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In cryptography, the Polybius square, also known as the Polybius checkerboard, is a device invented by the Ancient Greek historian and scholar Polybius, described in Hist. X.45.6 ff., for fractionating plaintext characters so that they can be represented by a smaller set of symbols.

The original square used the Greek alphabet, but can be used with any alphabet. In fact, it has also been used with Japanese hiragana (see cryptography in Japan). With the modern English alphabet, in typical form, it appears thus:

Each letter is then represented by its co-ordinates in the grid. Thus "BAT" becomes "12 11 44", for example. Because 26 characters do not quite fit in a nice square, we round down to the next lowest square number by combining two letters - I and J, usually. (Polybius had no such problem because the Greek alphabet he was using had 24 letters). Alternatively, we could add digits as well and get a 6 × 6 grid. Such a larger grid might also be used for the Cyrillic alphabet, which has 33 letters.

Polybius did not originally conceive of his device as a cipher so much as an aid to telegraphy; he suggested the symbols could be signalled by holding up pairs of sets of torches. It has also been used, in the form of the "knock code", to signal messages between cells in prisons by tapping the numbers on pipes or walls. In this form it is said to have been used by nihilist prisoners of the Russian Czars, and also by American prisoners of war in the Vietnam War. Indeed it can be signalled in many simple ways (flashing lamps, blasts of sound, drums, smoke signals) and is much easier to learn than more sophisticated codes like the Morse code. However, it is also somewhat less efficient than the more complex codes.

The simple representation also lends itself to steganography. The figures from one to five can be indicated by knots in a string, stitches on a quilt, letters squashed together before a wider space, or many other simple ways.

By itself the Polybius square is not terribly secure, even if used with a mixed alphabet. The pairs of digits, taken together, just form a simple substitution in which the symbols happen to be pairs of digits. However a Polybius square offers the possibility of fractionation, leading toward Claude E. Shannon's confusion and diffusion. As such it is a useful component in several ciphers such as the ADFGVX cipher, the Nihilist cipher and the bifid cipher.