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118 CHAPTER 7.
VIGENÈRE CIPHERS
unbreakable. So how finally was the Vigenère Cipher broken By turning the
power of the keyword against the cipher.
Let’s start by backing up. What enabled us to decrypt a Caesar cipher
We knew that every letter in the message was enciphered using the same key
letter. And we could detect this key letter from the frequency habits of normal
English. Why can’t we do this with a Vigenère cipher Because not all of the
letters are enciphered using the same key letter. In other words, a Caesar cipher
is monoalphabetic, a Vigenère cipher is polyalphabetic.
Now suppose we did know which letters were enciphered by the same letters
of the keyword. Then we could split up the ciphertext into groups in such a way
that all the letters in each group would be enciphered with the same keyletter.
Each group of letters would be like a (different) Caesar cipher. And we know
how to break Caesar ciphers. Since we could decrypt each of these groups of
letters, then we could decrypt all of the letters in the ciphertext, thus breaking
the message.
So (perhaps) we don’t actually need to know the keyword, but we do need to
determine which ciphertext letters have been enciphered with the same letter of
the keyword. How can we do this Imagine rewriting the ciphertext downward
into columns, with as many letters per column as there are letters in the keyword.
Of course, we’d need to know how many letters there are in the keyword,
but pretend for a moment we know that. Then the letters in the first row of our
re-written ciphertext would all have been enciphered using the first letter of the
keyword. And the letters in the second row of the re-written ciphertext would
all have been enciphered using the second letter of the keyword. Similarly for
the other rows. We would be left with several Caesar ciphers to break.
To make this a bit less abstract, let’s suppose the keyword contained 5
letters, and we number them k 1 k 2 k 3 k 4 k 5 , and similarly number the ciphertext
letters ct 1 ct 2 ct 3 · · · . Then the complex of rows and columns from the previous
paragraph takes the form
k 1 ct 1 ct 6 ct 11 ct 16 . . .
k 2 ct 2 ct 7 ct 12 ct 17 . . .
k 3 ct 3 ct 8 ct 13 ct 18 . . .
k 4 ct 4 ct 9 ct 14 ct 19 . . .
k 5 ct 5 ct 0 ct 15 ct 10 . . .
The letters ct 1 , ct 6 , ct 11 , ct 16 , . . . all have been enciphered by the key k 1 . So we
can treat ct 1 ct 6 ct 11 ct 16 . . . as a Caesar cipher with unknown key k 1 . Likewise,
ct 2 , ct 7 , ct 12 , ct 17 , . . . all have been enciphered by k 2 , so ct 2 ct 7 ct 12 ct 17 . . . can
be treated as a Caesar cipher.
So to decrypt a Vigenère-enciphered message, assuming we know the length
of the keyword, first rewrite the ciphertext in columns with as many letters per
column as letters in the keyword. Then the letters of each row will constitute a
Caesar cipher that can be broken with our techniques from Chapter 1.
To summarize, from what does the Vigenère cipher get its security Ob-