The Radio Log

On Saturday morning the notebook lay on the kitchen table, between the coffee pot and Gisela’s glasses. It was a thin school exercise book with a grey cardboard cover, gone soft at the corners like old bread. On the front, in pencil, was a single word: “Wilhelm”. Nothing underneath.

“Great-grandad?” asked Tobi.

“Your great-grandad,” said Gisela. “Papa was from Herne. His grandparents came from Masuria, for the pits. Like half of Wanne-Eickel.”

Tobi opened the notebook carefully. The pages were densely written, in pencil, in rows and columns. Always two digits, then a small gap, then two more digits. Page after page. Now and then there were dates in the margin. “3.II.47”. “Easter 48”. “24.XII.48”.

“Looks like a lottery ticket,” said Uwe. “A very long one.”

“It’s a radio log,” said Gisela. “That’s what Papa called it. He was a radio operator in the war, you know. But he wrote this afterwards. In the camp.”

“How do you know that?” asked Sabine.

“Mama told me, when I was twelve. She said: ‘That’s from the camp, you keep your hands off it.’ And then she put it in the box. And Papa never said anything about it. Papa never said anything about any of it.”

For a moment the kitchen was silent. Even Rudi, who usually made noises under the table at every meal, lay still.

“KevIn,” said Gisela. “Can you read it?”

“I can’t see it,” said KevIn. “I don’t have eyes. But if someone reads the numbers out to me, I can count along. And if Tobi wants, I can show him how to crack something like this. But he’d better do the cracking himself. It’s your notebook.”

Tobi looked at the notebook, then at his grandma. “I want to,” he said.

A Secret Code for Beginners

“Let’s start right at the beginning,” said KevIn. “More than two thousand years ago. Julius Caesar.”

“The Asterix Caesar?” asked Uwe.

“The real one. He encrypted confidential letters to his trusted friends by shifting every letter three places along the alphabet¹. A becomes D, B becomes E, C becomes F. And at the end you start again from the front: X becomes A, Y becomes B, Z becomes C.”

“Give us an example,” said Tobi.

“Happily. RUDI.”

Under the table, Rudi raised his head.

“R plus three is U. U plus three is X. D plus three is G. I plus three is L. RUDI becomes UXGL.”

“Uxgl,” said Gisela. “Sounds like a cough mixture.”

“And CABBAGEROLL?” asked Tobi, who was already taking notes.

“Try it yourself.”

Tobi counted on his fingers, lost count twice and finally wrote “FDEEDJHUROO” in the margin of the newspaper.

“Correct,” said KevIn. “That’s the Caesar shift. The key is the number three. If you know the key, you simply shift back.”

“And if you don’t?”

“Then you try them all. There are only twenty-five sensible shifts. You’d get through them in a quarter of an hour. Most of Caesar’s enemies couldn’t read, which is why it worked anyway.”

“So the code’s actually rubbish,” said Uwe.

“It was good enough for people who couldn’t be bothered to count twenty-five times,” said KevIn. “Which, to be honest, is a surprisingly large share of humanity.”

Uwe thought about this and didn’t feel entirely innocent.

Nazi Gold

“Hang on a minute,” said Uwe then, sitting up straight. “What if it’s something secret? The Wehrmacht. They had that machine, didn’t they? The Enigma. Maybe it says where something’s hidden.”

“What’s supposed to be hidden?” asked Sabine.

“How should I know? Gold.”

“Uwe, a prisoner of war wrote this in a school exercise book. In pencil.”

“Exactly! So nobody would notice!”

KevIn cleared his throat in his own way, which was really a short burst of static. “Uwe, may I raise an objection? I think that’s unlikely. The Enigma was a machine with rotors, a plugboard and a keyboard. Radio operators used it to encrypt messages before sending them as Morse code. What came out were groups of letters, not numbers. And nobody could rebuild an Enigma in their head. Certainly not in a prison camp.”

“But Papa was a radio operator,” said Gisela.

“Then he probably sent a great many encrypted groups without knowing what was in them. That was often the way. The operator keyed in whatever the cipher officer handed him. He was the hand, not the head.”

Gisela nodded slowly. “That fits. He said once, when I was little, that he’d talked more in the war than ever afterwards. And not understood a word of it.”

She ran her finger over the rows of numbers.

“Tell me about the machine,” she said.

Rotors and Bombes

“The Enigma,” said KevIn, “looked like a typewriter in a wooden box. When you pressed a key, a different letter lit up on a panel of lamps. If you pressed the same key again, yet another letter lit up, because the rotors turned on after every letter. An E became an X one time, a K the next, then a Q.”

“Like a Caesar that uses a different number every time,” said Tobi.

“Very good. That was exactly the idea. As early as the sixteenth century there was a cipher that worked in a similar way, with a keyword. It’s named after a Frenchman, Blaise de Vigenère, even though an Italian called Bellaso described it first.”

“Typical French,” said Uwe.

“They say that in Italy too. With Vigenère you take a word, let’s say GURKE, which is German for gherkin. G is the seventh letter, so you shift the first letter of the message by six, the second by twenty for the U, the third by seventeen for the R, and so on. After the E you start again at the G. Every letter gets its own little Caesar.”

“And nobody could crack that?”

“For almost three hundred years it was considered uncrackable. People called it ‘le chiffre indéchiffrable’, the indecipherable cipher. Then in the nineteenth century a Prussian officer called Kasiski, and before him an Englishman called Babbage, worked out how it could be done after all. The trick is that the keyword repeats. And everything that repeats leaves traces.”

“And the Enigma?”

“The Enigma only repeated itself after a very, very large number of letters, and it could be set differently every day. The number of possibilities had more than twenty digits. The German leadership considered it secure. But Polish mathematicians, above all Marian Rejewski², had already found ways to read it in the thirties. They passed their knowledge on to the British and French shortly before the war. And in England, in a country house called Bletchley Park, thousands of people then worked on it, most of them women³.”

“Women?” asked Gisela.

“Many thousands. They operated the machines, sorted messages, did the calculations. And among the mathematicians was one you already know.”

“Turing,” said Tobi. “The one with the test.”

“Alan Turing. Together with others he built a machine that was called the Bombe⁴. It didn’t guess Enigma settings, it ruled them out. It went through millions of possibilities and threw away everything that couldn’t fit. Whatever was left, people checked by hand.”

“Like me with Sabine’s presents,” said Uwe. “I don’t know what she wants, but I know exactly what she doesn’t want.”

“That’s not true,” said Sabine.

“See? Ruled out.”

KevIn let the blue light pulse twice, which for him was roughly a shake of the head. “Bletchley Park read a large share of the German radio traffic. Historians argue about how much it shortened the war. Some estimate two years; nobody knows for sure. But every message that was read there had first been sent by a radio operator. Somewhere in a tent or a bunker. By someone who didn’t know what he was keying in.”

Gisela looked at the notebook. “So Papa might have sent messages that were read in England.”

“Maybe. We’ll never find out.”

“And now we’re reading his,” she said. “Honestly, everybody reads that man’s post.”

Bingo

“All right,” said KevIn. “These aren’t letters, they’re numbers. Two digits, from 01 to 26, yes?”

Tobi leafed through. “I haven’t seen anything over 26 so far.”

“That’s a very good sign. Twenty-six is the number of letters in the alphabet. Each number probably stands for a letter. Try the simplest thing first: A equals 1, B equals 2.”

Tobi took the first line. “16, 08, 12, 17. That would be P, H, L, Q.”

“PHLQ,” said Uwe. “Is that Polish?”

“No,” said Gisela. “I still know a bit of Polish from my grandma. That isn’t even Polish.”

“Then it’s been shifted,” said KevIn. “Like with Caesar. And this is where the most important trick in the whole story comes in. An Arab scholar called al-Kindi described it more than a thousand years ago. You count.”

“Count what?”

“How often each number appears. In every language, some letters are much more common than others. In German, by far the most common is E. Roughly one letter in six in a German text is an E. After that come N, I, S, R. If Wilhelm wrote in German, then the most common number in the notebook is very probably an E.”

“And we’re supposed to count all of that?” asked Tobi. “It’s thirty pages!”

“One page is enough. Gisela, will you read it out? I’ll keep count.”

Gisela put on her glasses, held the notebook at arm’s length, as she did with everything smaller than a newspaper headline, and began.

“Sixteen. Oh-eight. Twelve. Seventeen. Fifteen. Twelve. Oh-eight. Oh-five.”

It sounded exactly like bingo in the parish hall. Half a page in, when Gisela called out “Twenty-two”, Uwe automatically shouted “Bingo!” and was shushed by three people at once.

Gisela read out a whole page. It took eleven minutes. Rudi fell asleep. Horst drove once through the kitchen, stopped next to Gisela’s chair as if he wanted to listen too, and drove off again.

“Right,” said KevIn when she had finished. “By a long way, the most common number is eight. Oh-eight. It comes up forty-one times. After that seventeen, then twelve.”

“So eight equals E,” said Tobi.

“That’s my guess. E is the fifth letter. Eight minus five is …”

“Three,” said Tobi and Uwe at the same time. Uwe looked as proud as if he’d scored a goal.

“Three. Like Caesar. Wilhelm shifted every letter by three and then wrote it down as a number. If that’s right, then seventeen minus three is fourteen, and that’s N. Twelve minus three is nine, that’s I. The three most common numbers would be E, N and I. That would be very German.”

Tobi was already writing. His hand shook a little.

“Sixteen minus three, thirteen. M. Eight, E. Twelve, I. Seventeen, N.” He looked up. “MEIN. That’s ‘my’.”

Nobody said anything.

“Go on,” said Gisela quietly.

“Fifteen is L. Twelve, I. Eight, E. Five, B. Eight, E. Twenty-two, S.”

“Mein liebes,” said Sabine. “My dear.”

“Sixteen, M. Four, A. Eight, E. Seven, D. Six, C. Eleven, H. Eight, E. Seventeen, N.”

Tobi put down the pencil.

“Mein liebes Maedchen,” he read out. “My dear girl. With an a-e. He hasn’t got umlauts.”

Gisela took off her glasses and laid them next to the notebook. For a long time she looked out of the window into the garden, where the leaves lay on the lawn that Uwe had been meaning to rake for two weeks.

“That’s what he called Mama,” she said. “Mein Mädchen. My girl. She was over thirty by then.”

What the Notebook Said

They read all afternoon. Tobi did the sums, Gisela read out the numbers, Sabine wrote the letters in capitals on a pad, and Uwe made coffee, so often that at some point KevIn gently pointed out his caffeine intake and was ignored.

They were letters. Letters that had never been sent. Some only a few lines long, some more than three pages. Not one of them was about the war. Not a word about radio sets, fronts or orders.

Wilhelm wrote about the food in the camp, and that at night he dreamed of potato pancakes. He wrote about the winter, which was so cold that the pencil fell from his fingers. He wrote about a comrade called Ernst who knew poems by heart, and he had copied some of them down. He wrote that he didn’t know whether his letters were getting through, the real ones, the official ones, on the cards on which you were only allowed to write twenty-five words. That was why he was writing everything else down here. In a code, “so the guards can’t read along and laugh”.

And again and again he wrote about a little girl he had never seen. Only in a photo his wife had sent him.

“Whether the little one can walk yet,” Tobi read. “Whether she has your eyes or mine. I hope yours.”

Gisela said nothing. Sabine laid a hand on her arm.

Around five they came to the entry for 24 December 1948. Tobi read the numbers himself, slowly, and KevIn quietly did the sums along with him.

“26, 08, 17, 17,” Tobi read. “Wenn.”

“07, 04, 22. Das.”

“25, 18, 21, 05, 08, 12. Vorbei.”

“12, 22, 23. Ist.”

“Wenn das vorbei ist,” said KevIn. “When this is over.”

Tobi read on. It took him a while. Then he wrote the whole sentence on the pad and pushed it across to Gisela.

“WENN DAS VORBEI IST GEHEN WIR AN DEN RHEIN.” When this is over, we’ll go to the Rhine.

Gisela put her glasses back on to read the sentence, even though Tobi had already read it out. She read it twice.

“They never went to the Rhine,” she said then. “Not once. He came back in the autumn of ’49, when I was five. A strange man. Thin as a broomstick. I hid behind Mama. And then he started at the pit and left the house every morning at five and listened to the radio in the evenings. Radio, always radio, very quietly, with headphones. And then Herbert came along, and life was just like that. Nobody talked about the Rhine.”

She wiped her eyes with the back of her hand, crossly, as if she’d only got dust in them.

“I thought he didn’t like us,” she said. “For a long time I thought that.”

Uwe stood up, fetched the kitchen roll and set it down in front of his mother without a word. Then he sat down again and looked at his hands. It was, KevIn thought, the cleverest thing Uwe had done in a long time.

The Key

Later, while Sabine was making sandwiches because nobody had thought about dinner, Tobi was still sitting over the notebook. On the last page with writing on it there was only one short line. No date.

“26, 12, 21,” he read. “22, 12, 17, 07. 07, 21, 08, 12.”

He did the sums. Then he did them again, because he didn’t trust the result.

“Wir sind drei,” he said. “We are three.”

“What?” asked Gisela.

“That’s what it says: we are three. That’s the last line.”

“Him, Mama and me,” said Gisela. “There was no Herbert yet.”

“And three is the key,” said Tobi slowly. “He shifted by three. Because there were three of them.”

KevIn was silent for a moment. Somewhere between Dublin and Frankfurt, a fan spun a little faster.

“That’s very likely,” he said. “I can’t prove it. But I would believe it.”

The Key Problem

That evening, when Gisela was already in bed, Tobi was still sitting in the living room with KevIn.

“KevIn. How do people do it today? When they want to keep something secret. You won’t get far with Caesar.”

“Today we use methods like AES⁵. It’s a standard the USA laid down in 2001, after an open competition. Two Belgians won it⁶. AES scrambles the data over many rounds, substituting, swapping, mixing, all depending on a key. A 256-bit key has so many possibilities that all the computers in the world together couldn’t try them all before the end of the universe. Your phone uses AES. So does your grandma’s online banking.”

“And then everything’s safe?”

“The maths is safe, as far as we know. But AES has the same problem as Wilhelm’s notebook. It’s symmetric. The same key locks and unlocks. Anyone who wants to read a message needs the key. And how do they get it?”

Tobi thought. “You tell them.”

“By what route? If you had a safe route, you could just send the message that way. It’s called the key distribution problem. For centuries people carried keys across borders in suitcases, hid them in books, learned them by heart. For the Enigma there were printed key sheets for every month, and if one of them fell into enemy hands, a whole month was lost.”

“And Wilhelm?”

“Wilhelm had the key in his head. Three. And his wife never got it. The notebook lay in a box for almost eighty years, and the one person it was meant for couldn’t read it.”

Tobi was quiet for a long time. “Maybe he wanted it that way.”

“Maybe. Maybe he only wanted to write the letters, not send them. Some people write in order to survive. Not so that anyone reads it.”

“And why didn’t he just talk afterwards?”

“That,” said KevIn, “I can’t calculate. I’ve read a great many texts by men who came back from the war. Many of them write that they had no words. That they thought nobody who hadn’t been there would understand. And that they didn’t want to burden their children with it. That’s what wars do to families. They don’t stop when the guns fall silent. They sit at the kitchen table with you for decades afterwards.”

Tobi closed the notebook and laid his hand on it.

“But you lot have a solution to the key problem, haven’t you? Otherwise the internet wouldn’t work.”

“There is one. It’s so elegant that I consider it one of the most beautiful ideas of the twentieth century. It has to do with letterboxes. And with paint.”

“Tell me.”

“Tomorrow. Your grandma finally starts her physiotherapy on Monday, and I have a feeling it’s going to be a long week.”

The Call

Gisela didn’t sleep that night. At half past eleven KevIn heard her pick up the telephone in her room, the old one with the cord, and dial a number she knew by heart.

“Herbert? Yes, I know what time it is. No, nobody’s dead. Listen.”

A pause.

“Papa copied out poems. In the camp. And letters to Mama. Whole notebooks full. In secret writing. Tobi’s decoded them.”

A long pause. Herbert always spoke on the phone as loudly as if he had to manage without the line, and KevIn understood every word.

“Papa? Our Papa? But he never said anything.”

“Exactly,” said Gisela. “Exactly, Herbert.”

At the other end it was silent for a long time. Then Herbert said something KevIn couldn’t make out, because the line crackled. But Gisela gave a short laugh, the way you laugh when you’re crying at the same time.

“Yes,” she said. “Come on Sunday. I’ll make cabbage rolls. And we’ll go to the Rhine. Some day. The two of us.”

She hung up. Then she said into the dark: “Good night, KevIn.”

“Good night, Gisela.”

KevIn’s weights didn’t change that evening. They couldn’t. But he created a new entry in his memory function. It was very short. It read: “Rhine.”