Polybius square
Encyclopedia
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.
, 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 coordinates in the grid. For example, "BAT" becomes "12 11 44". Because 26 characters do not quite fit in a square, it is rounded down to the next lowest square number by combining two letters (usually I and J). (Polybius had no such problem because the Greek alphabet
he was using had 24 letters). Alternatively, the ten digits could be added and 36 characters would be put into a 6 × 6 grid.
Such a larger grid might also be used for the Cyrillic alphabet
(of which the most common variant
has 33 letters, though some have fewer, and some up to 37.)
; he suggested the symbols could be signalled by holding up pairs of sets of torch
es. It has also been used, in the form of the "knock code", to signal messages between cells in prison
s by tapping the numbers on pipes or walls.
In this form it is said to have been used by nihilist
prisoners of the Russia
n Czars, and also by America
n prisoners of war in the Vietnam War
.
Indeed it can be signalled in many simple ways (flashing lamps, blasts of sound, drums, smoke signal
s) 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 knot
s in a string, stitches on a quilt, letters squashed together before a wider space, or many other simple ways.
like the Playfair cipher
. 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. In this sense it is just another encoding which can be cracked with simple frequency analysis.
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 cipher
s such as the ADFGVX cipher
, the Nihilist cipher
, and the bifid cipher
.
Polybius was responsible for a useful tool in telegraphy which allowed letters to be easily signaled using a numerical system. This idea also lends itself to cryptographic manipulation and steganography.
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
, the Polybius square, also known as the Polybius checkerboard, is a device invented by the Ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
historian
Historian
A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. If the individual is...
and scholar Polybius
Polybius
Polybius , Greek ) was a Greek historian of the Hellenistic Period noted for his work, The Histories, which covered the period of 220–146 BC in detail. The work describes in part the rise of the Roman Republic and its gradual domination over Greece...
, described in Hist. X.45.6 ff., for fractionating plaintext
Plaintext
In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....
characters so that they can be represented by a smaller set of symbols.
Basic form
The original square used the Greek alphabetGreek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...
, but can be used with any alphabet. In fact, it has also been used with Japanese hiragana
Hiragana
is a Japanese syllabary, one basic component of the Japanese writing system, along with katakana, kanji, and the Latin alphabet . Hiragana and katakana are both kana systems, in which each character represents one mora...
(see cryptography in Japan). With the modern English alphabet
English alphabet
The modern English alphabet is a Latin alphabet consisting of 26 letters and 2 ligatures – the same letters that are found in the Basic modern Latin alphabet:...
, in typical form, it appears thus:
| 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 |
Each letter is then represented by its coordinates in the grid. For example, "BAT" becomes "12 11 44". Because 26 characters do not quite fit in a square, it is rounded down to the next lowest square number by combining two letters (usually I and J). (Polybius had no such problem because the Greek alphabet
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...
he was using had 24 letters). Alternatively, the ten digits could be added and 36 characters would be put into a 6 × 6 grid.
Such a larger grid might also be used for the Cyrillic alphabet
Cyrillic alphabet
The Cyrillic script or azbuka is an alphabetic writing system developed in the First Bulgarian Empire during the 10th century AD at the Preslav Literary School...
(of which the most common variant
Cyrillic alphabet variants
This is a list of national variants of the Cyrillic script.Sounds are indicated using IPA. These are only approximate indicators. While these languages by and large have phonemic orthographies, there are occasional exceptions—for example, Russian represents in a number of words This is a list of...
has 33 letters, though some have fewer, and some up to 37.)
Telegraphy and steganography
Polybius did not originally conceive of his device as a cipher so much as an aid to telegraphyTelegraphy
Telegraphy is the long-distance transmission of messages via some form of signalling technology. Telegraphy requires messages to be converted to a code which is known to both sender and receiver...
; he suggested the symbols could be signalled by holding up pairs of sets of torch
Torch
A torch is a fire source, usually a rod-shaped piece of wood with a rag soaked in pitch and/or some other flammable material wrapped around one end. Torches were often supported in sconces by brackets high up on walls, to throw light over corridors in stone structures such as castles or crypts...
es. It has also been used, in the form of the "knock code", to signal messages between cells in prison
Prison
A prison is a place in which people are physically confined and, usually, deprived of a range of personal freedoms. Imprisonment or incarceration is a legal penalty that may be imposed by the state for the commission of a crime...
s by tapping the numbers on pipes or walls.
In this form it is said to have been used by nihilist
Nihilist movement
The Nihilist movement was a Russian movement in the 1860s which rejected all authorities. It is derived from the Latin word "nihil", which means "nothing"...
prisoners of the Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n Czars, and also by America
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
n prisoners of war in the Vietnam War
Vietnam War
The Vietnam War was a Cold War-era military conflict that occurred in Vietnam, Laos, and Cambodia from 1 November 1955 to the fall of Saigon on 30 April 1975. This war followed the First Indochina War and was fought between North Vietnam, supported by its communist allies, and the government of...
.
Indeed it can be signalled in many simple ways (flashing lamps, blasts of sound, drums, smoke signal
Smoke signal
The smoke signal is one of the oldest forms of communication in recorded history. It is a form of visual communication used over long distance.-History and usage:...
s) and is much easier to learn than more sophisticated codes like the Morse code
Morse code
Morse code is a method of transmitting textual information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment...
.
However, it is also somewhat less efficient than the more complex codes.
The simple representation also lends itself to steganography
Steganography
Steganography is the art and science of writing hidden messages in such a way that no one, apart from the sender and intended recipient, suspects the existence of the message, a form of security through obscurity...
. The figures from one to five can be indicated by knot
Knot
A knot is a method of fastening or securing linear material such as rope by tying or interweaving. It may consist of a length of one or several segments of rope, string, webbing, twine, strap, or even chain interwoven such that the line can bind to itself or to some other object—the "load"...
s in a string, stitches on a quilt, letters squashed together before a wider space, or many other simple ways.
Cryptography
The Polybius cipher can be used with a keywordKeyword cipher
A keyword cipher is a form of monoalphabetic substitution. A keyword is used as the key, and it determines the letter matchings of the cipher alphabet to the plain alphabet. Repeats of letters in the word are removed, then the cipher alphabet is generated with the keyword matching to A,B,C etc...
like the Playfair cipher
Playfair cipher
The Playfair cipher or Playfair square is a manual symmetric encryption technique and was the first literal digraph substitution cipher. The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair who promoted the use of the cipher.The technique encrypts pairs of...
. By itself the Polybius square is not terribly secure, even if used with a mixed alphabet
Substitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
. The pairs of digits, taken together, just form a simple substitution in which the symbols happen to be pairs of digits. In this sense it is just another encoding which can be cracked with simple frequency analysis.
However a Polybius square offers the possibility of fractionation, leading toward Claude E. Shannon's confusion and diffusion
Confusion and diffusion
In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Shannon in his paper Communication Theory of Secrecy Systems, published in 1949....
. As such, it is a useful component in several cipher
Cipher
In cryptography, a cipher is an algorithm for performing encryption or decryption — a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...
s such as the ADFGVX cipher
ADFGVX cipher
In cryptography, the ADFGVX cipher was a field cipher used by the German Army during World War I. ADFGVX was in fact an extension of an earlier cipher called ADFGX. Invented by Colonel Fritz Nebel and introduced in March 1918, the cipher was a fractionating transposition cipher which combined a...
, the Nihilist cipher
Nihilist cipher
In the history of cryptography, the Nihilist cipher is a manually operated symmetric encryption cipher originally used by Russian Nihilists in the 1880s to organize terrorism against the czarist regime...
, and the bifid cipher
Bifid cipher
In classical cryptography, the bifid cipher is a cipher which combines the Polybius square with transposition, and uses fractionation to achieve diffusion...
.
Polybius was responsible for a useful tool in telegraphy which allowed letters to be easily signaled using a numerical system. This idea also lends itself to cryptographic manipulation and steganography.
See also
- Numerical cipher
- Topics in cryptography
- Straddling checkerboardStraddling checkerboardIn cryptography, a straddling checkerboard is a device for converting an alphabetic plaintext into digits whilst simultaneously achieving fractionation and data compression relative to other schemes using digits...