Quagmire 4 Cipher

Quagmire IV is a periodic polyalphabetic substitution cipher, related to the Vigenère cipher.

It uses two mixed alphabets (plaintext and ciphertext) and a periodic keyword.

It belongs to the Quagmire cipher family and corresponds to plan K4.

Two methods can be used to encrypt a message.

Mathematical method: by numbering letters from A to Z from $ 0 $ to $ 25 $, encryption is expressed as $$ C = (P + K - I) \bmod 26 $$

— $ P $ is the rank of the plaintext letter in the mixed plaintext alphabet

— $ K $ is the rank of the periodic keyword letter in the mixed plaintext alphabet

— $ I $ is the rank of the indicator letter in the mixed ciphertext alphabet

— $ C $ is the rank of the encrypted letter in the mixed ciphertext alphabet

Visual method with a table:

Build the encryption table from the two mixed alphabets, the periodic keyword and the indicator letter.

Split the plaintext into blocks of $ N $ letters, where $ N $ is the length of the periodic keyword.

For each plaintext letter, locate its position in the mixed plaintext alphabet, then read the encrypted letter in the row corresponding to the periodic keyword letter, using the indicator letter column as reference.

— Build the mixed plaintext alphabet by writing the first keyword without its repeated letters, then adding the remaining letters of the natural alphabet in their usual order.

— Build the mixed ciphertext alphabet using the second keyword.

— Choose an indicator letter from the mixed ciphertext alphabet. This letter indicates the reference column.

— Choose a periodic keyword and build the rows of the table so that each row contains the mixed plaintext alphabet shifted so that the periodic keyword letter (taken from the plaintext alphabet) appears in the indicator letter column.

Decryption is the reverse operation of encryption. It requires knowledge of the first keyword or mixed plaintext alphabet, the second keyword or mixed ciphertext alphabet, the periodic keyword, and the indicator letter in order to reconstruct the table.

Split the ciphertext into blocks of $ N $ letters, where $ N $ is the length of the periodic keyword.

For each encrypted letter, locate that letter in the header (mixed ciphertext alphabet), then read the plaintext letter in the row corresponding to the current position of the periodic keyword, at the found column.

In the classic Vigenère cipher, the plaintext and the cipher alphabets use the natural alphabet from A to Z. Each cipher alphabet corresponds to a rotation of this alphabet.

In Quagmire IV, the alphabet used to locate plaintext letters is mixed using the first keyword, while the cipher alphabet is mixed using the second keyword. Moreover, the indicator letter is taken from the ciphertext alphabet.

Decryption therefore requires recovering both mixed alphabets, the periodic keyword and the indicator letter.

The markers are similar to the Vigenère cipher, but frequency analysis is made more complex by the presence of two mixed alphabets and by the use of an indicator letter taken from the ciphertext alphabet.