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The Polybius square, also known as the Polybius checkerboard, is a device invented by the ancient Greeks 
Cleoxenus and Democleitus, and made famous by the historian and scholar Polybius. 
The device is used for fractionating plaintext characters so that they can be represented by a smaller set of symbols, 
which is useful for telegraphy steganography, and cryptography. The device was originally used for fire signalling, 
allowing for the coded transmission of any message,
not just a finite amount of predetermined options as was the convention before. 

A key could be used to reorder the alphabet in the square, with the letters (without duplicates) of the key being 
placed at the beginning with the rest of the alphabet following it in regular order.

In his Histories, Polybius outlines the need for effective signalling in warfare, leading to the development of 
the square. Previously, fire-signalling was useful only for expected, predetermined messages, 
with no way to convey novel messages about unexpected events. According to Polybius, in the fourth century BCE, 
Aeneas Tacticus devised a hydraulic semaphore system consisting of matching vessels with sectioned rods labelled 
with different messages such as "Heavy Infantry", "Ships", and "Corn". 
This system was slightly better than the basic fire-signalling, 
but still lacked the ability to convey any needed message. 
The Polybius square was used to aid in telegraphy, specifically fire-signalling. 
To send a message, the sender would initially hold up two torches and wait for the recipient to do the same 
to signal that they were ready to receive the message. The sender would then hold up the first set of torches on his 
left side to indicate to the recipient which tablet (or row of the square) was to be consulted. 
The sender would then raise a set of torches on his right side to indicate which letter on the tablet was 
intended for the message. Both parties would need the same tablets, a telescope 
(a tube to narrow view, no real magnification), and torches.

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, 
contiguous letters before a wider space or many other ways.

The Polybius square is also used as a basic cipher called the Polybius Cipher. 
This cipher is quite insecure by modern standards, as it is a substitution cipher with characters 
being substituted for pairs of digits, which is easily broken through frequency analysis

The Playfair cipher is a polyalphabetic substitution cipher invented by Charles Wheatstone 
and promoted by Lyon Playfair based on a five x five square which accommodates the alphabet in a manner 
similar to the Polybius Square. The letters in the square are arranged by first inserting the 
letters of a key (without repetition), before the remaining letters (which appear subsequently 
in normal alphabetical order). A message is divided into pairs of letters, with a filler letter "x" inserted 
at the end if the message was of odd length. If both letters of a pair are the same, a filler "x" is inserted 
in between them with an extra "x" inserted at the end of the message to compensate for this. Each pair of 
letters are then encrypted using the Playfair key Table through "mapping rules"