Complete Columnar cipher

What the Complete Columnar cipher is

A transposition cipher keeps every letter of the message and changes only the order. In a columnar transposition the message is written left to right in rows of a fixed width, under a keyword with one letter per column. The columns are then read out top to bottom, starting with the column under the keyword’s alphabetically first letter, then the next, until every column has been read. Complete means the last row is filled out, here with X, so every column is the same length.

Columnar transposition has a long field history. Versions of it, often applied twice, were used by armies in both world wars, and it formed the second stage of a well-known German field cipher of the First World War, which paired a square-based substitution with a columnar transposition. On its own it is weak, since the letters keep their frequencies, but it hides word shapes thoroughly, and the re-ordering is the part a solver has to undo.

With the keyword, decoding is bookkeeping. Count the letters and divide by the keyword’s length to get the column length, cut the ciphertext into blocks of that length, number the keyword’s letters in alphabetical order, and stand each block under its letter. The rows then read across. Without the keyword, the solver tries each column count that divides the length, lays the blocks side by side, and re-orders them until the crib, or any English, appears across a row.

The mistakes are mostly in the counting. A column length worked out from the wrong letter count puts every block one letter off, and a keyword with repeated letters needs a tie rule that is easy to forget, which is why keywords for this cipher usually have no repeats. The X padding at the end belongs to the grid, not the message, and a student who reads it into the last word has decoded correctly and then misread.

How to solve a Complete Columnar cipher

No letter is replaced; the letters are only re-ordered. The message is written in rows under a keyword, one letter per column, with the last row filled out with X. Then each column is read top to bottom, in the alphabetical order of the keyword’s letters.

1. Count the ciphertext letters. The number of columns divides that count exactly, because the last row is completed.
2. Divide the count by the number of columns to get each column’s length, and cut the ciphertext into blocks of that length.
3. Put the keyword’s letters in alphabetical order. The first block is the column under the earliest letter, the second block the column under the next.
4. Stand the columns back under the keyword in its written order and read across the rows. X’s at the end are padding.
5. Without the keyword: try each column count that divides the length, lay the blocks side by side, and re-order them until the crib reads across a row.

A worked example

Decode USVNA ESDWO IA (keyword STAR)

12 letters and a four-letter keyword: four columns of three.
STAR in alphabetical order is A R S T, so the blocks are:
A: USV   R: NAE   S: SDW   T: OIA

Back under S T A R:
S T A R
S O U N
D I S A
W A V E

Plaintext: SOUND IS A WAVE

Complete Columnar in Codebusters

Among the Science Olympiad rule sets OlyPrep has read, the Complete Columnar is on the Division B Codebusters list and not on the elementary lists. The Division B rules OlyPrep has read allow up to nine columns and give a crib no shorter than one letter fewer than the number of columns. Unlike the other cryptanalysis types on the list, the crib’s position in the message is not shown, so finding where it sits is part of the solve. Scoring follows the usual rule, with a decoded message of up to two wrong letters commonly counted as solved.

The crib is what makes the search short. With the column count fixed, the crib’s letters must appear as a run across one row, or wrap from the end of one row to the start of the next, so the solver looks for blocks that hold the crib’s letters at the same depth. Two or three blocks lined up that way usually fix the order of the rest. Practising the count and the cut until they are automatic leaves the time for that search.

The lab below draws a science sentence, picks a keyword with no repeated letters, and writes the grid with four or five columns on the easy setting, six or seven on medium, and eight or nine on hard. The key line names the keyword and the column count, and a second line gives a crib without its position, as a Division B question would. Covering the key line turns the challenge into the crib solve. Check compares letters only, and an answer that keeps the trailing X padding is accepted. Reveal shows the plaintext.

Practice the Complete Columnar cipher

The lab below is set to the Complete Columnar cipher alone. Pick a difficulty, generate a challenge, decode it, then check your answer or reveal the solution. It runs in your browser, needs no account, and is unlimited on every OlyPrep plan.

Where the Complete Columnar cipher is tested

The Science Olympiad rule sets OlyPrep has read that name this cipher:

• Science Olympiad Division B — on the Codebusters list, up to nine columns, with a crib whose position is not shown

Cipher lists change with each season’s rules; a tournament’s own rulebook is the authority on what it tests.