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Code and ciphers: Julius Caesar, the Enigma and the internet

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220<br />

solutions to problems<br />

Chapter 4<br />

4.1 (Simple transposition)<br />

If <strong>the</strong> key length is 6 each column of <strong>the</strong> transposition box will contain<br />

five letters; we <strong>the</strong>refore write <strong>the</strong> cipher text out in columnar form in<br />

Table S.1.<br />

Table S.1<br />

1 2 3 4 5 6<br />

L S L A H I<br />

P C A M O R<br />

E E E H T T<br />

U O M S A M<br />

D E A S R Y<br />

The third line looks as if it might contain <strong>the</strong> trigraph THE which suggests<br />

that ei<strong>the</strong>r column 5 or column 6 should be immediately to <strong>the</strong> left<br />

of column 4. Examination of <strong>the</strong> o<strong>the</strong>r digraphs in 5-4 <strong>and</strong> 6-4 points to 5-<br />

4 as being more likely. If <strong>the</strong> ordering 5-4 is correct <strong>and</strong> <strong>the</strong> word THE is<br />

present <strong>the</strong>n column 4 must precede column 1, 2 or 3 which doesn’t help<br />

us much at this stage. We <strong>the</strong>refore look elsewhere <strong>and</strong> try to find which<br />

column might precede column 5 we see that <strong>the</strong> only digraph that looks<br />

plausible in row 1 is SH which implies that column 2 should be immediately<br />

to <strong>the</strong> left of column 5. We <strong>the</strong>refore have a partial tentative ordering<br />

2-5-4<br />

<strong>and</strong> if we write out those three columns in that order we have Table S.2.<br />

Table S.2<br />

2 5 4<br />

S H A<br />

C O M<br />

E T H<br />

O A S<br />

E R S<br />

The solution now follows fairly easily. The key is 2 5 4 1 3 6 <strong>and</strong> <strong>the</strong><br />

plaintext, with spaces inserted, is<br />

SHALL I COMPARE THEE TO A SUMMERS DAY.

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