Quagmire 2 Cipher

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

It relies on two keywords:

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

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

Quagmire II belongs to the Quagmire cipher family and corresponds to plan K2.

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 $$ C = (L + A - K) \bmod 26 $$

— $ L $ is the rank of the plaintext letter in the standard alphabet (unmixed)

— $ K $ is the rank of the letter of the second keyword in the standard alphabet (unmixed)

— $ A $ is the rank of the anchor 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 keywords and the anchor letter.

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

For each plaintext letter, locate its position in the standard alphabet, then read the encrypted letter in the row corresponding to the letter of the second keyword.

— Build the mixed ciphertext 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 anchor letter, usually A by convention. This letter belongs to the mixed ciphertext alphabet and indicates the reference letter to align.

— Choose a second keyword and build the rows of the table so that each row contains the mixed ciphertext alphabet shifted so that the anchor letter appears in the column corresponding to the letter of the second keyword associated with that row.

Decryption is the reverse operation of encryption. It requires knowing the first keyword, the second keyword and the anchor letter in order to reconstruct the table.

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

For each encrypted letter, locate that letter in the row corresponding to the current position of the second keyword, then read the plaintext letter at the top of the column (standard 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 II, the alphabet used to locate plaintext letters is the standard alphabet, while the cipher alphabet is mixed using the first keyword and the rows are rotations of this mixed alphabet.

Decryption therefore requires recovering the mixed cipher alphabet, the second keyword and the anchor letter.

The markers are identical to the Vigenère cipher.