All operations

Polybius square

Turn every letter into a pair of coordinates on a five by five grid.

The grid

The alphabet goes into a five by five grid, five letters to a row, and each letter is written as its row number then its column number. M is 32. T is 44. No digit above 5 can appear. The separator control spaces the pairs, as above, or runs them together.

Spaces, punctuation, numbers and case disappear before the lookup. Decode the example above and MEETMEATTHEIETTYATMIDNIGHT comes back, with the J in JETTY returned as an I.

Where it came from

Polybius set the grid out in the tenth book of his Histories, crediting Cleoxenus and Democleitus with the idea. His version was a torch telegraph: torches on the sender’s left gave the row, on his right the position within it, one letter at a time between two signal posts. It solved distance. Secrecy came later.

Twenty-six letters, twenty-five cells

Two letters have to share a cell, and which two is a convention rather than a rule. I with J is the usual English choice. C with K is what American prisoners of war used for the tap code. U with V follows Latin, which wrote one letter for both. The fourth setting leaves Q out.

Encoding is lossy whichever pair you pick: the decoder gets one letter back with no way to know which was sent.

Keying the square

A key word fills the grid first, each of its letters used once, and the rest of the alphabet follows in order. PSYSECURE builds a square starting P S Y E C U R A B D, which moves A from 11 to 23. Both ends need the same key word and the same shared-cell setting or the digits decode to noise.

The key field also takes a finished square: paste all twenty-five letters in grid order and that grid is used exactly, which is how a mixed square from a published example gets in.

What it protects

By itself, nothing. Each letter maps to one fixed pair of digits, so this is a substitution cipher written in numbers, and counting the pairs breaks it as fast as counting letters breaks Caesar.

Once a letter is two independent digits, they can be pulled apart, mixed with digits from other letters, relabeled, added to a key stream, or knocked on a wall. Every other cipher in this category is one of those moves applied to this grid.

ADFGX relabels the coordinates as five Morse-distinct letters and shuffles them. Bifid separates the rows from the columns and pairs the digits back up in a new order. Tap code is this grid sounded out through a cell wall.