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5.6. BASIC LETTER CHARACTERISTICS 77
the substitution for b, 24 for c’s substitute, etc. Thus there are
26! = 26 × 25 × 24 × · · · × 2 × 1
= 403, 291, 461, 126, 605, 635, 584, 000, 000
different monoalphabetic substitution ciphers. How large of a number is this
If we used a computer that could check one trillion different possibilities every
second, we’d need about 12 million years to check all the possibilities!
Of course, no one simply uses brute force to break monoalphabetic ciphers.
In our current example X almost positively must be e. And most of etaoinshr
probably comes from CFKQSTU. This cuts down immensely on the number of
possibilities. But to decrypt such a cipher in a truly finite amount of time we
must go beyond simple frequency counts to consider the behaviors of the letters.
5.6 Basic Letter Characteristics
We’ve seen which letters are the most common (etaoinshr) and least common
(vkjxqz). We next look at which letters appear first and last in words. We
begin with the frequency information from earlier. (The initial and final letter
percentages are from Sinkov’s study of 16410 words [Sinkov].)
8.2 1.5 2.8 4.3 12.7 2.2 2.0 6.1 7.0 0.2 0.8 4.0 2.4
a b c d e f g h i j k l m
6.7 7.5 1.9 0.1 6.0 6.3 9.1 2.8 1.0 2.4 0.2 2.0 0.1
n o p q r s t u v w x y z
Figure 5.1: Letter Frequencies – Anywhere.
11.0 4.6 5.6 2.8 2.5 4.1 1.8 3.9 5.6 0.6 0.5 2.1 3.5
a b c d e f g h i j k l m
2.4 7.2 4.7 0 3.1 7.4 15.9 1.4 0.6 5.1 0 0.7 0
n o p q r s t u v w x y z
Figure 5.2: Letter Frequencies – Initial Letters.
Summarizing, the most common individual letters are
1) Anywhere: etaoi, 4 vowels and t.
2) Beginning words: tasoic, with t easily the most common.
3) Ending words: edtsn (almost spells “endts”).
4) Doubles: lesot.
We put this summary into Figure 5.4.