Quagmire 3 Cipher

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

It relies on three keywords:

— The first is used to build a mixed plaintext alphabet.

— The second determines the successive shifts of the cipher alphabets and sets the repetition period.

Quagmire III belongs to the Quagmire cipher family and corresponds to plan K3.

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 ciphertext alphabet

— $ I $ is the rank of the indicator letter in the mixed plaintext 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.

— 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.

— Choose an indicator letter, usually A by convention. This letter belongs to the mixed plaintext alphabet and indicates the reference column.

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

Decryption is the reverse operation of encryption. It requires knowledge of the initial keyword or mixed 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 row corresponding to the current position of the periodic keyword, then read the plaintext letter at the top of the column (mixed plaintext alphabet).

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 III, the alphabet used to locate plaintext letters is mixed using the first keyword, while the cipher alphabet is mixed using the second keyword, and the rows are rotations of this mixed cipher 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.