Checkerboard cipher

What the Checkerboard cipher is

Like the Nihilist cipher, the Checkerboard starts from a Polybius square: 25 letters in five rows of five, with I and J sharing a cell, keyed by writing a keyword’s letters first and the rest of the alphabet after. Where the Nihilist numbers the rows and columns 1 to 5, the Checkerboard labels them with letters, the five letters of one word down the left and of another across the top. Each plaintext letter becomes two ciphertext letters, so the ciphertext is twice as long as the message.

Labelling a square with letters is an old idea. A well-known field cipher of the First World War used fixed letters as the row and column labels of its square, chosen because they were hard to confuse in Morse; the Checkerboard of puzzle tradition uses keywords instead, which is where the cryptanalysis comes in. The American Cryptogram Association lists it among its pencil-and-paper types, the source of the convention Codebusters follows.

Solving it starts from a count. Only five different letters open the pairs and five different letters close them; those are the row word’s and the column word’s letters. Each set spells a word, and unscrambling it fixes the order: the word’s first letter labels the first row or column. With the square built from the Polybius key and the labels in place, each pair is read by going along its row and down its column.

The mistakes are mixing up the order and the square. A pair is always row then column; reading it the other way round gives the cell reflected across the diagonal, which is always a real letter and so not an obvious error. A square built with a repeated keyword letter left in shifts every cell after it. And when a set of five letters unscrambles two ways, the crib, or the first few pairs tried each way, settles it.

How to solve a Checkerboard cipher

A 5 × 5 square of 25 letters, built from a Polybius key, with I and J sharing a cell. A five-letter word runs down its left side and another across its top. Each plaintext letter becomes two letters: its row’s label, then its column’s.

1. Build the square from the Polybius key: the keyword’s letters first, repeats dropped, then the rest of the alphabet, five to a row.
2. List the first letters of the pairs: five different ones appear, the row word’s letters. The second letters give the column word’s five.
3. Each set of five spells a word. Unscramble it; the word’s spelling fixes which letter labels the first row, the second, and so on.
4. Write the row word down the left of the square and the column word across the top.
5. For each pair, go along the row of its first letter and down the column of its second, and read the cell. If a set of five will not unscramble, the crib fixes some of the labels.

A worked example

Decode TK SA SL MB OL RC MC RB RK OC OC RA TL SK ML TB

Polybius key CARBON. The first letters are M O R S T; the second A B C K L.
They unscramble to STORM (the rows) and BLACK (the columns):

    B L A C K
S   C A R B O
T   N D E F G
O   H I K L M
R   P Q S T U
M   V W X Y Z

TK → G   SA → R   SL → A   MB → V   OL → I   RC → T   MC → Y
RB → P   RK → U   OC → L   OC → L   RA → S   TL → D   SK → O   ML → W   TB → N
Plaintext: GRAVITY PULLS DOWN

Checkerboard in Codebusters

Among the Science Olympiad rule sets OlyPrep has read, the Checkerboard is on the Division B Codebusters list and not on the elementary lists. The Division B rules OlyPrep has read give the Polybius key and make sure that every row and column letter appears somewhere in the ciphertext, so the two words can always be read off the pairs. At state and national level the same rules describe two five-letter keywords as the labels and add a crib of at least five letters. Scoring follows the usual rule, with a decoded message of up to two wrong letters commonly counted as solved.

The time goes into the unscrambling. A student who lists the opening letters and the closing letters before anything else, and tries the likeliest word for each set, often has the labels within a minute. Practising with common five-letter words that have no repeated letters helps; the words on a paper are usually ordinary ones.

The lab below draws a science sentence and a Polybius keyword, picks two five-letter words, and redraws until every row and column letter appears in the ciphertext, as the Division B rules ask. On the easy setting the key line names all three words; on medium and hard it names only the Polybius key, and the two words are the solver’s to find. Check compares letters only and treats I and J as one; Reveal shows the plaintext, the two words and the square.

Practice the Checkerboard cipher

The lab below is set to the Checkerboard 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 Checkerboard cipher is tested

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

• Science Olympiad Division B — on the Codebusters list, with the Polybius key given and every label letter in the ciphertext

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