Decoding the IRA (4 page)

The sender writes the message under the
key
in rows:

Key:

The sender then
alphabetises the key
, keeping the columns intact.

Key:

The sender completes the shuffling by reading the message out by columns, using the alphabetical order of the key. If the key contains two or more of the same letter, the leftmost one is used first. The encrypted message starts here with the A of
MONARCHY
, then the C and so on, so the final encryption is
OTENT REEZO ABNI DYSEB MSREU EITBH CHVAT CEGR
. Usually the message will be presented in five-letter groups to conceal any hints to a would-be codebreaker concerning column length or order. The receiver counts the letters in the message, sets up a frame with the correct number of letters in the last row and enters the encrypted message under the key, again in alphabetical order, finally reading the original plain text message in rows.

Counting letter frequencies quickly distinguishes between the two types: with transposition ciphers the most and least common letters of the cipher will be the most and least common letters of the underlying language. I assumed English was used for this set of six messages, since the surrounding text (‘Dear Sir', ‘Yours Faithfully') is in English. The most common letters of the cipher,
EARIOST
, are common letters in English. The least common letters of the cipher,
BQVKP
, are uncommon letters in English. The proportion of vowels in standard English text is about 40 per cent, and in this cipher is 47 per cent – rather high, but within normal variation. I was quite confident I was looking at a transposition cipher.

 

Solving the first cipher

The cipher may use any of scores of types of transposition: for example, the columnar transposition shown [p. 24] with the columns shuffled according to a secret key; pattern-based systems such as route transposition or railfence; the turning grille, using a square with cut-outs in which to write the message, turning it to each of four positions; nihilist transposition, where both the rows and columns of an array are shuffled; and many other variations on these themes. Each system uses a key: a secret piece of information intended to keep the message private even if the general system is known to the attacker, assuming the underlying cipher system is strong enough. The number of letters in this cipher serves to eliminate some of the possible systems: the 151 letters will not fill a square or rectangle evenly, so many of the common rectangle-based systems need not be considered.

I chose for my first attempts the columnar transposition system: it is simple to explain to a correspondent who may not be an experienced cipher clerk, it can be used for messages that do not fit in a complete rectangle, and it had been used rather widely before the 1920s, when these ciphers were composed. A cryptanalyst can solve normal columnar transpositions using only pencil and paper, depending on the length of the cipher, the length of the key, and in some cases the content of the message. The analysis can become more difficult if the encryption method is varied, if the key is very long, or if the message is short compared to the key length.

A message using a ten-letter key, meaning the message block will have ten columns, would be relatively straightforward to solve if it were, say, 75 or more letters long and used no tricks. A typical manual attack
would be to write the cipher message in a ten-column block and then cut it apart in vertical strips. Since the order of columns is not known, the cryptanalyst would not know in advance which columns were short and which were long in an incompletely-flled block, so extra letters would be added to the top and bottom of each column to allow for that difference. The cryptanalyst would then shuffle these columns around on a table, finding where they can be aligned to form the hidden message.

This process can be tedious to execute with pencil, paper and scissors, especially if many ciphers are to be attacked. Over the past forty years I have developed a wide array of computer programmes to help in my analysis and in many cases to solve common types of ciphers automatically. One of the most effective general-purpose automatic methods I call Shotgun Hillclimbing. This method picks a key length in what I consider a reasonable range, creates a key of that length with randomly chosen letters, ‘decrypts' the message using this key, then progressively changes the key to try to get a decryption that looks more English-like. When it reaches a plateau where simple changes to the key no longer improve the result, it compares the result with the best found so far, then goes back to try a new random starting point. The efficacy of the process depends on a number of factors, including the difficulty of the cipher itself, the length of the key, the methods used to modify each successive key, and the method used to score a decryption on the English-like scale. The process itself is, in principle, much like the pencil, paper and scissors method described above, trying the columns in different combinations until words and phrases begin to appear.

I unleashed my Shotgun Hillclimbing programme on this cipher, treating it as a columnar transposition with a partially-filled block of between eight and fifteen columns, and it returned the following, successively better, trial solutions, each using twelve columns:

The process stopped with the last of these – no better solutions were found using a few hundred more starting keys. The programme produced the key ‘fdbjalhcgkei': these letters give the conjectured order of the twelve
columns of the cipher, with the ‘a' of the key indicating that the beginning of the cipher text (
AEOOA IIIEO …
) goes down the fifth column.

This attempted solution looks rather close: we see some clear words such as
‘send stuff for'
that must be part of the original message. To see why the text is imperfect I set the message in a partially-filled block with twelve columns, yielding twelve rows of twelve letters and one row of seven, and used the programme's proposed key:

Key: 1 2 3 4 5 6 7 8 9 10 11 12 13

The cipher begins
AEOOA IIIEO AEAEW
, andstarts down column A, then continues to column B:

Key: 1 2 3 4 5 6 7 8 9 10 11 12 13

The next few groups are
LFRRD ELBAP RAEEA EIIIE AAAHO IFMFN
, and these are filled in the same way, continuing after the
EW
in column b and going on to columns c and d.

Key: 1 2 3 4 5 6 7 8 9 10 11 12 13

As I filled these in I noted that all the letters in columns
a
and
c
are vowels. This would not happen by chance: since only 40 per cent of English letters are vowels, the odds against having this many in a row appear by chance are astronomical. This means that the person encrypting the message put the vowels in independent of the plain text, and we will soon see the result. Filling in the rest of the cipher text in order gives the following result:

Key: 1 2 3 4 5 6 7 8 9 10 11 12 13