Cadenus Cipher

The Cadenus cipher is a columnar transposition cipher with an additional rotation of the columns.

The encryption requires a keyword and an alphabet (usually 25 letters).

Step 1: write the message by rows in a grid of 25 rows and N columns with N the size of the key (without repeated letters).

Step 2: shift each column by a number of steps equal to the value of its key letter (each column then starts with the letter that was in the row labeled by its key letter).

Step 3: sort the columns according to the alphabetical order of the keyword

Step 4: read the rows horizontally

Step 1: First write the encrypted block by rows in a table with N columns named after the N letters of the keyword sorted alphabetically.

Step 2: Reorder the columns into the original keyword order.

Step 3: Circularly shift each column downwards by a number of steps equal to the value of its key letter (inverse rotation of the encryption).

Step 4: Finally read the grid by rows to recover the plaintext.

No explanation seems to have been given. The cipher would work just as well with 26 letters (dCode offers this option).

The first key, the column permutation keyword, determines, after removing its repeated letters, the number N of columns as well as their final order, obtained by sorting its letters alphabetically.

The second key, the rotation key, is a permutation of the letters of the alphabet: rotating a column consists of bringing to the top of it the row whose label is its key letter.

It is possible to reuse a single keyword for both roles.

Split the text into blocks of 25 × N letters and encrypt each block independently, with the same grid, the same keyword and the same rotations, then concatenate the encrypted texts.

Messages encrypted with Cadenus theoretically have a length that is a multiple of 25 (with 25 being the alphabet size).

The frequency histogram and the index of coincidence are similar to that of the plaintext language.

The probable-word attack is the reference method: choose a supposed plaintext word, write it vertically in slices of N letters, then search for each slice in the columns of the ciphertext by scanning the 25 possible rotations of each column.

Brute force is also conceivable: treating rotations as independent, a period 6 represents 6!×24^6 configurations, i.e. about 140 billion.