Michael Gruber - The Book of Air and Shadows

“No kidding!”

“Not at all kidding. Robotnicy in 1971. I was one of young police in background, crushers of workers’ movement. A quite insane time, which I think is very much similar to the time of your man Bracegirdle. I should say also I have made progress of a sort on your cipher.”

“You cracked it already?”

“Alas, no. But I have identified its type. Extremely interesting for a classical cipher, I believe, even unique. Shall I show? Or wait for after this excellent supper of your mother?”

Mary Peg said, “Oh, please show us. I have to make a salad and we can eat the stew anytime.”

With his usual diffident little bow, Klim left the room. Crosetti immediately caught his mother’s eye and rolled his own.

“What?” she challenged.

“Nothing. It’s just this is all pretty fast. We’re living here all by ourselves for years and all of a sudden we’re in a Polish movie.”

Mary Peg made a dismissive gesture. “Oh, come on! He’s a dear man, and he’s really suffered-his wife died, he was in jail-Fanny’s been after me to meet him for years. You like him, right?”

“Well, yeah. Obviously, not quite as much as you do. So…are you two…?” He rubbed his palms together, as if smoothing cream between them. She snatched up a wooden spoon and cracked him smartly on the crown of his skull. “You be careful, buster. I can still wash your mouth out with soap.” And they both laughed out loud.

Klim came in on their laughter holding a thick sheaf of printer paper densely packed with lines of text and a legal pad covered with neat European pencilings. Klim sat down next to Crosetti and smiled politely. “We are having fun? Good. This also may be fun. So. You can see from my red eyes, I have been up most of this night with colleagues across the world and many have commented on this most fascinating cryptogram. So first of course we work Friedman’s superimposition. This is elementary, yes? We must distinguish the many different alphabets used in polyalphabetic cipher so we may do Kerckhoff ’s solution by frequency analysis; and we do this by superimposition of one string of ciphertext upon another to find coincidences; and if we have done this correctly, number of coincident letters will approach value kappa sub p or seven percent approximately. This is clear, yes?”

“No. Maybe you could just skip to the bottom line.”

Klim looked puzzled and began to riffle through the pages. “The bottom line? But the bottom line is enciphered like these others…”

“No, it’s a figure of speech. I mean, please summarize your findings without all the technical jargon.”

“Ah, yes. The bottom line. This bottom line is that we cannot do superimposition upon this cipher because the key does not repeat at all within the number of ciphertext characters we have available, which is 42, 466. Also, we find that the key has high entropy, much higher than expected for a running key from a book, so we cannot do simple analysis using common English words. So, either your man is not using an ordinary tabula recta, which I think highly unlikely, or he has discovered onetime system three hundred years earlier than Mauborgne did, in approximately 1918. Which also I cannot believe. There is no record of such a discovery. In fact, even the Vigenère cipher was not widely used. Most European intelligence services were satisfied with simple nomenclators until telegraphy came, and even afterward. There is no need for such very high security. It is a great flounder.”

“You mean a fluke,” said Crosetti. “So if it isn’t a onetime system, what is it?”

“Ah. I have a theory. I think your man started with a simple running key, from a book, as originally we thought. But I also think he was a very clever person and saw quickly how a running key from a book might be compromised through substitution. Now he might have changed his tabula into some mixed alphabet, in order to disguise common English digraphs like tt, gg, in, th, and so forth, but we do not think he did that. No, I think he merely combined two methods well known in those times. I think he combined a running key from a book with a grille. It is a way of easily generating a pseudorandom key of arbitrary length.”

“Which means what? I mean as far as deciphering goes.”

“Well, unfortunately it means we are stopped. As you know, onetime systems are unbreakable. Now, it is true that this is not a real onetime system. If we had ten thousand messages, I suppose we could make some progress, or even a thousand. But these few cryptograms are perfectly secure.”

“Even with computers, brute force…?”

“Yes, even with. I could show you mathematically-”

“No, I got a C in algebra.”

“Really? But you are intelligent person and it is so easy! Still, you will understand if I say it is like an equation with two unknowns, the unknowns being the key text and the ciphertext. Example: what is solution to x + y = 10?”

“Um…x is one, y is nine?”

“Yes. But also two and eight or three and seven, or one hundred and minus ninety, and so forth, an infinite number of possible solutions for such equations, and it is the same with onetime systems. To solve a cryptogram you must have a unique solution for each particular letter, no matter how it is disguised by multiple alphabets and keys. Otherwise, how to distinguish between ‘flee at once’ and ‘come to Paris’? Both can be derived from exact same ciphertext of a onetime system. Even if you capture some piece of plaintext you are still no better off because it is impossible to work backward from plaintext through ciphertext to determine what is key, because this key changes continually and is never used again. No, this is indecipherable, unless, of course, you have both the book he used and the grille.”

“I thought we had the book. You said it was the Bible.”

“I said probably the Bible. I have talked to Fanny of this and she says most probably they would have used the Geneva Bible edition of 1560 or later. This is the most popular Bible of that era, the Breeches Bible, so called, very common and also portable, nine inches by seven. The grille would be pasteboard or thin metal, perhaps punched out in a simple pattern to disguise secret use. Your Bracegirdle places the grille on pages he agreed on previously with control and copies out the letters that appear under these holes. This is his key. He copies out enough letters to encipher message and on the other end his control does the same, but in reverse. For the next message he uses another page. As I say, if we had millions of characters of ciphertext so that he must repeat same position of grille on pages, then we can solve by usual methods, but not as it is now. I am sorry.”

He really looked sorry too, the sorriest Crosetti had ever seen anyone look, almost comical, like a sad clown. But at that moment, Mary Peg declared that supper was ready and plopped a huge tureen of steaming lamb stew down before them, and the expression on Klim’s face changed in an instant to utmost delight. Crosetti felt a little brighter himself. It always made him secure to be in a movie plot, and now, as he had mentioned to his mother, they were in a Polish movie: people bent almost to breaking under the weight of history and insolvable problems coming alive at the prospect of a warm meal.

Toward the close of which, Klim returned to the subject they had avoided during the pleasant meal. “You know, I am baffled about one more thing,” he mused. “Why a cipher at all?”

“What do you mean?” asked Crosetti.

“Well, this man, your Bracegirdle, says he was spying on Shakespeare for the English government. Well, I too was a spy for the government and wrote reports, as did thousands of my countrymen. There are tons upon tons of these in archives in Warsaw and not one of them is in cipher. It is only foreign spies who use cipher. A Spanish spying on English people would use a cipher. Or if your man was abroad and sending messages back, then he would do the same. But government spies do not use ciphers. Why should they? It is governments who open mail, yes?”