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Chapter 8
Polyalphabetic Ciphers
The key cipher is the noblest and the greatest in
the world, the most secure and faithful that never
was there man who could find it out.
Matteo Argenti
Following our work in Chapter 7 we have a way to decrypt Vigenère ciphers:
the Kasiski Examination followed by frequency analysis. The frequency analysis
is relatively easy once we know the length of the keyword. However the Kasiski
Examination, although it works fine, is quite time consuming since we must go
through the message letter by letter looking for repetitions. It would be fifty
years before an improvement was found.
8.1 Coincidences
On what does the Kasiski test depend That repetition of parts of the ciphertext
are meaningful. To recall our original example:
plaintext
key
ciphertext
t o b e o r n o t t o b e t h a t i s t h e q u e s t i o n
R U N R U N R U N R U N R U N R U N R U N R U N R U N R U N
K I O V I E E I G K I O V N U R N V J N U V K H V M G Z I A
Kasiski’s idea is that the repeated KIOV and NU hint at the length of the keyword.
To have such repetitions we (the crytanalysts) need some luck: the same
plaintext part must lie under the same key part. Before Kasiski people presumably
thought of such repetitions as mere coincidences – unrelated events that
are unlikely to occur together but just happen to do so. Kasiski’s test showed
that sometimes these coincidences are, in fact, meaningful.
Can we look for these meaningful repetitions, these meaningful coincidences,
in another way A (relatively) quick way to see when individual letters are
repeated is to write the ciphertext one two slips of paper, and hold one under
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