Code Girls, page 11
But cracking the Japanese machine was proving elusive. By the time that Genevieve Grotjan was assigned to the project, the Americans had been struggling for months. The first message in the new machine cipher had been intercepted in March 1939, emanating from the Japanese embassy in Warsaw. The code breakers had known it was coming thanks to the fact that they had broken a simpler machine cipher that the Japanese used for much of the 1930s. The Japanese referred to the first machine by the prosaic name Angooki Taipu A—Cipher Machine Type A—and so this new one was called Angooki Taipu B. The Americans called the first one Red and the second one Purple. Purple didn’t work the way Red did. It was more complicated, which was why the code breakers were having such trouble with it.
The small number of Westerners who knew about the existence of the Purple cipher thought the Americans in William Friedman’s tiny Japanese unit were wasting their time. The British had tried to break the Purple machine—as had the Germans—but both abandoned the job as undoable. The U.S. Navy, in the wing next door, worked on Purple for four months but decided to concentrate on JN-25. William Friedman’s group of civilians were the only ones who refused to give up, or were temperamentally incapable of doing so.
The men Friedman had hired in 1930 had benefited from years of training. Now, with war raging in Europe and Asia, and America’s involvement looming—ever since the fall of France, it had become inevitable—new hires like Genevieve Grotjan were flung directly into the work. Frank Rowlett, the southerner, was supervising the Purple effort. He was a big man, friendly, and tended to play up his rural-boy persona as a way of masking his strategic intelligence and competitive instincts, saying things like, “I’m just a country boy from the sticks, but…” Grotjan found him personable and easy to work for.
As he built his team, Friedman had scoured the civil service rosters. The kind of person he wanted was hard to define. He sought intelligence but also persistence. Though a penchant for crossword puzzles is sometimes seen as an indicator of code-breaking talent, Friedman scoffed at the idea that breaking codes is truly akin to solving newspaper crossword puzzles. Crossword puzzles are easy; once you get a clue, you feel spurred on, you feel encouraged. Small victories and incentives are built in. Crossword puzzles are designed to be solved, while codes and ciphers are designed to prevent solution. With codes, you have to be prepared to work for months—for years—and fail.
In September 1940, failing was exactly what they seemed to be doing. After more than a year of frustration, the only thing the code breakers knew for sure was this: One weakness of the Japanese Purple machine stemmed from the fact that Tokyo had been a little too eager to save money. In the 1930s, when Japanese cryptographers were designing the earlier Red machine, messages often were transmitted in groups of four or five letters. Groups that could be pronounced were cheaper to send. (Friedman attended the conferences where telegraph companies in different countries laid down rules of the road like these, coordinating things like costs and structure and allocation of frequencies.) To be pronounceable, a five-letter group had to contain at least two vowels. The Red machine therefore transformed vowels into vowels, and consonants into consonants, to ensure that “marus” ended up as something like “biyav” and not, say, “xbvwq.” That way, the messages remained pronounceable.
Friedman’s team had figured out that the old Red machine employed two mechanisms to achieve this, one of which transformed the six vowels, the other the twenty consonants. They referred to these mechanisms as the “sixes” and the “twenties.” The Friedman team had managed to build a facsimile of the Red machine, using Western parts. Their facsimile worked so well that Friedman’s code breakers often were able to decipher a Red message and deliver the contents to U.S. military intelligence before the Japanese code clerks had gotten the same message to their own bosses. When the Red machine began to go off-line, in 1939, American officials found it frustrating to be deprived of the fruits they had become accustomed to enjoying.
By the time the Purple machine came along, cable companies had relaxed the rule about groups needing to be pronounceable, so there was no need for sixes and twenties. Even so, new systems often contain elements of older ones: This is known as “cryptographic continuity.” Banking on this, the code breakers hypothesized that the Purple machine also used two mechanisms, one that transformed six letters—any letters, not just vowels—and one that transformed twenty. Sure enough, when the Purple intercepts started appearing, Friedman’s code breakers were able to see that six letters appeared more often than others. But the twenties were the stumbling block. No matter what kind of system they conjectured, the Americans could not discern how the remaining twenty letters were enciphered.
Every code breaker had his or her method of coping with frustration. Frank Rowlett liked to go to bed early, then wake up in the middle of the night and see if inspiration struck him. William Friedman often thought of solutions while shaving; he was a big believer in the problem-solving power of the subconscious. Genevieve Grotjan was one of the most patient team members. She would sit for hours contemplating streams of letters, making notations, creating charts.
William Friedman had taught his students that if you scrutinize a cipher long enough, from as many angles as possible, a pattern must declare itself. The goal of any code maker is to come up with a system that is random and therefore unbreakable. But this is a hard thing to do. Most machines used switches or rotors—set in new orders each day or couple of days, according to the key or setting—to transform one letter into another, often several times, so that A might become D, and then P, and emerge as, say, X. The next time, the same letter would follow a whole new path. But wheels and rotors will eventually work through an entire cycle; at a certain point, they will come back to the beginning and encipher the same letter the same way. A will again become D, and then P, and then X. The more elaborate the mechanism—the more wheels involved, the more complex the settings—the longer the interval before the repetition occurs. But at some point, something, somewhere, will repeat.
What Friedman also understood, and managed to teach his team, was that there are mathematical ways of detecting the underlying behavior not only of language but also of individual letters. In English, E is the most frequent letter. If you are making a cipher and turn every E in a message into a Z, then Z will behave exactly as E does: It will become the most frequent letter. One of the first things a cryptanalyst does is take a “frequency count” of all the letters in an enciphered message. If Z appears most frequently, this likely means Z stands for E. Ciphers quickly get much, much trickier, but statistical methods always help. It’s remarkable what can be done with math.
What Friedman had also taught them during their training is that you can break a foreign cipher without understanding the language, as long as you know how the letters in that language behave. Certain letters, like S, often travel alongside certain other letters, like T, and he taught his staff to count how many times certain pairs—digraphs—appeared together, as well as trigraphs like ing or ent or ive or tetragraphs like tion. He knew on average how many vowels—between thirty-three and forty-seven—typically appear in one hundred letters of plain English. He knew which letters rarely appear side by side. He had even figured out how many blanks—or letters not occurring—tend to appear in one hundred letters. He had identified which consonants (D, T, N, R, S) are most frequent in ordinary English and which are least frequent (J, K, Q, X, Z). He studied how French letters behaved (common digraphs: es, le, de, re, en, on, nt) and how English behaved when sent over the telegraph. Since “the” is often omitted from a telegraphed message, the statistical behavior of E changes slightly in a telegram. These are the kinds of nuances—random variations, standard deviations—that statisticians live and breathe for.
Over a span of months, the code breakers had come up with every attack on Purple that they could think of. They had mastered the behavior of romanized Japanese, in which pairs of vowels often occurred, such as oo, uu, ai, ei, and they knew that Y almost always was followed by O or U, often doubled, as in ryoo, ryuu, kyoo, and kyuu. They reviewed the workings of known machines on the Western market, in case the Japanese had borrowed ideas from them. Among these was the Kryha, a noisy thing with a gear-like mechanism that resembled clockwork; something they called the “Damm machine,” an easily penetrated contraption named after its inventor, a Swedish engineer named Arvid Damm; and those invented by the horse thief Hebern. All used devices that could take a letter and turn it into another letter. Some advanced step by step. Some would skip forward several letters, or skip once and then not skip the next time. When the Purple machine was being installed in Japanese embassies, Friedman’s team was able to follow the itinerary of the installer—a Japanese expert identified in memos only as Okamoto, who traveled city by city putting in the new machines—by reading updates he sent back to Tokyo over the old Red system. They kept hoping he would use Red to send home a report, some kind of clue as to what the Purple machine was and how it worked. Alas, Okamoto did not.
Friedman’s team was under enormous pressure. When Purple first came online, they thought they could break the machine in a matter of months. As 1940 progressed and Jews in Europe were rounded up, more concentration camps opened, the blitzkrieg advanced, Roosevelt was anxious to know whether Japan would join in a formal alliance with the Axis powers of Germany and Italy, and if so, what the terms might look like. Emissaries from military intelligence visited Friedman every day, nudging him, filling him with anxiety, asking whether he was doing everything he could. The code breakers talked to radio intercept operators in the field, urging them to ensure that the circuits carrying Purple messages were fully covered. They set up more IBM machines—tabulators that could count and sort very fast—that had been modified to sort the Purple messages they were getting. And still: nothing.
Friedman liked his team to do their own pen work—copying out each letter—so as to have a palpable, physical connection with the cipher. One technique was to write out the text of an enciphered message and print above or below it something they called a “crib.” Cribbing is an essential component of code breaking—perhaps the essential component. Cribs are educated guesses about what the message says, or even what just a word or phrase probably consists of. Some minor Japanese ministries and embassies were still using the old Red machines, and sometimes Tokyo would send a message to all embassies—known as a circular—using both Red and Purple. Circulars were a great source of cribs. The code breakers could decipher the Red version and set it against the Purple cipher, hunting for correlations.
They also knew that Japanese diplomats, like diplomats everywhere, relied on formal beginnings—“I have the honor to inform Your Excellency” or some such. Sometimes they would jot something like that below their Purple cipher and fiddle around to see if it worked. The fact that they had broken the sixes meant they had a few skeletal letters to work with to confirm the position of the crib, as in a game of hangman. It also helped that the U.S. State Department was negotiating with Japan over a commercial treaty, so messages sometimes came through that contained quotes in English. At Friedman’s urging, the State Department would quietly slip the code breakers the originals, to use as cribs.
The code breakers formed a hypothesis about Purple, without quite being able to say why. They theorized that the Purple machine was using some kind of switching device (rather than wheels) to transform the letters. They thought these devices likely resembled the kind of “stepping switch” employed in ordinary telephone circuitry, which routed calls by passing electrical pulses from one switch to the next, using something called a wiper. The design they hypothesized “envisaged a set of four twenty-five point, six-level stepping switches, operating in tandem,” Rowlett later wrote. They thought there might be more than one set of four switches, using a cascading rhythm to suppress repetitions. They had a hypothesis that, buried in a stream of message text, it might be possible to spot coinciding letters that would show this; juxtaposing a cipher against a crib, a code breaker might detect a pattern showing the work of the switching devices. If this was true, there would be many letters between each cyclical repetition. But the repetition would exist. Somewhere. You needed a long message to find this; you needed more than one long message, really, and the messages had to have been sent on the same day, so as to have been enciphered by the same key.
Their progress thus far had consisted of conjectures like these, followed by feverish attempts at confirmation, followed by disappointment. Their hopes renewed by this latest theory, Frank Rowlett and his Purple team eagerly looked for three long messages sent on the same day and, after ransacking their file cabinets, managed to find them. Now they needed a crib. Mary Louise Prather—keeping her meticulous files—happened to recall a message transmitted on the same day in a lesser Japanese system they had broken. It was a marvelous feat of memory and gave them the crib they needed.
Frank Rowlett had work sheets made up with the same messages and cribs. He assigned the same sheets to different people, to see if anybody could find anything. They were sitting at tables in a room of about thirty by fifteen feet, scanning and studying. “We were looking for this phenomenon,” he would later say, “without actually being aware of precisely what we were seeking.”
It was September 20, 1940, at around two o’clock in the afternoon. Rowlett, who was one of the more mechanically minded team members—he was a tinkerer and a hoarder and tended to scrounge spare telephone parts, which he kept in his basement behind a woodpile—was talking with some of the other men. Sitting there engrossed in what Rowlett later rather sheepishly called a “gabfest,” they looked up and saw that Genevieve Grotjan, the would-be math teacher and former railway annuity statistician, had materialized beside them. As Rowlett later recalled, she was holding her work sheets clutched to her chest. “Excuse me,” she told them shyly. “I have something to show you.”
They looked at her with interest and a measure of hope. She was “obviously excited,” Rowlett saw. “We could see from her attitude that she must have discovered something extraordinary.”
Laying the work sheets on the table, Grotjan took her pencil and circled a place where two letters came together, one from the coded message, one from the crib, one above, one below. Then she went to a second work sheet and circled another coincidence, of two letters whose occurrence confirmed the very pattern they were looking for. Then, at the end of a long stream of letters, she circled a third. And a fourth. And she stood back. There it was. She had found the repetitions. She had uncovered the cycles and confirmed the hypothesis. She had broken the twenties.
Grotjan was a junior mathematician armed with a college degree, an uncompleted master’s thesis, and less than a year of on-the-job training. Many of the men she was working for had far more experience—years, decades. They had written the textbooks she had studied from. Nobody quite understood how she’d done it, then or ever. Grotjan had a powerful ability to concentrate and, in that state of concentration, to see in a different way. In code breaking, counting and making charts and graphs and tables are part of the process. But when you have exhausted that, sometimes, in a deep moment of concentration, pure insight happens, and you just, simply, see the thing you are looking for. And you apprehend that it is right.
The men knew instantly what they were looking at. Grotjan had given them their entering wedge. While she stood quietly, they erupted in cheers. Frank Rowlett began yelling, “That’s it! That’s it! Gene has found what we were looking for!”
Others crowded around to see. William Friedman came in to see what the noise was about. Grotjan, “obviously thrilled,” as Rowlett described her, removed her eyeglasses and was unable to speak. Rowlett started talking to Friedman, narrating what had occurred and pointing out the cycles. It took a while to convince their boss they had succeeded. Friedman slumped, placing his arms on the table and collapsing against it, as if all the stuffing had gone out of him. He congratulated Grotjan, with whom he had barely spoken before. “I was just doing what Mr. Rowlett told me to do,” she replied. She was already thinking about the next steps they would need to take, such as figuring out how to break the daily keys. But everybody knew this was the victory they needed. Celebratory Cokes were poured. Friedman went into his office to collect himself, and the others gathered around the table while Grotjan recounted her discovery and explained how she arrived at it.
The team could now construct a machine to decipher the messages. “When Gene… brought in those worksheets and pointed out these particular things,” Frank Rowlett would later say, “we knew that we were into the Purple machine and that it would be solved.”
Here is the thing about a machine cipher: It’s hell to break, but once you break it, you’re in. In the aftermath of the Purple breakthrough, William Friedman—harrowed—spent the first three months of 1941 in Walter Reed General Hospital, recovering from exhaustion. It was a nervous breakdown. During the long ordeal he had not been able to say anything to anybody outside the office, not even his wife. Elizebeth would find him in the kitchen in the middle of the night, making a sandwich and unable to sleep. Even on the day of Grotjan’s breakthrough, he went home for dinner and said nothing. He couldn’t. “My husband never opened his mouth about anything,” she said. The bottled-up stress broke him. He was never the same.
Three years later, Friedman wrote a top secret memo praising Genevieve Grotjan, Mary Louise Prather, and other members of the team in the highest possible terms. He described the Purple cipher as “by far the most difficult cryptanalytic problem successfully handled and solved by any signal intelligence organization in the world.”
