Two-square cipher

The Two-square cipher, also called double Playfair, is a manual symmetric encryption technique . It was developed to ease the cumbersome nature of the large encryption/decryption matrix used in the four-square cipher while still being slightly stronger than the (single-square) Playfair cipher.

The technique encrypts pairs of letters (digraphs), and thus falls into a category of ciphers known as polygraphic substitution ciphers. This adds significant strength to the encryption when compared with monographic substitution ciphers which operate on single characters. The use of digraphs makes the two-square technique less susceptible to frequency analysis attacks, as the analysis must be done on 676 possible digraphs rather than just 26 for monographic substitution. The frequency analysis of digraphs is possible, but considerably more difficult - and it generally requires a much larger ciphertext in order to be useful.

The two-square cipher comes in two varieties - horizontal and vertical. The vertical two-square uses two 5 by 5 matrices one above the other. The horizontal two-square has the two 5 by 5 matrices side by side. Each of the 5 by 5 matrices contains the letters of the alphabet (usually omitting "Q" or putting both "I" and "J" in the same location to reduce the alphabet to fit). The alphabets in both squares are generally mixed alphabets, each based on some keyword or phrase.

To generate the 5 by 5 matrices, one would first fill in the spaces in the matrix with the letters of a keyword or phrase (dropping any duplicate letters), then fill the remaining spaces with the rest of the letters of the alphabet in order (again omitting "Q" to reduce the alphabet to fit). The key can be written in the top rows of the table, from left to right, or in some other pattern, such as a spiral beginning in the upper-left-hand corner and ending in the center. The keyword together with the conventions for filling in the 5 by 5 table constitute the cipher key. The two-square algorithm allows for two separate keys, one for each matrix.

As an example, here are the vertical two-square matrices for the keywords "example" and "keyword:"

Encryption using two-square is basically the same as the system used in four-square, except that the plaintext and ciphertext digraphs use the same matrixes.

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