Polybius Square – A device used by the ancient Greeks

Polybius square is a method in which a chosen alphabet is layed out in a grid that is then being used to represent each letter by its coordinates.

How does the Polybius cipher work?

The Polybius square cipher first distributes the letters of a chosen alphabet into a grid (typically 5×5). Here’s the original square used by the Greeks who invented the cipher.

    ┌───────────────┐
    │ 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    │
└───┴───────────────┘
Original square using the Greek alphabet

For the Latin alphabet to fit into a 5×5 square, two letters must be combined (usually I and J or C and K). For this, we first replace one letter by the other before encrypting. This is why the letter J is not present in the following square.

    ┌───────────────┐
    │ 1  2  3  4  5 │
┌───┼───────────────┤
│ 1 │ A  B  C  D  E │
│ 2 │ F  G  H  I  K │
│ 3 │ L  M  N  O  P │
│ 4 │ Q  R  S  T  U │
│ 5 │ V  W  X  Y  Z │
└───┴───────────────┘
Typical modern square using the Latin alphabet

To encode a message, each letter is translated to its coordinates in the grid – typically first row, then column. For instance, the letter X is at row 5 and column 3. Thus, the plaintext letter X translates to the ciphertext 53.

For the typical Latin alphabet square above we get the following map:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
11 12 13 14 15 21 22 23 24 24 25 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55

What makes the Polybius cipher special?

By applying a Polybius cipher encryption you shrink the set of symbols necessary to represent a message from the original alphabet (typically 26 symbols) to the set of symbols you need to denote the coordinates of each letter in the ciphertext (typically 5 symbols). This can be very useful for telegraphy, steganography, and cryptography.

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