Anna felt properly admonished. Later, when she got around to seeing Liwicki, she would make a point of apologizing.
“And remember,” concluded Henryk. “We're not here just to decode any single message. Most of all, we're trying to figure out the German system. Even when you're doing this sort of drudge job, ask yourself: are there clues, how their system works?"
The third afternoon, Anna hit the jackpot. When she came to the setting QRT, she could read the message:
FROMGENHEINRICHSCHIMITZTOALLDIVISIONCOMMANDERSTWENTYTWODECEMBERTHIRTYSIX
ALLIN FANTR YDIVI SIONS SHOUL DBEGI NTOPR EPARE FORTH EINTE GRATI ONOFT ENADD ITION ALANT ITANK GUNSP ERREG IMENT….
When she put the spaces in the right places, the message was clear: ALL INFANTRY DIVISIONS SHOULD BEGIN…
In her excitement, she was about to rush in to tell Henryk, but decided to try another puzzle. Could she do anything with the beginning of the message: those six first letters, in two groups of three? Let's see. Suppose that they were also part of the same setting. That would mean that the setting was not initially QRT, but became QRT only after six letters had been sent. She went back six letters and tried the setting QRN. No luck; the first six letters produced gibberish.
She went to Henryk with the news. Almost immediately, Marian and Jerzy appeared. Anna quickly explained what she had done.
"Very good. Very good.” Henryk responded. “A bit of beginner's luck—you only had to go from MMM to QRT.”
“Indeed,” said Anna. “Suppose the setting had been MML. You wouldn't have seen me for a month. Unless I'd found a shortcut.”
“We're in the process of bringing together several dozen messages which the staff has been able to decode,” said Marian, “to see what we can make of them. But you said something about a shortcut. Did you have something in mind?”
“Well, yes. You said that the first line was probably the address. That means it would start with “From,” or VON in German—as my message in fact did. I was playing with the idea of doing a quick run, to look for settings where the first letter was V.”
“Very good. Very good,” Henryk repeated.
“Just think how easy it would be,” Anna continued. “In the encoded message, the first letter of the address was K. Starting with a setting of MMM, I could just hit the one letter K. If it showed up as a V, then I would go on, to see if I got VON. But if I got any other letter but V, then I could simply hit K again. The right-hand wheel would already have turned one notch, giving a setting of MMN, and that's the one I would want to try next.
“In other words, we can cut way down on the brute force,” Anna concluded. “Simply push the first letter—K in this case—over and over again until it comes out V. Whenever we get a V—one time in twenty-five—we can go on to the second letter. If it's an O, we keep right on going.”
“Very good. Very good,” Henryk said once more. “Brilliant.”
In fact, as Anna would soon discover, the “brute force” exercise had been a test, to see if she would pick up the V clue. The staff were already using this approach, with impressive results. Looking just for the first letter V worked in about half the cases, giving a quick decryption. As for the other half, many started with the date, not the address, so the V test didn't work.
“We now come to the main event,” said Marian, thoughtfully stroking his beard. “How do we tackle the first six letters—the inscrutable six?”
He looked around the room. Silence.
Finally, Henryk cleared his throat and spoke: “Can everybody get back together at 8:00 a.m. tomorrow?” The professors nodded. He looked at Anna.
She nodded too. She was delighted to be included with the big boys. There goes the topology class, she thought.
Henryk wound up the meeting: "Let's focus on our next big puzzle: that irksome group of six. Let's sleep on it.”
Anna had trouble sleeping on it. In fact, she had trouble getting to sleep at all; she was too excited. She had successfully decoded the German message. More important, she had figured out how to shortcut the process by using the V test. She had been accepted as one of the core group struggling with the Enigma. True, she had hit one pothole in the road during her first day. That bit about her eight year old mother was childish. But it was out of character, she reassured herself; it could be written off to her initial nervousness. There was no reason to fear a repeat.
As she began to drift off, she had a warm, satisfied feeling. She had broken a long-standing, unwanted habit. When she was younger, she realized that it might not be such a good idea to answer the toughest math questions in class; her classmates resented it. And, with a few well chosen errors, she could keep her exam scores to a respectably mediocre B+, a practice she discarded—spectacularly—when it came time to take the university entrance examinations. Now, she noticed, she was giving direct answers to direct questions. After just a few days, she felt comfortable with her colleagues. There wasn't the slightest risk that she would make brilliant men like Henryk or Marian or Jerzy look bad.
Henryk resumed the meeting at 8:00 a.m. sharp. In front of each of their places was a pile of about a dozen messages, in both the original and decrypted versions. Across the top of each decrypted message, three letters were printed in colored ink; they gave the rotor settings that had been used to encode that particular message.
"You'll observe," said Jerzy, “that the rotor settings are different for each of the messages, even though they're all Blue, and they were all sent within a few days. That indicates that, as we suspected, the settings are changed for every message—not just once a month or even once a day. Well, we can't expect the Germans to make life easy for us."
“And again, we were probably right in our guess,” responded Henryk. “The inscrutable six tell recipients the correct setting for that specific message.
“You mean,” asked Jerzy, “they not only send the three-letter settings for the wheels, but then repeat them?”
“Exactly,” replied Henryk. “They send them twice so the recipients can be sure they've gotten them right. Otherwise, if they made a mistake, the message would be gibberish."
Jerzy puffed at the stub of his cigar, with a skeptical frown. "But the three letters aren't repeated. He glanced down at the messages. “DSI FDR, in Anna's message, for example. And there seem to be no repeats in the other messages, either.” He leafed through the papers in front of him.
Anna spoke. "The Germans have a cipher machine. Why should they send the wheel settings in the clear? If they did, then anyone who captured one of their machines, or anyone who already has one," she smiled as she glanced across at the machine, "could read the message. Just as Henryk read my 'Merry Widow' the other day. Instead, why not use the machine to encrypt them?"
"In other words," said Henryk, “there are two settings. The first we might call the basic setting, indicated by the discriminant—Blue in this case. Anyone with access to the Blue codebook can look up the basic wheel setting currently in use. Using this setting, the signalman receiving the message reads the inscrutable six. That gives him the three letters to reset the wheels, to read the body of the message—what we might call the message setting.”
“Now we can see why they call it an Enigma machine,” observed Jerzy. “A puzzle within a puzzle."
"And so," said Henryk with finality, tapping his pencil on the table, "we can't really break the enigma machine. That's impossible. All we can do is read specific messages, or, at the best, figure out the basic wheel setting—for Blue messages, for example. It will be good only for a fraction of the Enigma traffic, and only until they change the setting."
All eyes turned to Marian. He had been sitting silently stroking his beard, deep in thought.
5
Anna's Idiots:
The Opposite of Genius
Gentlemen do not read each other's mail.
Secretary of State Henry Stimson, expressing shock when shown deciphered Japanese communications in 1929.
(Stimso
n had the “unethical” decoding shut down, but it was soon revived.)
"Things aren't quite so bad.” Marian broke his silence, lightening the gloom. "I think we're just about there. If Henryk's right—if the inscrutable six represent a repeat of the message setting—we've got the key to unlock the basic setting, the one which all Blue operators start with. We can find it by working backward, through trial and error. Let's use brute force to find the wheel setting that translates the inscrutable six—DSI FDR in Anna's message—into the setting for her message, QRT QRT. When we do, we should have the basic Blue setting. Then we should be able to decode all the Blue traffic. I'll have the staff work on this. Any questions?"
As they broke up, Henryk glanced toward Anna and raised his index finger, a sign that he wanted to talk to her. When they got to his office, her eyes were again drawn out the wide window. The earlier cold, crisp snow had been softened by warming air; the moist snowflakes were now ideal for packing. Young boys were engaged in a glorious snowball fight. Off to the north, a young couple, surrounded by their entranced children, were leaning against a snowman, struggling to raise the head to its rightful place. For a fleeting moment, Anna wondered if she would pay too high a price for her challenging new job.
"Now that you've proven yourself—even faster than I expected—I want to talk about your role. We're dividing our operation into two groups. One will look at ways to deal with brute force problems: how to go through the multitude of possibilities quickly. Marian Rejewski will be working with me in this group. He has some very promising ideas for a machine to speed up the process.
"The other group—which I'd like you to join—will be headed by Jerzy. Your job will be to find patterns or other ways of reducing the number of iterations we have to wade through to read a message, so we don't have to slog through all 17,000. We've already got a start. As you discovered, messages often start with V; that makes trial and error much easier.
"In brief," concluded Henryk, "your job will be to rule out some of the 17,000 possibilities—to cut it down to a few thousand. Or even less, if we're lucky.”
"Rule out things that seem possible but are in fact impossible," mused Anna. "The opposite of genius. Geniuses find out how to do the impossible; they show that things that seem impossible are in fact possible."
In the coming weeks, Anna wished that she had kept that little comment to herself. It leaked out, and the junior members of their team quickly began to call themselves "Jerzy's Idiots," using a signature logo of what was, apparently, a cross-eyed imbecile. A few—perhaps those who had a crush on their pretty new boss—went so far as to call themselves "Anna's idiots," using a drawing of an imbecile of uncertain gender.
Of course, the other group were not to be outdone. They began to use a picture of a gorilla dragging its hands on the ground, with "Brute Force" written below.
Even more than Anna, Henryk wished he hadn't passed her quip along to his secretary. He wondered if the names could cause a security breach; jokes could lead to blabbering at the local bistro. He finally issued a written order:
Personnel may joke about “idiots” and “gorillas” inside this building, but the two terms and their logos are to be kept strictly inside; they are not to be mentioned outside under any circumstances. And please, no scrawling of idiots or gorillas on bathroom walls. From time to time we have visitors. Some of them, at least, should leave with the illusion that we're doing serious work on weather forecasting.
Indeed, thought Anna one day, looking out to the quadrangle. There was Jerzy, playfully releasing several balloons, measuring their rise with a stopwatch and sextant. Henryk was delighted to humor him in his hobby as an amateur meteorologist; those outside the building would see the rising balloons and conclude that the Special Meteorology Project was, as advertised, working on weather forecasting. Jerzy also had another talent: he could talk knowledgeably to outsiders about forecasting.
The job was enough to make the researchers into manic depressives. There were the early inspirations—particularly the decoding of the first inscrutable six, which gave them the basic settings and led to a rapid deciphering of a whole set of Blue intercepts from December. But when they tried January's intercepts, nothing. The old Blue settings didn't work for the new Blue messages; the Germans had apparently changed the settings at the beginning of the year.
Also, the V clue—which had made the process so much quicker—became useless. The Germans were putting a set of between five and a dozen random letters right after the inscrutable six, to prevent codebreakers from working backward. It was only after three weeks of dreary work that the codebreakers figured that out, and started the decoding effort with the twentieth letter rather than first. But the process was now tedious. When they started in the middle, there was no point in looking for V. In fact, the twentieth letter was likely to be in the middle of a word, which made it much more difficult to figure out when they were actually reading a German passage, not just gibberish.
Then, disaster struck. At the beginning of April 1937, they found that even the Blue messages were indecipherable. That wasn't such a surprise. The Germans had apparently changed the basic settings again; they could now presumably be counted on to do so every three months or so. But, as the months passed into May, June, July, and August, with no deciphering of any message after March, it was clear that something more fundamental was wrong. They couldn't even get to the first step, of reading a single message with brute force, no matter where they started. Henryk asked the core group of four to set aside everything for a brainstorming meeting the first Monday of September, after everyone was back from vacation.
He started the meeting with a broad statement, what everyone already knew: they'd been unable to crack anything for five months. The General Staff in Warsaw was impatient, wondering if they had hit a stone wall. But that wasn't the worst of it. Over the weekend, Jerzy had run into a problem with the Enigma machines.
"Suppose we look at this methodically," Henryk suggested. “Let's look first at the puzzle we've had for the past five months, then turn to Jerzy's problem. But, before we begin, I think the time has come to start keeping detailed records of what we've done, what's worked and what hasn't."
All eyes turned toward Anna. "There goes not only topology, but my whole university program," she thought. But she nodded. In spite of the drudgery of note-taking and record-keeping, the project would be just as interesting as university work. Also, it could be a whole lot more important: the security of the nation might depend on it.
“Thank you, Anna. Now, let's come back to our first problem: What could the Germans have done five months ago to make their messages indecipherable?"
"One," responded Jerzy, "they may have scrapped the old machine, and are now working with a completely different design."
"Well," said Henryk, taken aback, "that certainly puts it on the line. If so, it seems that we have only two ways out. We might be able to steal one of their new machines. I wonder what kind of talent we have in our jails?" he mused, only half joking. "The second option—try to reconstruct the new machine from the messages we've intercepted. What do you think, Marian?"
"That would be tough—much tougher than the first time I did it back in 1932, because then I had both messages and wheel settings. If it's the same machine, with different wheels, I could calculate how many intercepts of the same type—Blue, say—we would need to reconstruct the wheels. I bet it will be a pile, but I may be able to have some rough calculations by the end of the week.
"If they've done something other than introduce new wheels—for example, if they're now using a bigger keyboard and larger wheels to accommodate numbers as well as letters, all bets are off. In that case, I don't know what to suggest."
Jerzy picked up his line of thought. “Another possibility: The Germans may be using double encryption. That is, once a message goes through the Enigma scrambler, they may send it through a second encryption—for example, with a codebook, or by somehow modifying the Enigma
machine."
"In other words," responded Henryk, "we're not sure if we just want to steal a new machine, or whether we want our burglars to pick up codebooks while they're at it…. Any other thoughts?"
There was no response. “Let's come back to this later,” said Henryk. “It's time for Jerzy's problem.”
Jerzy puffed on his cigar, laying a pall of smoke over one end of the conference table. "When I got back from vacation, I dropped by the office late Saturday evening and found something peculiar. The staff were all confused. The two machines were no longer giving the same results. I called Henryk about it yesterday. "
There was thunderstruck silence.
"Are they sure?" asked Marian.
"Yes, they're sure, and, what's more, they're right. I checked. When the wheels are all set to AAA, one machine gives T when you press the A key, as always. The other gives R."
"How long this has been going on?" Marian asked. He seemed indignant. But at the misbehaving machine, or at the delay in letting him know?
"Just since Saturday.... Late last week, one of the machines was balking. The wheels weren't clicking cleanly from one letter to another, and sometimes no letter at all would show up when they pressed a key. They thought maybe a tooth on one of the wheels was broken. Saturday morning, they removed the wheels. There was nothing broken, or even severely worn, as far as they could tell. But the pins were dirty, perhaps breaking the electrical connection. They cleaned the wheels and reinstalled them. They get a result now, but it's wrong. That is, it disagrees with the first machine."
"Then we'd better call in technical services, to go over the machine to see what's wrong.” Henryk was usually calm and businesslike, but now he became forceful. “Just be certain they don't touch the first machine. If it misbehaves, too, we won't know what we're doing.”
That week, there were two major developments. The first was Marian's quick calculation. Based on his earlier work, it would take at least two months to reconstruct wheels from intercepted messages, perhaps longer. It would depend on the volume of intercepted traffic.
THE LAST GOOD WAR: A Novel Page 4
