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Four-Square Cipher

 

Background

The Four-Square cipher is similar to the Playfair cipher. It was developed by the Frenchman Felix Marie Delastelle (*1840; † 1902)1. He also developed the Bifid cipher.

 

Principle

Contrary to the Playfair cipher, two Polybius matrices are used for the Four-Square cipher. Both matrices should ideally be constructed with a different password. Both Polybius matrices are then assigned to two ordered plaintext matrices. In figure 1, plaintext matrices have a blue background and Polybius matrices have a green background. The right upper matrix has been created with the key "KRYPTOGRAPHIE" and the lower left matrix has been created with the key "BEISPIEL".

four-square2
Fig. 1: Four-Square cipher (GE → IE)
For the message "GEHEIMNIS" the characters in the message are split up into pairs analogous to the Playfair cipher. It is not necessary to replace doubly occurring characters. For an uneven number of characters, an additional character has to be inserted at the last position. "GEHEIMNIS" therefore is split up into "GE HE IM NI SX". Now, a rectangle is drawn with the corners being the G in the upper left matrix and the E in the lower right matrix. The two remaining corners of the rectangle, which lie in the green fields, determine the characters in the ciphertext. GE is therefore encoded by IE. And HE is encoded by II, as can be seen in figure 2.

four-square3
Fig. 2: Four-Square cipher (HE → II)
The complete ciphertext is therefore: "IE II GM DC NX".

 

Security

The Four-Square cipher is very similar to the Playfair cipher in terms of security. It can be cracked very fast for a sufficiently long enough message. It also is quite difficult to handle because of the presence of two keys and four matrices. But this also leads to one advantage over the Playfair cipher:. There the word OTTO for example would be encoded by XY YX; the characters are reversed in both the cleartext and the ciphertext. In the Four-Square cipher, this pattern is not conserved in the ciphertext. OTTO is encoded, according to figure 2 by DT QM.

 

Details

The Four-Square cipher belongs to the monoalphabetic ciphers just like the Playfair cipher. Since pairs of characters are created during the encoding process, it also belongs to the class of bigraphic methods.

 

Weblinks

http://en.wikipedia.org/wiki/Four_square_cipher

 

References

1 o.V.: "Félix Delastelle", http://en.wikipedia.org/wiki/Felix_Marie_Delastelle, 2009-02-20

 
   
     
 
 
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