Simple Ciphers - Modern Cryptanalysis: Techniques for Advanced Code Breaking - page 14

We can encrypt this using the key romeo (the key in this case has length 5), to obtain the following cipher-
text:
These repetitions occur at the paired positions:
(0, 160), (34, 169), (61, 131), (99, 114), (140, 155), (174, 189)
This corresponds to differences of 160, 135, 70, 15, 15, and 15. We can factor these, giving us 160 = 2 × 2 ×
2 × 2 × 2 × 5, 135 = 3 × 3 × 3 × 5, 70 = 2 × 5 × 7, and 15 = 3 × 5.
The only common factor of all of them is 5. Furthermore, the sequence with difference 15 occurs many times
(once with five-character repetition), and 70 occurs with a four-character repetition, giving us strong evidence
that the key length is a common factor of these two numbers.
Now that we know how many different alphabets are used, we can split the ciphertext into many ciphertexts
(one for each character in the key), and then perform frequency analysis and other techniques to break these
ciphers. Note that each of these ciphertexts now represents a monoalphabetic substitution cipher.
1.5.3 Breaking Columnar Transposition Ciphers
Breaking the simple transposition ciphers is not incredibly difficult, as the key space is typically more limited
than in polyalphabetic ciphers (the key space being the total possible number of distinct keys that can be
chosen). For example, the key space here is limited by the size of the grid that the human operator can draw and
fill in reliably.
The preferred method is performing digraph and trigraph analysis, particularly by hand. 1 A digraph is a pair
of letters written together. Similarly, a trigraph is a set of three letters written together. All languages have cer-
tain letter pairs and triplets that appear more often than others. For example, in English, we know that characters
such as R, S, T, L, N, and E appear often — especially since they appear on Wheel of Fortune's final puzzle —
thus it should come as no shock that letter pairs such as ER and ES appear often as well, whereas letter pairs
such as ZX appear very infrequently. We can exploit this property of the underlying language to help us decrypt
a message. Tables 1-5 and 1-6 show some of the most common digraphs and trigraphs for English (again, from
Shakespeare) and Klingon, respectively.
Table 1-5 Most Common Digraphs and Trigraphs in The Complete Works of William Shakespeare