thumb|The Greek letters of a Polybius square
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 number of predetermined options as was the convention before. For example, the key phrase "polybius cipher" would lead to the reordered square below.
{| class="wikitable"
!
!1
!2
!3
!4
!5
|-
!1
|P
|O
|L
|Y
|B
|-
!2
|I/J
|U
|S
|C
|H
|-
!3
|E
|R
|A
|D
|F
|-
!4
|G
|K
|M
|N
|Q
|-
!5
|T
|V
|W
|X
|Z
|}
Encryption principle
There are several encryption methods using the Polybius square. Three of them are described below.
{| class="wikitable"
|-
!
! 1 !! 2 !! 3 !! 4 !! 5
|-
! 1
| A || B || C || D || E
|-
! 2
| F || G || H || I/J ||K
|-
! 3
| L || M || N || O || P
|-
! 4
| Q || R || S || T || U
|-
! 5
| V || W || X || Y || Z
|}
Method 1
Let us encrypt the word "SOMETEXT" with a Caesar cipher using a shift equal to the side of our square (5). To do it, locate the letter of the text and insert the one immediately below it in the same column for the ciphertext. If the letter is in the bottom row, take the one from the top of the same column.
{| class="wikitable"
|+
|-
!Letter of the text
|s
|o
|m
|e
|t
|e
|x
|t
|-
!Cipher text letter
|x
|t
|r
|k
|y
|k
|c
|y
|}
Thus, after encryption, we get "xtrkykcy".
Method 2
A more complicated method involves a Bifid cipher without a key (or, in other words, with a key of plain alphabet):
{| class="wikitable"
|-
!
! 1 !! 2 !! 3 !! 4 !! 5
|-
! 1
| A || B || C || D || E
|-
! 2
| F || G || H || I/J ||K
|-
! 3
| L || M || N || O || P
|-
! 4
| Q || R || S || T || U
|-
! 5
| V || W || X || Y || Z
|}
The message is transformed into coordinates on the Polybius square, and the coordinates are recorded vertically:
{| class="wikitable"
|+
!Letter
|s
|o
|m
|e
|t
|e
|x
|t
|-
!Horizontal coordinate
|3
|4
|2
|5
|4
|5
|3
|4
|-
!Vertical coordinate
|4
|3
|3
|1
|4
|1
|5
|4
|}
Then the coordinates are read row by row:
34 25 45 34 43 31 41 54
Next, the coordinates are converted into letters using the same square:
{| class="wikitable"
|+
!Horizontal coordinate
|3
|2
|4
|3
|4
|3
|4
|5
|-
!Vertical coordinate
|4
|5
|5
|4
|3
|1
|1
|4
|-
!Letter
|s
|w
|y
|s
|o
|c
|d
|u
|}
Thus, after encryption, we get "swysocdu".
Method 3
{| class="wikitable"
|-
!
! 1 !! 2 !! 3 !! 4 !! 5
|-
! 1
| A || B || C || D || E
|-
! 2
| F || G || H || I/J ||K
|-
! 3
| L || M || N || O || P
|-
! 4
| Q || R || S || T || U
|-
! 5
| V || W || X || Y || Z
|}
An advanced variation, which involves the following: the obtained primary ciphertext (result From Method 2) is encrypted again. In this case, it is written out without being split into pairs.
3425453443314154
The resulting sequence of digits is cyclically shifted to the left by one step (an odd number of steps [move 3 to the end]):
4254534433141543
This sequence is again divided into groups of two:
42 54 53 44 33 14 15 43
And is replaced with the final ciphertext according to the table:
{| class="wikitable"
|+
!Horizontal coordinate
|4
|5
|5
|4
|3
|1
|1
|4
|-
!Vertical coordinate
|2
|4
|3
|4
|3
|4
|5
|3
|-
!Letter
|i
|u
|p
|t
|n
|q
|v
|o
|}
Thus, after encryption, we get "iuptnqvo".
Applications
Telegraphy
alt=|thumb|Diagram of a fire signal using the Polybius cipher
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.
Arthur Koestler describes the code being used by political prisoners of Stalin in the 1930s in his anti-totalitarian novel Darkness at Noon. (Koestler had been a prisoner-of-war during the Spanish Civil 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 more complex codes.
Steganography
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.