Cryptology - Unofficial St. Mary's College of California Web Site

122 CHAPTER 7.
VIGENÈRE CIPHERS
Kasiski’s Test:
1. Look for repetitions in the ciphertext of two, three, or more letters.
Determine the distances (= position of first letter in second appearance
minus position of first letter in first appearance) between the
beginnings of these repetitions. This is doing a Kasiski Examination.
2. Find the largest number that divides most of your distances in step
1 by first factoring those distances. This number should give a good
idea of the length of the keyword. We call this length the keylength.
Be aware that longer repetitions are more significant than shorter
ones, so repeated triples are more meaningful than repeated pairs,
and 4 letter strings are even more significant. Also, repetitions can
arise that do not come from a repeat in the text. So the keylength
will not necessarily divide all of the repetition distances.
3. Write the ciphertext in columns, with the number of letters per column
being equal to the keylength. This will result in a keylength
number of rows, with each row being simply a Caesar cipher. This is
building up a depth.
4. Use frequency analysis on each row to determine the keyletter for
each, and put the keyletters together to find the keyword. Then
decipher the message.
Example: Determine the keylength of the following ciphertext using Kasiski’s
method. To ease the counting, there are 50 letters to a line. (This
example is stolen from [Kahn], page 209)
ANYVG YSTYN RPLWH RDTKX RNYPV QTGHP HZKFE YUMUS AYWVK ZYEZM
EZUDL JKTUL JLKQB JUQVU ECKBN RCTHP KESXM AZOEN SXGOL PGNLE
EBMMT GCSSV MRSEZ MXHLP KJEJH TUPZU EDWKN NNRWA GEEXS LKZUD
LJKFI XHTKP IAZMX FACWC TQIDU WBRRL TTKVN AJWVB REAWT NSEZM
OECSS VMRSL JMLEE BMMTG AYVIY GHPEM YFARW AOAEL UPIUA YYMGE
EMJQK SFCGU GYBPJ BPZYP JASNN FSTUS STYVG YS
We start by listing the repetitions, their starting positions, the distance between
the starting positions, and the factorization of that distance in Figure 7.3.
What factors appear in (almost) every distance All the distances are divisible
by 2, most are divisible by 2 × 3, and many by 2 × 2. The key length is
probably either 6 or 4. (The factors 5, 7, 19, and 137 appear only once each,
and 11 only twice, and can be ignored.) If the keylength is 4 then the long
repetition LEEBMMTG would have to be ignored, while if the keylength is 6 we
only need ignore the short repeat STY. The keylength is most likely 6. 14 ⋄
14 key = SIGNAL, “If signals are to be displayed in the presence of an enemy, they must be