out the surreptitious instructions, but Bellerophon successively battled the Solymi, defeated the Amazons, and slew the best warriors of Lycia, who had ambushed him. In the end the Lycian king relented, realizing that the youth stood under the divine protection of the gods, and gave him his daughter and half his kingdom.
This is the only mention of writing in the Iliad. Homer’s language is not precise enough to tell exactly what the markings on the tablets were. They were probably nothing more than ordinary letters—actual substitution of symbols for letters seems too sophisticated for the era of the Trojan War. But the mystery that Homer throws around the tablets does suggest that some rudimentary form of concealment was used, perhaps some such allusion as “Treat this man as well as you did Glaucus,” naming someone whom the king had had assassinated. The whole tone of the reference makes it fairly certain that here, in the first great literary work of European culture, appear that culture’s first faint glimmerings of secrecy in communication.
A few centuries later, those glimmerings had become definite beams of light. Several stories in the Histories of Herodotus deal specifically with methods of steganography (not, however, with cryptography). Herodotus tells how a Median noble named Harpagus wanted to avenge himself on his relative, the king of the Medes, who years before had tricked him into eating his own son. So he hid a message to a potential ally in the belly of an un-skinned hare, disguised a messenger as a hunter, and sent him off down the road, carrying the hare as if he had just caught it. The road guards suspected nothing, and the messenger reached his destination. At it was Cyrus, king of Persia, whose country was then subject to Medea and who had himself been the target of a babyhood assassination attempt by the Medean king. The message told him that Harpagus would work from within to help him dethrone the Medean king. Cyrus needed no further urging. He led the Persians in revolt; they defeated the Medes and captured the king, and Cyrus was on his way to winning the epithet “the Great.”
Herodotus tells how another revolt—this one against the Persians—was set in motion by one of the most bizarre means of secret communication ever recorded. One Histiaeus, wanting to send word from the Persian court to his son-in-law, the tyrant Aristagoras at Miletus, shaved the head of a trusted slave, tattooed the secret message thereon, waited for a new head of hair to grow, then sent him off to his son-in-law with the instruction to shave the slave’s head. When Aristagoras had done so, he read on the slave’s scalp the message that urged him to revolt against Persia.
One of the most important messages in the history of Western civilization was transmitted secretly. It gave to the Greeks the crucial information that Persia was planning to conquer them. According to Herodotus,
The way they received the news was very remarkable. Demaratus, the son of Ariston, who was an exile in Persia, was not, I imagine—and as is only natural to suppose—well disposed toward the Spartans; so it is open to question whether what he did was inspired by benevolence or malicious pleasure. Anyway, as soon as news reached him at Susa that Xerxes had decided upon the invasion of Greece, he felt that he must pass on the information to Sparta. As the danger of discovery was great, there was only one way in which he could contrive to get the message through: this was by scraping the wax off a pair of wooden folding tablets, writing on the wood underneath what Xerxes intended to do, and then covering the message over with wax again. In this way the tablets, being apparently blank, would cause no trouble with the guards along the road. When the message reached its destination, no one was able to guess the secret until, as I understand, Cleomenes’ daughter Gorgo, who was the wife of Leonidas, discovered it and told the others that, if they scraped the wax off, they would find something written on the wood underneath. This was done; the message was revealed and read, and afterwards passed on to the other Greeks.
The rest is well-known. Thermopylae, Salamis, and Plataea ended the danger that the flame of Western civilization would be extinguished by an Oriental invasion. The story is not without a certain bitter irony, however, for Gorgo, who may be considered the first woman cryptanalyst, in a way pronounced a death sentence on her own husband: Leonidas died at the head of the heroic band of Spartans who held off the Persians for three crucial days at the narrow pass of Thermopylae.
It was the Spartans, the most warlike of the Greeks, who established the first system of military cryptography. As early as the fifth century B.C., they employed a device called the “skytale,” the earliest apparatus used in crypto-logy and one of the few ever devised in the whole history of the science for transposition ciphers. The skytale consists of a staff of wood around which a strip of papyrus or leather or parchment is wrapped close-packed. The secret message is written on the parchment down the length of the staff; the parchment is then unwound and sent on its way. The disconnected letters make no sense unless the parchment is rewrapped around a baton of the same thickness as the first: then words leap from loop to loop, forming the message.
Thucydides tells how it enciphered a message from the ephors, or rulers, of Sparta, ordering the too-ambitious Spartan prince and general Pausanius to follow the herald back home from where he was trying to ally himself with the Persians, or have war declared against him by the Spartans. He went. That was about 475 B.C. About a century later, according to Plutarch, another skytale message recalled another Spartan general, Lysander, to face charges of insubordination. Xenophon also records the skytale’s use in enciphering a list of names in an order sent to another Spartan commander.
The world owes its first instructional text on communications security to the Greeks. It appeared as an entire chapter in one of the earliest works on military science, On the Defense of Fortified Places, by Aeneas the Tactician. He retold some of Herodotus’ stories, and listed several systems. One replaced the vowels of the plaintext by dots—one dot for alpha, two for epsilon, and so on to seven for omega. Consonants remained unenciphered. In a steganographic system, holes representing the letters of the Greek alphabet were bored through an astragal or a disk. Then the encipherer passed yarn through the holes that successively represented the letters of his message. The decipherer would presumably have to reverse the entire text after unraveling the thread. Another steganographic system was still in use in the 20th century: Aeneas suggested pricking holes in a book or other document above or below the letters of the secret message. German spies used this very system in World War I, and used it with a slight modification in World War II—dotting the letters of newspapers with invisible ink.
Another Greek writer, Polybius, devised a system of signaling that has been adopted very widely as a cryptographic method. He arranged the letters in a square and numbered the rows and columns. To use the English alphabet, and merging i and j in a single cell to fit the alphabet into a 5 × 5 square: Each letter may now be represented by two numbers—that of its row and that of its column. Thus e = 15, v = 51. Polybius suggested that these numbers be transmitted by means of torches—one torch in the right hand and five in the left standing for e, for example. This method could signal messages over long distances. But modern cryptographers have found several characteristics of the Polybius square, or “checkerboard,” as it is now commonly called, exceedingly valuable—namely, the conversion of letters to numbers, the reduction in the number of different characters, and the division of a unit into two separately manipulable parts. Polybius’ checkerboard has therefore become very widely used as the basis of a number of systems of encipherment.
These Greek authors never said whether any of the substitution ciphers they described were actually used, and so the first attested use of that genre in military affairs come from the Romans—and from the greatest Roman of them all, in fact. Julius Caesar tells the story himself in his Gallic Wars. He had proceeded by forced marches to the borders of the Nervii, and
There he learned from prisoners what was taking place at Cicero’s station, and how dangerous was his case. Then he persuaded one of the Gallic troopers
with great rewards to deliver a letter to Cicero. The letter he sent written in Greek characters, lest by intercepting it the enemy might get to know of our designs. The messenger was instructed, if he could not approach, to hurl a spear, with the letter fastened to the thong, inside the entrenchment of the camp. In the dispatch he wrote that he had started with the legions and would speedily be with him, and he exhorted Cicero to maintain his old courage. Fearing danger, the Gaul discharged the spear, as he had been instructed. By chance it stuck fast in the tower, and for two days was not sighted by our troops; on the third day it was sighted by a soldier, taken down, and delivered to Cicero. He read it through and then recited it at a parade of the troops, bringing the greatest rejoicing to all.
The garrison, heartened, held out until Caesar arrived and relieved them.
Later, Caesar improved on this technique and, in doing so, impressed his name permanently into cryptology as he did into so many other fields. Suetonius, the gossip columnist of ancient Rome, says that Caesar wrote to Cicero and other friends in a cipher in which the plaintext letters were replaced by letters standing three places further down the alphabet, D for a, E for b, etc. Thus, the message Omnia Gallia est divisa in partes tres would be enciphered (using the modern 26-letter alphabet) to RPQLD JDOOLD HVW GLYLVD LQ SDUWHV WUHV. To this day, any cipher alphabet that consists of the standard sequence, like Caesar’s:
is called a Caesar alphabet, even if it begins with a letter other than D. A later writer, Aulus Gellius, seems to imply that Caesar sometimes used more complicated systems. But Caesar’s nephew Augustus, first emperor of Rome and less able than his uncle in a number of ways, also employed a weaker cipher. “When Augustus wrote in cipher,” said Suetonius, “he simply substituted the next letter of the alphabet for the one required, except that he wrote AA for x” (the last letter of the Roman alphabet).
