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In cryptography, the Polybius square, also known as the Polybius checkerboard, is a device invented by the Ancient Greeks Cleoxenus and Democleitus, and perfected by the Ancient Greekhistorian and scholar Polybius,[1] for fractionatingplaintext characters so that they can be represented by a smaller set of symbols.
Basic form[edit]
The original square used the Greek alphabet:
1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|
1 | Α | Β | Γ | Δ | Ε |
2 | Ζ | Η | Θ | Ι | Κ |
3 | Λ | Μ | Ν | Ξ | Ο |
4 | Π | Ρ | Σ | Τ | Υ |
5 | Φ | Χ | Ψ | Ω |
With the modern Latin alphabet, this is the typical form:
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 fit in a 5 × 5 square, two letters must be combined (usually I and J as above, though C and K is an alternative). (Polybius had no such problem because the Greek alphabet has 24 letters.) Alternatively, a 6 × 6 grid may be used instead. This would allow numerals to be included as well as letters.
A 6 × 6 grid may also be used for the Cyrillic alphabet (the most common variant has 33 letters, but some have up to 37).
The Polybius square has also been used with Japanese hiragana (see cryptography in Japan).
Telegraphy and steganography[edit]
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. It is said to have been used by nihilist prisoners of the RussianCzars and also by USprisoners of war during the Vietnam War.
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.
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.
Cryptography[edit]
The Polybius cipher can be used with a keyword 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 ciphers such as the ADFGVX cipher, the Nihilist cipher, and the bifid cipher.
See also[edit]
References[edit]
External links[edit]
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Contents.Quotes. In all human affairs, and especially in those that relate to.leave always some room to, and to accidents which cannot be foreseen. The General History, Book II, Ch. By ). It is a course which perhaps would not have been necessary had it been possible to form a state composed of wise men, but as every multitude is fickle, full of lawless desires, unreasoned passion, and violent anger, the multitude must be held in by invisible terrors and suchlike pageantry. For this reason I think, not that the ancients acted rashly and at haphazard in introducing among the people notions concerning the gods and beliefs in the terrors of hell, but that the moderns are most rash and foolish in banishing such beliefs. Histories, VI, 56:10-12.
Often quoted in the version found in The Fine Art of Baloney Detection by from The Demon-Haunted World:. Since the masses of the people are inconstant, full of unruly desires, passionate, and reckless of consequences, they must be filled with fears to keep them in order. The ancients did well, therefore, to invent gods, and the belief in punishment after death.
This is a sworn treaty made between us, Hannibal and Xenophanes the Athenian in the presence of all the gods who possess Macedonia and the rest of Greece. Histories, VII, 9:4 (Loeb, W.R. Paton). How highly should we honor the Macedonians, who for the greater part of their lives never cease from fighting with the barbarians for the sake of the security of Greece?