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192 CHAPTER 10. TRANSPOSITION CIPHERS
Do this twice more. Since the plaintext has only 31 letters we add five
nulls letters at the end. (I chose stopt as the nulls.) Then pull off the
ciphertext in rows and regroup.
(2) Decipher UTOWL MHHDE IAFTO NADOG MBIHD OEAEU CNCOS Y using the same
grille. 4
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄
For about four months in 1917 the German Army used Turning Grilles. (The
German Army was quite lost, cryptographically, during much of World War I,
and tried just about every method they could get their hands on.) ANNA was
5 × 5, BERTA was 6 × 6, all the way up to FRANZ, who was 10 × 10. The
French, who were crytologically far more advanced than the Germans, treated
Anna, Berta and Franz as old friends, and happily read most of the messages
sent in this manner.
10.4 Columnar Transposition
Columnar transposition is the transposition method. It was widely used,
especially in World War I, and fell out of favor only because of the rise of
machine ciphers. 5
To encipher, pick a keyword and write the message under the keyword in
rows with as many columns as letters in the keyword. Number the columns
alphabetically from the code word, just as in the keyword transposed ciphers
from Section 1.5.3. (Remember we decided to consecutively number repeated
letters, so REPEATER is numbered 62531847.) Then pull the columns out oneby-one
in this numerical order. Separate the letters into groups of five and you
have enciphered your message. (It is possible that your message will not make
a perfect rectangle. That is fine. Either ignore the blanks, or fill them with
nulls.)
To decipher the message we need to know not only what the proper ordering
of the the columns is (which we do, as we know the keyword), but also how
many letters go into each column. Suppose we have a message N letters long,
and the keyword has k letters. Start by drawing a rectangle with k columns.
Next divide the columns into rows. There will be N ÷ k full rows (here N ÷ k
means this integer part of division), and a final row that will contain N%k
letters at its beginning and be blank at the end. Cross out these blank spaces
so you won’t be tempted to put letters into them. Now put in your ciphertext
4 (1) MACGA IRITA DHNER ASOMN TALOO OWMTP SOIAT C. (2) who did anything he could to
become famous, (which is true about Cardano, as his biographers can attest.)
5 Machine ciphers are clearly much faster than ciphering by hand. Further, since transposition
generally deals with large groups of letters at one, as opposed to substitution which
enciphers small groups at once, the early limits on computer memory made pure transposition
machine-ciphers less secure than substitution machine-ciphers.