For The Love of Ciphers: Félix-Marie Delastelle

Two-square, three-square and four-square

The French cryptographer Félix-Marie Delastelle was born in 1850 and died in 1902. For most of his life, he worked as a bonded warehouseman at a local port. After his retirement in 1900, he published a 50-page book named Traité Élémentaire de Cryptographie. His love of creating ciphers was basically his hobby, and he was unusual as most of the people who worked in the field at the time were either academics, diplomats, or were in the military.

His core contribution includes fractionation and transposition, and from these, he created the Bifid cipher (created with two squares), the Trifid cipher (created with three squares) and the Four Square cipher. These types of ciphers are generally known as polygraphic substitution ciphers, and where two or more letters are taken at a time and then ciphered.

Four square cipher

The four-square cipher uses four squares, and where we take pairs of letters and, using the first and last square, we find the letters that are bounded by the two letters (like Playfair). It was invented by Félix Delastelle and published in 1902.

It uses four 5x5 matrices arranged in a square. Each matrix contains 25 letters. The upper-left and lower-right matrices are the “plaintext squares” and each contains a standard alphabet. The upper-right and lower-left squares are the “ciphertext squares” and have a mixture of characters.

First, we break the message into bi-grams, such as ATTACK AT DAWN gives:

AT TA CK AT DA WN

We now use the four ‘squares’ and locate the bigram to encrypt in the plain alphabet squares. With ‘AT’, we take the first letter from the top left square and the second letter from the bottom right square:

    a b c d e   Z G P T F
    f g h i k   O I H M U
    l m n o p   W D R C N
    q r s t u   Y K E Q A
    v w x y z   X V S B L
     
    M F N B D   a b c d e
    C R H S A   f g h i k
    X Y O G V   l m n o p
    I T U E W   q r s t u
    L Q Z K P   v w x y z