Polybius square May 28, 2010

A cryptographic tool for accomplishing one or more of the following with an alphabetic message:

- coding to make it easier to transmit (using simple techniques such as flashes of light)
- encrypting to make it more difficult for others to read (aside from your intended recipient)

The square is a grid of letters which is often 5x5 or 6x6 (for our alphabet):

  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

* J is treated the same as I, since there are only 25 spots.

  1 2 3 4 5 6
1 A B C D E F
2 G H I J K L
3 M N O P Q R
4 S T U V W X
5 Y Z 0 1 2 3
6 4 5 6 7 8 9

Squares may also be arranged with a keyword, such as this one with "subway":

  1 2 3 4 5
1 S U B W A
2 Y C D E F
3 G H I K L
4 M N O P Q
5 R T V X Z

To encode a message, use the row and column numbers for each letter:
(I will use the 6x6 square above.)

Y  O  U  R  J O B  I S  T O  F I N D  K I T T E N
51 33 43 36 243312 2341 4233 16233214 252342421532

Now you can tap out these numbers to your loyal minion while you both sit at your local library, innocently reading last year's almanac and garnering the glaring stares of the other patrons. Tap tap tap tap. Tap tap tap. Tap tap tap tap. Tap. Tap. Tap tap tap tap tap. Tap tap tap. Tap tap tap. Tap tap tap tap. Tap tap. Tap tap. Tap tap. Tap. Tap tap tap tap tap. Tap tap tap. Tap tap tap tap tap tap. Tap. Tap tap tap tap. Tap tap tap. Tap tap tap tap tap tap. Tap tap tap. Tap tap tap. Tap tap tap. Tap tap tap tap. Tap. Tap tap. Tap tap tap. Tap tap tap. Tap tap tap tap. Tap tap tap tap tap tap.

Even if you use a keyword-ordered square, someone who can solve a monoalphabetic substitution cipher will probably be able to solve your 41241111153124 without the keyword.

This is where the "square" part comes in. Because of this, any sequence of numbers 1-5 or 1-6 can be decoded into the corresponding square's alphabet. Thus if we rearrange the numbers of our encoded message, even splitting up the numbers which compose single letters (Y = 51), we can decode the new sequence of numbers into a string of completely different letters. This also conceals the use of the Polybius square, as we have returned to the original alphabet instead of numbers 1-6 which are more easily identified as resulting from a method such as this.

As a simple example, take the encoded kitten message from above (51334 33624 33122 34142 33162 33214 25234 24215 32) and split it into two by removing every other number:

5 3 4 3 2 3 1 2 4 4 3 1 2 3 1 2 2 4 4 1 3
 1 3 3 6 4 3 2 3 1 2 3 6 3 2 4 5 3 2 2 5 2

Writing these two lines one after the other, we get: 534323124431231224413 133643231236324532252. And finally, using the 6x6 square to turn these newly arranged number pairs into letters again, we arrive at:

53 43 23 124431...
0  U  I  B V M IBJSMO7NMI6J0HZ

Key to this method is choosing a difficult-to-crack rearrangement.

See also: the similar but more complex straddling checkerboard.


Linked from: eriko-chan-cipher, straddling-checkerboard