A History of Cryptography - Introduction to Cryptography with Java Applets - page 11

TABLE 1.8

Key Length = 5

Category 1 Category 2 Category 3 Category 4 Category 5

XIPGL ZIASN QSWGO TTRPX YNTOF

Suppose we have the ciphertext message

XZQTY IISTN PAWRT GSGPO LNOXF.

If the analyst assumes (correctly) that the keyword is of length 5, she would separate the
ciphertext into 5 categories, as described in Table 1.8.
She then does a separate frequency analysis for each category; in this way she can derive
the shift values for all letters in categories 1, 2, 3, 4, and 5. (Of course, this example does
not provide nearly enough ciphertext to do this, but the method works as described.) How
does one determine the key length? Random guessing may work, but perhaps only after a
lot of work. The method described here is often useful.

1.8 THE KAISISKI METHOD OF DETERMINING KEY LENGTH

The Kaisiski method is a way of determining key length. This method takes advantage of
the fact that languages contain not only frequent individual characters, but also frequently
occurring letter pairs and letter triples. We can use this to spot recurring triples in the cipher-
text. This will happen when a common triple falls on, and is enciphered by, the same por-
tion of the keyword. By noting the distance between these recurring blocks of text in the
ciphertext, we can make a good guess for the key length.

E XAMPLE . Suppose the triple FSI appears in the ciphertext 12 times, and the distance between
the first character (F) of each is as shown in Table 1.9.
Note that all but 2 of the distances in the table are multiples of 7. (The sixth appearance
of FSI came about probably by coincidence, and probably does not represent the same plain-
text triple). A good guess for the key length being used here is 7.

E XAMPLE . Consider the following ciphertext, which was formed using a Vigenere cipher on
uppercase English letters:

LJVBQ STNEZ LQMED LJVMA MPKAU FAVAT LJVDA YYVNF JQLNP LJVHK
VTRNF LJVCM LKETA LJVHU YJVSF KRFTT WEFUX VHZNP

If we use the Kaisiski method, we see that the triple LJV keeps reappearing. The distances
between each occurrence of LJV are shown in Table 1.10.
This tells us that it is very likely that the key length is 5. We now separate the ciphertext
into 5 categories, and do a frequency analysis on each category, as shown in Table 1.11.
In each category, the most common letter probably corresponds with the plaintext letter
E, T, I, N, or R. It would be easier to determine the shift values if we had more text to work