The Book of Air and Shadows

by Michael Gruber

  For the next six days he did nothing else but go to work, study cryptography, and work on the cipher. On Sunday he again went to church and found himself praying with unaccustomed fervor for a solution. Returning home he made for his room, ready to begin once more, when his mother stopped him.

  “Take a break, Allie, it’s Sunday.”

  “No, I thought of something else I want to try.”

  “Honey, you’re exhausted. Your mind is mush and you’re not going to do yourself any good spinning around like a hamster. Sit down, I’ll make a bunch of sandwiches, you’ll have a beer, you’ll tell me what you’ve been doing. This will help, believe me.”

  So he forced himself to sit and ate grilled-cheese sandwiches with bacon and drank a Bud, and found that his mother had been right, he did feel a little more human. When the meal was over, Mary Peg asked, “So what have you got so far? Anything?”

  “In a negative sense. Do you know much about ciphers?”

  “At the Sunday paper game-page level.”

  “Yeah, well that’s a start. Okay, the most common kind of secret writing in the early seventeenth century was what they called a nomenclator, which is a kind of enciphered code. You have a short vocabulary of coded words, box for army, pins for ships, whatever, and these words and the connecting words of the message would be enciphered, using a simple substitution, with maybe a few fancy complications. What we got here isn’t a nomenclator. In fact, I think it’s the cipher Bracegirdle talks about in his letter, the one he invented for Lord Dunbarton. It’s not a simple substitution either. I think it’s a true polyalphabetic cipher.”

  “Which means what?”

  “It’s a little complicated. Let me show you some stuff.” He left and came back with a messy handful of papers. “Okay, the simplest cipher substitutes one letter for another, usually by shifting the alphabet a certain number of spaces, so that A becomes D and C becomes G and so on. It’s called a Caesar shift because Julius Caesar supposedly invented it, but obviously you can crack it in a few minutes if you know the normal frequencies of the letters in the language it’s written in.”

  “ETAOIN SHRDLU.”

  “You got it. Well, obviously, spies knew this, so they developed ciphering methods to disguise the frequency of letters by using a different alphabet to pick every substitution in the ciphertext.”

  “You mean a literally different alphabet, like Greek?”

  “No, no, I mean like this.” He pulled a paper out of the sheaf and smoothed it on the table. “In the sixteenth century the architect Alberti invented a substitution cipher that used multiple alphabets arranged on brass disks, and a little later in France a mathematician named Blaise Vigenère supposedly invented what they call a polyalphabetic substitution cipher using twenty-six Caesar-shifted alphabets, and I figured it or something like it would be known to Bracegirdle if he was studying the cipher arts at that time. This here is what they call a tabula recta or a Vigenère tableau. It’s twenty-six alphabets, one on top of the other, starting with a regular A through Z alphabet and then each successive one starts one letter to the right, from B through Z plus A, then C through Z plus A and B and so on, and there are regular alphabets along the left side and the top to serve as indexes.”

  “So how do you use it to disguise frequencies?”

  “You use a key. You pick a particular word and run it across the top of the tableau, lining each letter of the key up with each column and repeating it until you reach the end of the alphabet. For example, let’s pick Mary Peg as a key. It’s seven letters with no repeats, so it’s a good pick.” He wrote it out several times in pencil and said, “Now we need a plaintext to encipher.”

  “Flee, all is discovered,” suggested Mary Peg.

  “Always timely. So we write the plaintext over the key, like so…

  F L E E A L L I S D I S C O V E R E D

  M A R Y P E G M A R Y P E G M A R Y P

  “And then to encipher, we take the first letter of the plaintext, which is F, and the first letter of the key, which is M, and then we go to the tableau, down from the F column to the row and we write the letter we find at the intersection, which just happens to be R. The next combination is L from flee and A from Mary, so L stays L, and the next is E and R, which gives V. And now see how this works: the next E is over the letter Y in our ‘Mary Peg’ key which gives C. The two Es in flee have different ciphertext equivalents, which is why frequency analysis fails. Let me knock this out real quick so you can see…”

  Crosetti rapidly filled in the ciphertext and produced

  F L E E A L L I S D I S C O V E R E D

  R L V C P P R U S U G H G U H E I C S

  “And notice how the double L in all is disguised too,” he said. “Now you have something that can’t be broken by simple frequency analysis, and for three hundred years no one could break a cipher like that without learning the key word. That’s mainly what they tortured spies for.”

  “How do you break it?”

  “By finding the length of the key word, and you do that by analyzing repeating patterns in the ciphertext. It’s called the Kasiski-Kerckhoff Method. In a long enough message or set of messages, FL is going to line up with MA again, and give you RL again, and there’ll be other two-and three-letter patterns, and then you count the distance between repeats and figure out any common numerical factors. In our example, with a seven-letter key you might get repeats at seven, fourteen, and twenty-one significantly more than would be the case by chance. Obviously, nowadays you use statistical tools and computers. Then when you know our key has seven letters, it’s a piece of cake, because what you have then is seven simple substitution alphabets derived from the Vigenère tableau, and you can break those by ordinary frequency analysis to decrypt the ciphertext or reconstruct the key word. There are downloadable decrypting programs that can do it in seconds on a PC.”

  “So why haven’t you cracked it?”

  He ran his hand through his hair and groaned. “If I knew that, I’d know how to crack it. This thing’s not a simple Vigenère.”

  “Maybe it is, but it has a really long key. From what you said, the longer the key, the harder it would be to factor out the repeating groups.”

  “Good point. The problem with long keys is that they’re easy to forget and hard to transmit if you want to change them. For instance, if these guys wanted to change the key every month to make absolutely sure that no spy had discovered it, they’d want something an agent could receive with a whisper in the dark or in a totally innocent message. What they do nowadays is that the agent gets what they call a onetime pad, which is a set of preprinted segments of an infinitely long, totally random key. The agent enciphers one message and then burns the sheet. It’s totally unbreakable even by advanced computers. But that kind of method wasn’t invented in 1610.”

  “So what else?”

  “It could be a grille, in which case we’re screwed.” Seeing her puzzled look, he added, “A Cartan Grille, a literal piece of stiff paper with holes punched in it that reveals the message when you place it over the page. That would mean it’s not a cipher at all. For example, assume the ciphertext I wrote is just random noise, but if you slide a grille over it you can get RUG or USE or RUSE…”

  “But surely, if they were using a grille, the ciphered message would look like a normal letter. ‘Dear Mom, having a great time in London, bought a new doublet, baited some bears, wish you were here, love, Dick.’ And the grille would reveal the plaintext: ‘flee, all is discovered.’ I mean the point would be to allow the concealed message to pass as innocent, no?”

  Crosetti tapped his head in the what-a-jerk gesture. “Of course. Obviously, I’m losing it. Anyway, I’m stumped-I have no idea where to go from here.”

  “I rest my case. Like I said, you need a break.”

  “You’re right.” He rubbed his face with both hands and then asked, “What day is this?”

  “October 14. Why?”

  “There’s a Caribbean film festiv
al at BAM, and I wanted to catch Of Men and Gods. Maybe if I lose myself in gay Haitian voodoo, I’ll come back to it fresh.”

  “That’s a good plan, dear,” said Mary Peg.

  Something about her tone and the expression on her face made him pause. He regarded her narrowly: “What?”

  “Nothing, hon. I thought that if you didn’t mind I’d take a look at it myself.”

  “Hey, knock yourself out!” said Crosetti, with just a trace of smugness. “It’s not a crossword puzzle.”

  He was gone for over four hours because after the movie played he ran into some film freak pals of his and went for coffee and they took the film apart technically and artistically, and he enjoyed the usual amusing and astringent conversation common to such groups, and made a couple of good points and got to talking with a small intense woman who made documentaries, and they exchanged numbers. Crosetti felt like a real person for the first time in what seemed to him a long while. It had been nearly two months since that thing with Rolly started and ended, leaving a peculiar emotional ash. Not love, he now thought. Chemistry, sure, but as his mother had pointed out, in order for chemistry to transmute into connection there had to be reciprocity and a modicum of commitment, which he had certainly not got from Rolly…just a nothingness and that stupid letter, oh, and P.S., bid a heartfelt bye-bye to Albert. It still griped him, not so much as a blow to his self-regard but as an insult to his aesthetics. It was wrong; he would never have written a plot point like that into a screenplay, and since he was a realist sort of auteur, he believed that such an event could not exist in the real world. Thus the subway thoughts of Crosetti.

  When he got home, he found Mary Peg in her living room, drinking vodka with a strange man. Crosetti stood in the doorway and stared at his mother, who coolly (rather excessive, suspicious, coolness, Crosetti thought) introduced the man as Radeslaw Klim. This person rose to a considerable height, perhaps six inches more than Crosetti’s, and shook hands with a stiff little bow. The man had an intelligent aquiline face, a foreign face, although Crosetti could not have pinned down why it was not an American one. Washed blue eyes looked out through round wire-rimmed glasses, under a great shock of stiff silver hair, which stuck up above his broad forehead like the crest on a centurion’s helmet. He was about the same age as Mary Peg, or a little older, and he was wearing a baggy rust-colored suit with a dark shirt under it, no tie, the suit a cheap one that hung badly on his long slender frame. Despite this, the man had a nearly military bearing, as if he had temporarily misplaced his beautifully tailored uniform.

  Crosetti sat in an armchair and his mother supplied him with a glass of iced vodka, a substance for which he found an unfamiliar but urgent need. After he’d drunk a slug he looked challengingly at Mary Peg, who said blandly, “Mr. Klim is Fanny’s friend. I asked him to come by and take a look at your cipher. Since you were stuck.”

  “Uh-huh,” said the son.

  “Yes,” said Klim. “I have looked, examined it somewhat. As you have guessed, it is a polyalphabetic substitution cipher and also is true that it is not a simple Vigenère. That is of course elementary.” He had a slight accent that reminded Crosetti of Fanny’s; his mien was gentle and scholarly enough to at least partially assuage Crosetti’s nascent resentment.

  “So what is it?” Crosetti asked sharply.

  “I believe it is a running key,” said Klim. “From a book of some kind. You understand how these work? The key is of very long extent compared to the plaintext, so the Kasiski-Kerckhoff Method is of no use.”

  “Like a book code?”

  “No, this is not the same thing. A book code is a code. The codetext is, let us say, 14, 7, 6, and that means you go to World Almanac or some such and look at page 14, line 7, word 6. Or you can use letters if you like, the fourth letter, the tenth letter. A running key uses a book, the same, but uses the book text as a continuous key. These are not so secure as people think, however.”

  “Why not? It’s similar to a onetime pad.”

  Klim shook his head. “Not so. Onetime pad has very high entropy, because the letters are randomly generated. That is, given one letter of your key you have no idea which of the other twenty-six will follow. Whereas, in a running key based on any English text, let us say, if you see Q, what is next letter for sure?”

  “U.”

  “Exactly. Low entropy, as I say. How we break these is we run probable plaintext alongside ciphertext until we see something intelligible.”

  “What do you mean by ‘probable plaintext’?”

  “Oh, words always appearing in English text. The, and, this, and so on and so forth. We run against ciphertext and suppose we find once that the gives us ing or shi when we work back through the tableau? We use such clues to discover more English words in key. Eventually we recognize actual source of running key, I mean, the book it comes from, in which case we have completely broken cipher. It is not very complex, but we would need a computer, or else large squads of intelligent ladies.” Here he smiled, showing small stained teeth, and his glasses glinted. Crosetti got the impression that Klim had at one time supervised such squads.

  “Would mine do?” asked Crosetti. “My PC, not my squads of ladies.”

  “Yes, if networked to others, which can be done. There are numbers of people in the world who like cracking ciphers for amusement and they will let one borrow computer cycles they are not using, late at night for example, and is always late at night somewheres. I can set this up if you like. Also, we are fortunate this is cipher from the year 1610.”

  “Why so?”

  “Because there are many less, many fewer, printed texts that could be used as running key source. In fact, taking what your mother has informed me of the character of these people, I would venture that the text is almost certainly the English Bible. So, shall we begin?”

  “Now?”

  “Yes. Is there objection?”

  “Well, it’s kind of late,” said Crosetti.

  “Does not matter. I sleep very little.”

  Mary Peg said, “I’ve offered Radeslaw Patty’s old room.”

  Crosetti finished his vodka and suppressed the usual shudder. He stood up and said, “Well, you seem to have arranged everything, Mom. I guess I’ll just go to bed.”

  In the morning, Crosetti woke not to the buzz of his alarm but to the brisk knock and then the vigorous shoulder shaking of his mother. He blinked at her. “What?”

  “You have to read this.” She rustled the New York Times at him, opened at the pages devoted to local crime, corruption, and celebrity.

  English Professor Found Murdered in Columbia Faculty Housing

  This headline brought him up to full wakefulness. He rubbed the blur from his eyes and read the article, then read it again. It was a short one, the police being their usual closemouthed selves, but the reporter had used the word torture, and that was enough to start Crosetti’s belly fluttering.

  “Call Patty,” he said.

  “I already did,” said Mary Peg, “but I got voice mail. She’ll call back. What do you think?”

  “It doesn’t look great. He disappears right after I sell him the manuscript, he’s probably in England for a couple of months, maybe with Carolyn, maybe not, and then he comes back here and someone tortures him to death. Maybe the play manuscript really exists and he found out where it was and someone found out he knew and tortured him to get him to give it up.”

  “Albert, that’s a movie. Things like that don’t happen to English professors in real life.”

  “Then why was he tortured and killed? Not for his ATM password.”

  “Maybe the mother of another silly boy he cheated took her revenge. From what we know about his character, he may have been mixed up in any number of sleazy deals.”

  “Mom, believe me, movie or not, that’s what went down. I need to get up.”

  This was the signal for his mother to leave, and she did. Crosetti in the shower found his thoughts floating back to Rolly and the plot of h
is movie and the possibility that she could actually be the villainess of the piece, Brigid O’Shaughnessy as played by Mary Astor in The Maltese Falcon. His mother was wrong. Not only was life like a movie, movies were why life was like it was. Movies taught people how to behave, how to be a man, how to be a woman, what was funny and what was horrid. The people who made them had no idea of this, they were just trying to make money, but it was so.

  And here they were in the Falcon, his next favorite after Chinatown, which was essentially a reimagining of the same movie, updated for the ’70s, and why did he like movies about bad girls? Bonnie and Clyde, naturally, and La Femme Nikita and dozens more. He wondered what part he was playing, the dead Miles Archer, or the dead sea captain in the backstory, or Sam Spade. You killed Miles and you’re going over for it. And, I hope they don’t hang you, precious, by that sweet neck. Yes, angel, I’m gonna send you over. He had nearly the whole script by heart and now he said those lines to the showerhead with the Bogart hissing lisp and wondered whether, if it ever came to it, he could send Carolyn Rolly over, if she’d really helped kill Bulstrode. Or maybe he would be her sap. The mere imagination of it made his heart race. He turned the temperature of the water down a notch and let it run onto his heated face.