“That,” announced Henryk, pointing to the switchboard, “is a plugboard, or, as the Germans call it, a Steckerboard. It comes to us, compliments of Army intelligence.
“Its purpose is just what Jerzy suggested—a second encoding. It's an integral part of the machine, and that makes it easy to use. Each of the short cables can be plugged into two sockets connecting any two letters—say C and K; then C and K are steckered together. When a key is pushed, and C comes out of the three-wheeled scrambler, the current is routed through the steckerboard, changing the C to a K; the K appears in the lighted board at the top. As the connections run both ways, the steckerboard will also switch every K to the letter C. So the machine works like the original: at any initial setting, it can be used either to code or decode a message.”
Jerzy was leaning over the machine, obviously fascinated—like an eight-year old preparing to take a watch apart.
“Yes, Jerzy, you may play with it; the present settings don't mean anything in particular.”
Jerzy began to unplug the cables, resetting them in a different order. Each time, he set the wheels to AAA and pushed one of the keys, scribbling the results on a pad.
“The steckerboard seems like a very simple second coding,” Henryk continued, “and it is. C always becomes K, and K always becomes C, as long as the cable settings remain unchanged. If that were the only coding, it would be child's play to decipher it. But it's not. We have two codings in tandem: first the scrambling from the three wheels, with the results then passed through the steckerboard.
“Unfortunately, this simple system has spectacular results. Consider. The first letter, A, may be steckered to any of the other 25 letters, obviously giving 25 possibilities.”
Marian squirmed in his seat; he had been suffering most acutely from the frustration of preceding months. His mind was now racing ahead; he interrupted Henryk.
“Once A is steckered, there are 24 remaining unsteckered letters. The next one, B, can be steckered to any of the other 23 open plugs, and so on. Thus, the number of possible combinations is 25 x 23 x 21.... That comes to a total of...”
Henryk paused to let Marian demonstrate his impressive ability to do calculations in his head. He waited expectantly, head slightly forward, brows raised, his ten long fingers pressed against the table.
“What? Almost 10 trillion?” Marian reported after a few seconds.
“Actually, only 8 trillion.” Henryk paused to let the number sink in. “For each of these possibilities, there are the 100,000-plus combinations coming through the three-wheeled scrambler. In very rough terms, that makes almost a quintillion possibilities—or, if you like it straight and simple, a billion billion.”
Without realizing it, Anna sighed.
“I think,” Henryk said in a record understatement, “that this will require the best from both our gorillas and idiots. Indeed, the next round goes to the idiots. Brute force, by itself, simply won't work any more. We're to the end of the line with that approach. We expect a lot from Marian's brute of a machine, but not magic.”
The responses of his small audience varied. Marian smiled slightly; it was the first time that Henryk had allowed himself to use the terms gorillas and idiots. Jerzy and Anna, as the chief idiots, were now on the spot; they looked decidedly glum at the huge odds against them. In the past two years, the possible encodings had escalated from a “mere” 17 thousand to a billion billion. To read a message by brute force would take many trillion times as long. They should live so long.
“I also think,” concluded Henryk, “that we might all turn the problem over in our minds before meeting again—next Wednesday morning, I would suggest.”
They didn't get anywhere the next Wednesday. Nor the following Wednesday, nor the next, nor any of the Wednesdays until mid November.
Then they collectively found the key that would be used, not only by the Poles, but also by the French and especially the British all the way up to the time of the invasion of France in May 1940, when the Germans would have another particularly nasty surprise.
When they sat down for the regular Wednesday meeting, Henryk asked Anna, as the raporteur, to sum up the current situation as she saw it; this would give them a starting point.
Unconsciously, Anna sat a bit straighter in her chair, giving a formality to her report. “There are obviously two parts of the puzzle: the wheels from the original Enigma—the scrambler, in other words—plus the steckerboard. Our basic problem is: how can we solve the scrambler settings without first knowing the steckerboard settings, and vice versa? In other words, we have to solve both sets of settings—the wheels and the steckerboard—simultaneously.”
Anna noticed that Marian was stroking his beard. She continued.
“What do we know that might be helpful?
“First, some of the messages start with 'From,' or VON in German. It's not clear how much help that is. After it goes through the steckerboard, VON may be transmogrified into any three other letters. In spite of it all, there might be something here,” she said, trying to be upbeat. “We've also collected a list of other similar cribs.”
Marian was now stroking his beard even more slowly, more thoughtfully. Anna hoped he was still listening. She took up her story.
“Second, the pattern of messages has remained the same: a preamble followed by two sets of three letters, followed by a string, followed by groups of five letters. Thus, it is reasonable to assume that the two sets of three letters—the inscrutable six—still give the wheel settings. But how can we use that information? Again, it will go through the steckerboard, which will change all the letters from the scrambler. Again, we're driven back to our fundamental problem: it's hard to see how we can crack any corner of the problem without figuring out everything—wheels and steckerboard—at once. We will have to...”
Her voice trailed off because it looked as if Marian was ready to say something.
“I'm not so sure,” he began. “If we do what we did before, it's true that we would have to decode a message to figure out the inscrutable six. That brings us to our little problem of a billion billion possible settings.... But suppose we attack the inscrutable six directly, without a decoded message. Would that be possible?”
Henryk was about to say “How?” but caught himself; Marian was already continuing, slowly and thoughtfully.
“The way to start, it seems to me, would be to look for some clue in the six letters themselves. What would that be?”
He swallowed a sip of water and continued:
“What are the inscrutable six? Instructions on how the recipient should set the wheels to decode the incoming message. The instructions are repeated, giving two sets of three letters. For example:
PQR PQR
“But of course, this information is encrypted; any six letters may show up. Suppose we find an intercept that happens to give the same letter for the first and fourth position, for example:
ABC AFG
“Then we would know that we're at an interesting place in the wheels. If we first push a P, it comes out A after encryption. Three letters later, when we push P again, it once more comes out A. We might use that to pry open the problem.”
He paused for about a minute; everybody at the table was deep in thought.
“But I'm not sure that will help. There's still the steckerboard problem....”
“But is there?” responded Jerzy, his words tumbling out. “Isn't the steckerboard beside the point? Suppose, for example, that the A is steckered to K. Then, looking at the first and fourth positions of your example, the scrambler part of the machine would be kicking out
Kxx Kxx.
“In other words, the steckerboard is irrelevant for your basic conclusion. The initial setting of the wheels gives the same letter in positions 1 and 4—although we don't have any idea of what that letter might be.”
Now Henryk was smiling. The billion billion, he thought, has just been cut down to something like a “mere” billion.
An excite
d conversation—interspersed with long, thoughtful silences—ensued. After an hour, Henryk brought this part of the meeting to a close.
“So we need to figure out some way of using messages in which the first and fourth letters of the inscrutable six are the same—or the second and fifth letters, or third and sixth.
“I think it might be better if we broke into two groups. We might think along different lines; we won't all chase down the same dead-end path. I suggest Marian and me in one group, and Jerzy and Anna in the other.
“Let's take a two-hour break, to recharge our batteries and have lunch,” Henryk suggested, “and come back at two o'clock. I'd like Marian to report on the impressive progress with his new machine. If we all know what it will do, our problem may not seem quite so formidable. Also, some of us may be able to make suggestions for his next model.”
After lunch, Marian gave a detailed account of his machine; it would quickly run through the results from possible wheel settings. This first version worked, spitting out answers several hundred times as fast as a skilled operator entering letters in an Enigma machine by hand.
Marian was already hard at work on a version at least ten times as fast, and explained in detail the modifications he had in mind. There was an intense discussion of the new model—Mark II—and how it might be improved even more.
“With the new model, a thousand times faster than hand, the billion has been cut down to a million,” observed Henryk. “We may win after all.”
Anna had never studied the inner workings of machines—the penalties of being a college dropout, she thought—and felt left out of the conversation. Afterward, she saw that her notes were garbled, but Jerzy was most helpful in explaining patiently and in detail what Marian was doing.
She certainly appreciated Jerzy's help.
But, as she and Jerzy worked closely together in his tiny office, his cigar smoke began to bother her. When Henryk asked to see her on an administrative matter, she cautiously raised the subject. To soften her complaint, she began on a positive note:
“Jerzy's brilliant. And he's exceptionally helpful, patiently explaining stuff I don't understand. In many ways, he's a joy to work with.... But there's one problem. Normally, I don't mind cigars, but his office is so small and his cigars so cheap. I'm finding them hard to take.”
“Sorry. We try to put up with eccentricities.”
Anna was concerned that Henryk might dismiss her problem. “Maybe vee should take up a Kollekshun, and buy him deszendt Zigars,” she said, flippantly, in a mock German accent.
“Wouldn't recommend it. He might smoke more. You've noticed how often he has an unlighted cigar in his mouth? And a collection? He might take it as an insult.”
Anna hadn't meant her suggestion—for a collection—to be taken seriously; she just wanted to keep the conversation focused on smoking. In future, she'd have to be more careful with offhand little jokes. She and Henryk usually communicated so well. But when it came to humor, they were on a different wavelength.
Now, she wasn't sure exactly what she wanted. But she continued. “He puzzles me. So often, he seems like a perfect gentleman, even a patrician. Impeccable manners, a light sense of humor, and thoughtful. At other times....”
“Ah, I'm afraid he's had a rather, um, uneven upbringing.”
Anna gazed attentively in order to encourage Henryk to continue.
“He comes from an aristocratic, land-owning family in the Ukraine. But his father....”
Henryk's voice trailed off. Shifting uncomfortably in her chair, Anna thought that perhaps the time had come to leave. Just as she leaned forward, about to get up, Henryk continued.
“A jolly type. But not much of an example. Heavy drinking. Gambling. More than the usual eye for the ladies.”
Again there was a pause, again Anna shifted in her chair, and again Henryk continued.
“To compensate, Jerzy's mother expected a lot from him. One day, when he was only four, she caught him signaling under the table, helping his older brother with a math problem. After scolding him—gently, because she was so proud of his precocious abilities—she expressed her greatest hope: 'One day, you'll be a great man. I'll be proud of you.' Nice, in some ways. But quite a burden to lay on a four-year old.”
Again Henryk stopped. This time, Anna sat tight. Henryk had his chin resting on his loosely clenched fist, the other arm across his chest to support his elbow. Apparently, he was trying to think something through.
“There is one way out of our problem. With the expansion, we're about to get new offices. I can find an office for Jerzy next to a conference room. As the construction is not yet complete, I think I can arrange both an upgrade in the air circulation system and a connecting door from his room. I'll arrange to keep the conference room as free as possible; your meetings are likely to migrate there naturally. If they don't, please let me know. I'll suggest to him—as tactfully as I can—that the two of you meet there, rather than in his small office.
“We need Jerzy. We need you—we're delighted, how quickly you proved you belonged in the senior group. And we need the two of you to work together. If you find you can't stand the smoke, we might ask him to stay in his office while he's puffing away. But let me think about it.”
Anna expressed her thanks. She had been embarrassed to raise the subject of smoking. Now she was glad she had.
The Wednesday meetings were canceled until further notice. Henryk really did want the two groups to work independently, not simply follow the same approach. A good idea, perhaps. But Anna and Jerzy—in their new conference room—sweated away, day after day, which stretched into week after week. They weren't getting anywhere, and Anna took Marian's earlier advice. She decided she would be more productive if she took more time off. Whenever Kaz could get away.
Then, one afternoon in March 1939, Henryk's secretary called. The core group of four was to meet right away. There were some ideas to consider.
“Let's look at the machine and its settings,” Henryk began. “Rather than trying to work directly toward a solution, we propose to go at the problem from the opposite direction—to rule out impossible settings. Settings that could not give a repeat. Then we can focus our work on what remains—the ones that are possible.”
“Ah,” said Jerzy, “you've intruded into the idiot's territory. We welcome you.”
Henryk ignored the interruption. “What information do we have? We're going to pick out German messages where there's a repeat in the inscrutable six. But there are thousands of possible wheel settings. How can we keep track of the absolute blizzard of detail? What we propose is to use square sheets—26 spaces across, labeled from A to Z for each setting of the second wheel, and 26 spaces down for each setting of the third wheel. We will need 26 such sheets, one for each setting of the first wheel.
“Consider an example, where the three wheels are set at the letters BDH. This will show up on the second—B—sheet, in the D column and the H row. If it is possible for that setting to give a repeat on the third press of the key, our staff will mark that box.
“It will be tedious to make the sheets. But whenever there's a repeat within the inscrutable six, the sheets will tell us which settings are worth testing with our new machine. We can ignore the unmarked boxes; they're not possible.”
“Mention the six sets,” interjected Marian. “Mention the six sets.”
“Oh yes,” said Henryk, trying to add a light touch to a difficult topic. “I left out one little detail. As we know, the three wheels can be set in six different orders. We will have to have one set of sheets for each ordering—that is, 6 sets of 26 sheets each.”
Anna lowered her head. She was very much afraid that she was going to start rolling her eyes; that wouldn't be very good form.
“But we'll have help,” said Marian. “We'll be producing six of the new machines as soon as possible, one to test each of the possible wheel orderings.”
Henryk wound up the meeting. “Finally—and this must remain secr
et, just among the four of us—I've asked the General Staff for permission to inform the British and French of our progress. With the barbaric behavior of Germany, we need to give our allies as much help as possible.”
This was the first time that Anna could remember Henryk speaking harshly of the Germans; thus far, their work had seemed like a dispassionate, intricate academic puzzle. But they were all aware, in the backs of their minds, just how much might be at stake. The events of the past week had driven home the dangers facing Poland. Hitler's legions had goose-stepped into the remnants of Czechoslovakia. The Czech government, shorn of its Sudetenland defenses by the British-French capitulation at Munich, chose not to resist. If they did, Hitler threatened, he would bomb Prague flat. This, after promising the umbrella-toting British Prime Minister that Sudetenland was his “last territorial demand,” and that “peace in our time” could be gained by selling out the Czechs.
Hitler already had his eyes on his next victim; he was threatening Poland. In response, France and Britain declared that they would guarantee Poland's independence. The Poles were going out of their way not to provoke the ranting Führer; they did not want to give him the slimmest pretext to invade. But the prospects were grim.
Marian asked Anna to come to his office.
“I notice from your file that your mother was British.”
“That's right.”
“You speak English?”
“Some.”
“Let's not be coy. This is important. Didn't you spend your first eight years in Britain, when your father was at the Embassy?”
“Yes.”
“So English was your first language. You speak it comfortably?”
THE LAST GOOD WAR: A Novel Page 6
