A Simple Introduction to Transposition Ciphers

Rearranging, Not Replacing

Most beginners meet cryptography through the substitution cipher: the Caesar shift, where each letter is swapped for another further along the alphabet. A transposition cipher works on a completely different principle. It never changes a single letter; it only shuffles the order in which those letters appear. If your plaintext contains four letter Es, your ciphertext contains four letter Es too, just sitting in different places.

That sounds almost too simple to be useful, and in a sense it is. But the idea underpins a great deal of real encryption history and makes an excellent playground for anyone learning to think like a codebreaker. The rules are easy to hold in your head, the arithmetic is trivial, and yet cracking one by hand is a genuine puzzle.

Building a Columnar Cipher by Hand

The classic method is the columnar transposition, and it takes about a minute to learn.

• Write your message into rows of equal length, ignoring the spaces, so that it fills a rough grid.
• Read the letters downwards, one complete column at a time, working from left to right.
• Write those letters out as one continuous string. That is your ciphertext.

Try it with the message ENEMY ATTACKS AT DAWN. Strip the spaces and you have eighteen letters, which fits neatly into three rows of six:

ENEMYA / TTACKS / ATDAWN

Now read down each column. Column one gives ETA, column two NTT, column three EAD, column four MCA, column five YKW, and column six ASN. Joined together, the ciphertext reads ETANTTEADMCAYKWASN.

Decrypting means reversing the process. Count the letters, work out that six columns of three will fit, chop the ciphertext back into equal columns, and read across the rows. It is the same grid, walked in the opposite direction.

Using a Keyword to Order the Columns

A plain columnar cipher has a weakness: the columns are read in their natural order, so anyone who guesses the width can simply try reading across the rows. Real users therefore added a keyword, which does no encrypting itself but decides which column is read first, second, third, and so on.

Take the keyword CIPHER. Number its letters according to alphabetical order: C is first, E second, H third, I fourth, P fifth, R sixth. Reading off those letters' original positions gives the order 1, 5, 4, 2, 3, 6.

Reusing our grid, we now read column one, then five, then four, two, three, and six. That produces ETAYKWMCANTTEADASN — eighteen letters, identical to the ones we started with, arranged differently again. Anyone intercepting this has to guess both the width and the keyword before they can even begin unjumbling it.

The Fingerprints a Transposition Leaves Behind

Breaking a cipher begins with recognising which family you are facing. Transposition ciphers leave a very distinctive set of clues.

• Letter frequency is untouched. Everyday English is roughly twelve per cent Es. A substitution cipher flattens that profile; a transposition cipher preserves it exactly. Count the letters and you will see the usual suspects in the usual proportions.
• The vowels stay in roughly the same ratio. Around two in five letters in ordinary prose are A, E, I, O or U, and that proportion survives the shuffle intact.
• Short repeated patterns survive. If a word or letter pairing appears twice in the plaintext, its letters still appear the same number of times, though the distance between them may change.
• It feels like an anagram rather than a code. Nothing has been disguised, only displaced. Squint at the text and your brain will insist there is a message in there somewhere, which is exactly right.

The practical consequence is that counting letters tells you almost nothing. What matters is their arrangement, which is why transposition puzzles are so enjoyable to solve by hand.

How to Start Cracking One

If you suspect a transposition, your task is to work out the dimensions of the grid, then find a reading order that turns nonsense into English.

• Factor the message length. Forty-eight letters could be six rows of eight, eight rows of six, or twelve rows of four. Try each in turn.
• Guess a width and test it. Write the ciphertext into columns of your guessed width and read across the rows. Wrong guesses still often cough up fragments such as TH or ING.
• Hunt for a crib. If you expect the message to say ATTACK or begin with a greeting, look for those letters scattered sensibly.
• Be patient with anagramming. Once you are close, rearranging columns by eye is often faster than any systematic method. Pencil and paper beat brute force here.
• Expect padding. Encoders frequently add filler letters, often X, to square off the final row. A stray X or two is a clue, not a mistake.

Your Turn

Here is a short challenge. The following ciphertext was produced with a plain columnar transposition, a width of four columns, spaces removed, and a single X added as padding to fill the final row:

MMTIEEHLEAELTTMX

Sixteen letters means four rows of four. Chop the string into four-letter columns — MMTI, EEHL, EAEL, TTMX — lay them side by side, and read across each row. You should find a perfectly ordinary arrangement of a very ordinary request. Work it through slowly, and once you have the plaintext you will have done precisely what a professional codebreaker does: spotted the shape, guessed the structure, and let the letters fall back into place.