Simple Ciphers - Modern Cryptanalysis: Techniques for Advanced Code Breaking - page 12

Another popular mechanism is to use monophones — where one plaintext letter can be represented by more
than one ciphertext letter. They can be chosen randomly or with some certain pattern. This is slightly more dif-
ficult to detect, since it will have the property of flattening the distribution a bit more. Since using monophones
quickly depletes the normal alphabet, extra symbols can often be introduced.
The opposite of a monophone is a polyphone — where multiple plaintext characters are encoded to the same
ciphertext character. This requires the receiver to know this is happening and be a bit clever about decrypting
the message, since there may be multiple interpretations of the characters.
There are no good ways of automatically detecting and removing these security measures — a lot of them
will involve a human using the preceding and following tools, along with practice, and simply trying out differ-
ent ideas.
1.5.2 Breaking Polyalphabetic Ciphers
The key to breaking a polyalphabetic cipher of a keyed type (such as Vigenère) is to look for certain patterns
in the ciphertext, which might let us guess at the key length. Once we have a good guess for the key length,
it is possible to break the polyalphabetic ciphertext into a smaller set of monoalphabetic ciphertexts (as many
ciphertexts as the number of characters in the key), each a subset of the original ciphertext. Then, the above
methods, such as frequency analysis, can be used to derive the key for each alphabet.
The question is, how do we guess at the key length? There are two primary methods: The first is a tool we
described above — the index of coincidence.
As stated above, the index of coincidence is the probability of having repeated characters and is a property of
the underlying language. After a text has been run through a monoalphabetic cipher, this number is unchanged.
Polyalphabetic ciphers break this pattern by never encrypting repeated plaintext characters to be the same char-
acterintheciphertext.Buttheindexofcoincidencecanstillbeusedhere—itturnsoutthatalthoughtheciphers
eliminate the appearance of repeated characters in the plaintext being translated directly into the ciphertext,
there will still be double characters occurring at certain points. Ideally (at least from the point of view of the
person whose messages are being cracked), the index of coincidence will be no better than random (0.03846).
But, luckily (from the viewpoint of the cryptanalyst), the underlying language's non-randomness comes to the
rescue, which will force it into having a non-perfect distribution of the repeated characters.
Just as longer keys for polyalphabetic ciphers tend to flatten out the frequency distributions, they also flatten
out the non-random measurements, such as the index of coincidence. Hence, a smaller key will result in a high-
er index of coincidence, while a longer key gives us an index of coincidence closer to 0.03846. Table 1-4 shows
us the relationship between the number of characters in the key and the index of coincidence.
Table 1-4 Relationship between Key Length of a Polyalphabetic Cipher and the Resulting Index of Coincidence of the Ciphertext in The
Complete Works of William Shakespeare [3]