The Book of Air and Shadows

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