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

8.4. MULTIPLE ENCIPHERINGS 145
Being confident of our keyword length, we now have five simple Caesar ciphers
to break and soon the message is decrypted. 8
To further emphasize the power of Friedman’s Index, we provide the values
of Φ that are produced assuming various keylengths.
Keylength Φ 1 Φ 2 Φ 3 Φ 4 Φ 5 Φ 6 Φ 7 Average
One .045 .045
Two .046 .042 .044
Three .047 .043 .045 .045
Four .048 .044 .052 .036 .045
Five .077 .059 .062 .058 .059 .063
Six .048 .045 .046 .041 .038 .043 .043
Seven .044 .052 .044 .043 .048 .048 .040 .046
The values in the Keylength Five row are clearly the largest. In particular, the
average of .063 stands out. Five must indeed be the keylength. Especially when
coupled with a computer program, Friedman’s Test provides for the almost
routine determination of keylength.
⋄
As a method for computing the keylength for a ciphertext of only a couple
hundred letters the Friedman Test is too highly influenced by quirks of the individual
ciphertext and keyword. However, as the ciphertext grows, the Friedman
Test hones in on the keylength with amazing accuracy.
8.4 Multiple Encipherings
Kasiski’s and Friedman’s tests are a very powerful one-two combination to use on
polyalphbetic ciphers, especially when used on a computer, enabling the almost
automatic detection of a polyalphabetic cipher’s keylength. Is there anything
about the polyalphabetic ciphers that might be saved
Ever since Section 7.6 we have been working under the (often implicit) assumption
that determining the keylength of a polyalphabetic ciphertext was
hard, but once we know the keylength breaking the cipher was easy. This is
because the polyalphabetic ciphers are really just several Caesar ciphers twisted
together – once we could pull the strands apart we were back to Chapter 1
material.
Since it appears relatively easy to pull the strands apart, is there a way to
make the strands shorter That is, to make the number of letters per Caesar
alphabet so small that decryption of the individual Kasiski depths is difficult
For example, if our message has 1000 letters in it, but we could use a 100 letter
keyword, there would be only 10 letters per alphabet! Even Linquist’s method
8 Keyword is CODES. “Cryptography and cryptanalysis are sometimes called twin or reciprocal
sciences, and in function they indeed mirror one another. What one does the other
undoes. Their natures, however, differ fundamentally. Cryptography is theoretical and abstract.
Cryptanalysis is empirical and concrete.” David Kahn