The Book of Air and Shadows

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