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200 CHAPTER 10. TRANSPOSITION CIPHERS
columns, using the chart in Figure 10.3. 12
columns 1 6 2 6 3 6 5 6 7 6
E A 98 L A 46 G A 21 O A 13 S A 62
E I 39 A I 28 N I 40 E I 39 S I 63
R Y 19 R Y 19 E Y 16 R Y 19 E Y 16
H T 22 G T 15 D T 40 E T 80 R T 47
E T 80 E T 80 H T 22 T T 49 T T 49
totals 258 185 139 200 237
The column pairs 16 and 76 have the highest totals so one of these is
probably right. The pair 16 has the largest total but this is build from
two big and three small values. The pair 76, on the other hand, has four
good pairs and the one given EY pair. For this reason I would probably
start with 76 rather than 16, despite the slightly smaller total. 13
Since y occurs almost exclusively at the end of words we next try to see
which columns could come before our column pair 76.
columns 1 7 6 2 7 6 3 7 6 4 7 6 5 7 6
E S A L S A G S A O S A S S A
E S I A S I N S I E S I S S I
R E Y R E Y E E Y R E Y E E Y
H R T G R T D R T E R T R R T
E T T E T T H T T T T T T T T
None of these look encouraging. The TTT triplets in 476 and 576 force us
to reject those combinations. Similarly 276 and 376 have bad GRT and DRT
triplets. Only 176 works at all, and even then the HRT is not good.
We can always come back, so let’s temporarily abandon the 5 × 7 and try
7 × 5. This give the columns
1 2 3 4 5
E R H E T
E G I R T
R E W E S
H G I T S
E N D A E
L E D I R
A D O Y T
12 Note again the difference between Figures 10.3 and 10.2. When we knew we were working
with y but didn’t know which letter came before it we used 10.2. Now that we have definite
pairs of letters we use 10.3.
13 Some authors advise taking the product of the contact values, rather than their sum.
This prevents a column with a couple very large contact counts and the rest very small from
“winning.” The product counts demonstrate much more clearly the superiority of the 76
combination. For simplicity, we will stick with sums.