THE CODEBREAKERS

by DAVID KAHN

  To the inventor, it appears that because the cryptanalyst does not know the coordinates of the letters, which are necessary to reconstruct the intermediate numerical text—which in turn seems essential to the recovery of the plaintext—he cannot make an entry into the cryptogram. A smooth unbroken surface, upon which the cryptanalyst can find no purchase, apparently protects the cipher. But the cryptanalyst does not think like that. Analyzing the structure and not the operation of the cipher, he observes that the second, or column, coordinate of the ciphertext letter K is the first, or row, coordinate of the unknown plaintext letter, and that the first, or row, coordinate of the next ciphertext letter, B, forms the second, or column, coordinate of that same plaintext letter. This observation circumvents any need to find the actual numerical coordinates, and from there the cryptanalyst can proceed with his solution.

  Many inventors also invoke the vast number of combinations of keys afforded by their system as proof of its invulnerability. To exhaust the possible solutions would take eons, they contend, unwittingly using the same argument to defend their systems as Cardano used to defend a monalphabetic—and with the same lack of validity. For, as Shannon has shown, the cryptanalyst does not go after these possibilities one by one. He eliminates millions at a time. Moreover, the trials progress from the more probable to the less probable hypotheses, increasing the cryptanalyst’s chance of striking the right one early. “Whereas complete trial and error requires trials to the order of the number of keys,” Shannon wrote, “this subdividing trial and error requires only trials to the order of the key size in bits,” a very much smaller number.

  Such observations seldom have much effect upon a determined inventor. If a cryptologist points out a chink in the cryptologic armor, the inventor patches it with an extra complication. The less the inventor knows about cryptology, the more stubbornly will he cling to his conviction of unbreakability; and the more intelligent he is, the more ingeniously will he palter with the cryptologist. If the cryptologist objects that the cipher will not stand up to heavy traffic or will engender too many bad errors, the inventor replies that the cipher must be used properly for it to remain unbreakable. By “properly” he means the conditions that obtain only in cryptography’s Utopia—no enciphering or transmission errors, no traffic volume exceeding the prescribed bounds for a particular key.

  But this at once reduces his cipher to triviality as a practical method of cryptography. For with such a definition of “properly” any cipher may be regarded as unbreakable. Even a monalphabetic substitution would be used properly, in this sense, if only a single, very short cryptogram were sent in it. The inventor, concentrating on those rare occasions on which his cipher would be used properly, refuses to see the vast domain in which it will not serve. But the ratio of the area in which a cipher will serve to the area in which it will not counts as much in evaluating it as its intrinsic merits. The cryptologist of course sees this, but when he attempts to direct the inventor’s gaze to this outside world the inventor tells him, “I am not talking about that.” The cryptologist and the inventor are indeed talking about two different things, and each in his way is right. The inventor is right when he says that the cipher is impregnable within its tiny duchy. But the cryptologist is even more right when he says that it is insignificant.

  Classic in the annals of cryptographic invention is the case history of J. F. Byrne, who stuck with his cipher through repeated rebuffs for more than 35 years. Byrne was an intimate of James Joyce; they were students together at Dublin, and Joyce modeled Cranly in his Portrait of the Artist as a Young Man upon Byrne, and made Byrne’s residence, 7 Eccles Street, Dublin, the home of Leopold and Mollie Bloom, the two protagonists of his great Ulysses.* It was in 1918 that Byrne hit upon the principle of his “Chaocipher,” which he never disclosed publicly but was an autokey. It required nothing more than a cigar box and a few bits of string and odds and ends for its operation. When he showed it to his cousin, she exclaimed that it would bring him a Nobel Prize—not for science, apparently, but for ushering in an age of universal peace by conferring the gift of perfect security upon the communications of all nations and all men. Wrote Byrne:

  When I first set out to discover a system for concocting an indecipherable cipher, I had it clearly in mind that such a system would and should be universally available. I envisioned, for instance, the utilization of my method and machine by business men for business communications, and by brotherhoods and social and religious institutions. I believe that my method and machine would be an invaluable asset to big religious institutions, as for example the Catholic Church with its world-wide ramifications. I had, and still have in mind the universal use of my machine and method by husband, wife, or lover. My machine would be on hire, as typewriter machines now are, in hotels, steamships, and, maybe even on trains and airliners, available for anyone anywhere and at any time. And I believe, too, that the time will come—and come soon—when my system will be used in the publication of pamphlets and books written in cipher which will be unreadable except by those who are specially initiated.

  Byrne corresponded with Colonel Parker Hitt, and in 1922 demonstrated his machine before Friedman and Colonel Frank Moorman, former head of G.2 A.6, then handling cryptography for the Signal Corps. They did not want it. He offered it to the State Department, which replied with a form letter stating that its “ciphers are adequate to its needs”—a statement that Byrne rightly damned as “a paragon of smugness.” He submitted it to the Navy in 1937-38, negotiating apparently with Commander Joseph N. Wenger, and to A. T. & T.’s Ralzemond D. Parker, chief of company development and research and Vernam’s boss when he invented the on-line mechanism. Nobody took it.

  Byrne’s faith remained undaunted. He had a little brochure printed in which he enciphered known texts in his Chaocipher and defied the world to break it. Toward the close of his life, he wrote a book of reminiscences. It told much about his days with Joyce, but his real reason for writing it was not to shed light on early Joyce but to get his Chaocipher before a larger audience. The 21st and last chapter of Silent Years: An Autobiography with Memoirs of James Joyce and Our Ireland, comprising fully one eighth of the book, recapitulated the story of his Chaocipher. Byrne concluded by betting $5,000 or the total royalties of the first three months after publication of his book that no one would be able to solve the message in Chaocipher that he printed in extenso in the final pages. He flung the challenge also at the amateurs of the American Cryptogram Association and the New York Cipher Society and at Norbert Wiener, father of cybernetics, and to other believers in the capabilities of the electronic calculating machines.

  Nobody ever claimed the money, and Byrne died a few years later. One may presume that the reason both for the failure of the public to read his cipher and the failure of the government to adopt it was that while the cipher probably had many merits, its many demerits outweighed them for practical use. Byrne, like many inventors, both won and lost. His cipher was never broken. But his dream never came true.

  Codemaking appears to be such a popular sport because it is literally fancy-free. If cryptography is a form of abstract algebra, then inventing a new cipher system is nothing more than building abstract castles in the air with material and design of one’s own choosing. To make the system work is little more than to avoid self-contradiction, yet when the answer comes out right it always satisfies the inventor. Codemaking is much more popular than codebreaking because it is easier and more esthetic; it flings together shining theories however it pleases, whereas cryptanalysis forces the mind to concentrate upon the data, upon the coarse rubble of reality. But cryptanalysis is much more rewarding. For it subdues these hard and unyielding facts; it represents a victory of the mind over something, whereas codemaking represents a triumph over nothing. This mental mastery is the keen pleasure-pang of solution; it is what men of the intellectual caliber of Babbage and Wheatstone see in cryptanalysis, and it explains the most extraordinary testimonial ever given to cryptanalysis
. The testimonial’s phraseology is undistinguished and the cryptogram was elementary; what gives it its weight is that it was uttered by Harry Houdini. “I managed, after some worry, to solve the message, and very few things in after life gave me as much pleasure as did the unraveling of that code,” wrote the man who, one would think, would say that about his ability to untangle the physical puzzles of knotted ropes and straitjackets and of locks on trunks thrown into the water to which he daily owed his life.

  Consequently it is not surprising to learn that those addicted to this mental enjoyment have banded together to assure themselves of it. The American Cryptogram Association was founded in 1932 by members of the National Puzzlers League who wanted to concentrate more on cryptology, taking as their motto “The cryptogram is the aristocrat of puzzles.” Today the A.C.A. numbers about 500 members, including some from Japan, Australia, New Zealand, India, Israel, Algeria, England, Netherlands, Spain, Northern Ireland, Germany, Sweden, Argentina, Venezuela, and Canada. Their professions are varied; included are lawyers, editors, physicians, professors, civil servants, teachers, housewives, widows, engineers, mathematicians, computer programmers, a puzzle maker, and retired people. Most of the members affect a nom de plume, or sort of sprightly codename, like B. NATURAL, AB STRUSE, FRINKUS, DR. CRYPTOGRAM; this is a carry-over from the National Puzzlers League and is alleged to increase informality among the membership. Every other month, the association publishes The Cryptogram, a magazine usually of 24 pages with articles on cryptanalysis, new ciphers, and cryptologic history. It offers the members several kinds of cryptograms for solution—monalphabetics with word divisions ranging from the simplest to the kind with the most twisted syntax and vocabulary (these are called “Aristocrats” in recognition of the association’s motto), monalphabetics without word divisions (“Patristocrats”), cryptograms in all the varieties of cipher that can be solved within the compass of a 150-letter message, sometimes with tips, and cryptograms in foreign languages, including occasionally Esperanto, Latin, and Hungarian. Solvers’ noms and scores are listed. The association holds an annual convention at which members hear talks on cryptology, engage in a cipher contest, are interviewed by slightly befuddled newspapermen, and banquet. In the larger cities, members have banded together to form local groups, such as the New York Cipher Society, which usually meet monthly to talk, exchange ideas, and socialize. The association appears to be the only one of its kind in the world, though France has an Amicale des Réservistes du Chiffre, a quasi-official organization of Army, Navy, and Air reservists and active officers in cryptology.

  Tens of thousands of people not in the A.C. A. get the thrill of cryptanalysis by solving the monalphabetic substitutions printed in daily newspapers as puzzles much like the crossword puzzle. Some of these are relatively simple, using ordinary words in a quotation from a famous author, while other newspapers print short, rather tough cryptograms made of rare and almost nonsensical words. Most of these cryptograms are syndicated. In addition, crossword puzzle magazines usually include a few monalphabetics. One magazine, which paid a dollar apiece for the cryptograms, got most of its supply from an inmate of an Ohio prison.

  While many people make and break ciphers in sport, others do it in earnest. The variety and quantity of nonpolitical cryptography can only equal the number of motives that impel people to secrecy, and these motives, like their ciphers, are most heterogeneous.

  In the graveyard of New York’s Trinity Church, on Broadway at the foot of Wall Street in the very heart of the financial district, stands a tombstone with an epitaph partly in cipher. Under it lies James Leeson, who died September 28, 1794, aged 38. The cipher inscription is in the ancient pigpen cipher, whose use goes back hundreds of years, and it reads Remember Death. Why Leeson had it carved there no one, perhaps, will ever know, but his motive may well have been that of the ancient Egyptians who first used cryptography in their sepulchral inscriptions: to stay passersby and bring the dead to life in their memory.

  More obscure are the motives that led several people to encipher entries in church registers, though the conjectures can be tantalizing. At Cleator, Cumberland, England, someone used the very simple cipher

  with the rest of the plaintext letters left unenciphered to record in Latin the baptism on January 1, 1645, of Janet Barne, daughter of William Barne, curate of the parish. The mother’s name is not given. Could the encipherer have been Barne himself? And if so, was he perhaps hiding an illegitimate birth? The same system was used in the fee-book for the parish of Iver near Uxbridge, England, to note on January 17, 1767, the marriage of 188 b58y48. Why Ann Bunyon’s name should be veiled while her husband’s was left in clear remains unknown. In two spirals on a minute of a letter of September 14, 1750, Gabriel Cramer, a teacher of mathematics at the Calvin Academy in Geneva, who corresponded with the most learned men of his time, inscribed two cipher messages. Simple columnar transpositions, they counseled: “The oracle tells thee to fear nothing; thou art permitted to hope for everything; dare boldly; banish fear; thou canst surely give thyself over to joy.” Cramer almost certainly composed the messages only for his own pleasure or encouragement, perhaps choosing the spiral because it symbolized unrolling time and so a future to which he may have looked forward.

  The location of a hidden treasure remains concealed beneath a cryptogram that has resisted the digging of cryptanalytic treasure hunters for more than a century. The story begins in 1817, when one Thomas Jefferson Beale and his company of 30 men were following an immense herd of buffalo about 250 miles north of Santa Fe. They camped for the night in a small ravine, and in the firelight something sparkled in the rocks: gold! For 18 months, Beale and the others mined quantities of both gold and silver. He and ten companions returned to Virginia in November, 1819, to hide half a ton of gold and almost two tons of silver in an excavation six feet deep “in the county of Bedford about four miles from Bufords.” Two years later he deposited almost a ton of gold, half a ton of silver, and $13,000 worth of jewels. Beale then left again for the West. He never returned. But he had left a locked box with Robert Morris, a tavern keeper for whose integrity he had great respect, asking Morris to wait ten years and then, if Beale had not returned, to open it.

  Morris waited more than twenty years before breaking the lock. Inside he found several sheets of paper covered with numbers and two letters addressed to him. They told the story of the discovery of the gold and directed him to divide the treasure into 31 equal parts—one part for himself and one to be given to the next of kin of each of the 30 men. The cryptograms gave the names of the next of kin and the location of the treasure. The letters promised that their key would be sent to Morris, but none had ever arrived.

  Morris set about trying to solve the cryptograms. He got nowhere. After a number of years of failure, he shared the secret with James B. Ward, of Campbell County, Virginia, who also strove to read the messages. Ward eventually succeeded in breaking the cipher of the paper marked No. 2, which specified the amount of the treasure and how and when Beale had buried it. But it did not say where. The message ended: Paper Number One describes the exact locality of the vault, so that no difficulty will be had in finding it.

  The key to Paper No. 2 lay in the Declaration of Independence. Beale had numbered each word from 1 to 1322 and had used the word’s number as the cipher equivalent for the first letter of the word. But the Declaration of Independence did not unlock the desperately sought cryptogram of Paper No. 1. This is a numerical message of 496 groups ranging from 1 to 2906, with a moderate quantity of repeats. Cryptanalysts—or more accurately, would-be cryptanalysts—have attacked it repeatedly, trying the Constitution, books of the Bible, plays of Shakespeare. Nothing has worked. A copy was sent to Fabyan’s Riverbank Laboratories, but no solution came back. In 1964, Dr. Carl Hammer, of Washington, D.C., ran elaborate statistical tests on an electronic computer, the Univac 1107, to determine the cryptogram’s properties. “Among others,” he wrote, “I have analyzed the distribution of the numb
ers themselves, their residues modulo 26, their cross sums, and even their autoregressive patterns ranging from frames 2 to 100.” These have confirmed to his satisfaction that Paper No. 1 is indeed enciphered in the same general system as Paper No. 2. But he has not solved the cryptogram. To the man who does will go one of the richest rewards in cryptanalysis.

  Cryptography has protected not only material secrets, but spiritual ones as well. Secret societies have long used ciphers. The Free and Accepted Masons monopolized the antique pigpen cipher to such an extent that it is often called the Freemasons’ cipher. Its most common modern form is this:

  Thus Scottish rite would be enciphered . These symbols stand out here and there in the printed manuals of Masonry; they comprise part of the mixture of cryptography, abbreviation, and rebus with which the Masons disguise their secret rituals. In the postbellum South, the Knights of the Golden Circle, a kind of Ku Klux Klan, used essentially the same cipher for their occasional correspondences.

  In its early days, Phi Beta Kappa had strong strains of secrecy, and a charter sent to Harvard in 1780 from the parent body at Williamsburg required that “all correspondencies shall be through the President of each Society by means of the Table herewith transmitted.” It consisted of 13 reciprocal substitutions, and the Harvard chapter used it in a letter of March 23, 1782, to the Yale chapter, beginning IZ BUGZ BPWX ZUNDWZXB FHHFNBARWBG … (We take this earliest opportunity …), to inform them of the establishment of the Harvard chapter and to invite them “to the advantages of a literary correspondence.” The members took their cryptography rather seriously, for the president of the Yale chapter wrote Harvard on October 10: “I must observe that I have now written many things which ought to have been written by the T[abl]e but as I forgot to obtain it before I left N. Haven it is not in my power to avail myself of it.”