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.”