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

196 CHAPTER 10. TRANSPOSITION CIPHERS
cipher will generally have too many jvkxyq’s and too few etaoinshr’s. To
our eyes, trained to read English, transposition ciphers will look like a salad
of letters (to mis-translate Bazeries’ quote), worthwhile components but oddly
mixed, whereas substitution ciphertexts look unappetizing, with too many odd
letters.
10.6 Letter Connections
Decrypting a transposition cipher is a bit like putting Humpty Dumpty back
together again – all the pieces are given, we just need to determine which goes
where. When doing this, we will continually have a letter and will be wondering
which letter most likely came just before it in the message, and which letter
likely came just after it. These are questions of conditional probability. Notice
the difference between
and
“This letter is a T. How likely is it that the next letter an H”
“How likely is it that this letter is a T and the next letter is an H”
Figure 10.2 provides the answer to the first question, in percent. 9 In the row
centered by T, just to the right of T appears H 32 , which indicates that T is followed
by H almost 1/3 of the time. Similarly, the appearance of U 4 E 17 O 18 A 22 I 26 just
before N show that N is almost always preceded by a vowel, with that vowel
being I about 1/4 of the time. And that when the rare V does appear, it is
usually followed by E. 10
For comparison, the answer to the section question (“how likely is it that
this pair is “TH”) appears in Figure 10.3. This figure is the bigram companion
to our standard frequency chart Figure 1.3, as it shows how likely each possible
bigram is in standard English. 11
9 These percentages were computed using “The Brown Corpus.” The Brown Corpus of
Standard American English was compiled by W.N. Francis and H. Kucera at Brown University,
Providence, RI, from one million words of American English texts printed in 1961. The texts
sampled came from fifteen different categories ranging from “Reportage” (The Philadelphia
Inquirer, May 10, 1961, p.49) to “Popular Lore” (Jack Kaplan, “The Health Machine Menace:
Therapy by Witchcraft”) to “Romance” (Samuel Elkin, “The Ball Player,” Nugget, October,
1961). By modern standards, this corpus is considered small and dated.
10 We remarked back in Chapter 6 that vowels like to combine with consonants. Look at
the vowels rows to ascertain the validity of this statement. Likewise, that H is more likely to
precede vowels while N and S are more likely to follow them.
11 The numbers are in %%, meaning that you should divide by 100 and add % to the end.
So the 13 in the BA entry means that BA appears .13% of the time, about 1/10 of 1 percent of
the time. Values smaller than 0.01% have been left out.