Polyalphabetic

The Bifid Cipher is a Fractionating Transposition cryptographic technique that was invented by the French amateur cryptographer Félix Delastelle in 1901. It is a fractionating transposition cipher that combines elements of both substitution and transposition methods.

The Bifid Cipher operates on a square grid known as the Polybius square or Polybius checkerboard. This square consists of a 5x5 grid containing the letters of the alphabet (usually excluding the letter J).

The encryption process in the Bifid Cipher involves the following steps:

1. Key Generation: A keyword or passphrase is chosen, and any duplicate letters are removed. The remaining unique letters of the keyword are then combined with the remaining letters of the alphabet to form the key.
2. Polybius Square: A 5x5 Polybius square is created, with the letters of the key filling the first row, and the remaining letters of the alphabet filling the subsequent rows in order.
3. Message Conversion: The plaintext message is divided into individual letters and each letter is replaced with its corresponding row and column numbers in the Polybius square.
4. Fractionation: The row and column numbers obtained in the previous step are combined into pairs, creating a new sequence of numbers.
5. Transposition: The pairs of numbers obtained from the fractionation step are written as a single sequence and divided into two equal parts.
6. Encryption: The row and column numbers corresponding to each part are located in the Polybius square, and the corresponding letters are identified.

The resulting encrypted text is a substitution cipher, where each letter in the plaintext is replaced with a pair of letters in the ciphertext. To decrypt the Bifid Cipher, the process is reversed, using the same key and Polybius square.

The Bifid Cipher offers a level of security by fractionating the plaintext, making it more resistant to frequency analysis and other classical cryptographic attacks. However, modern cryptanalysis techniques have rendered the Bifid Cipher relatively easy to break.

Despite its susceptibility to modern cryptographic analysis, the Bifid Cipher remains an interesting historical cipher and serves as a foundation for more complex cryptographic systems.

The Beaufort Cipher is a polyalphabetic substitution cipher that was invented by Sir Francis Beaufort in the 19th century. The cipher is closely related to the Vigenère Cipher but works slightly differently. Unlike the Vigenère Cipher, the Beaufort Cipher uses a reversed encryption and decryption algorithm, which means the ciphertext is produced by reversing the order of the alphabets used in the Vigenère method. This unique approach makes it distinctive and more challenging to break compared to similar ciphers.

The Beaufort Cipher was historically used in military applications due to its robustness in creating encrypted messages that are harder to decipher through simple cryptanalysis. Although it is not commonly used today, it stands as an important part of cryptographic history and was utilized up until more advanced encryption techniques became standard.

To encrypt with the Beaufort Cipher, one uses a keyword, and the plaintext characters are "subtracted" from the keyword characters rather than added, as with the Vigenère Cipher. This results in an encryption pattern that is inverse to Vigenère.

Example

Let’s say the keyword is ROYAL and we want to encrypt the plaintext ATTACK.

1. Key: ROYAL repeated as necessary to match the length of the plaintext.
2. Resulting Key Sequence: ROYALR.

Each letter in the plaintext is encrypted by using the Beaufort Cipher's reversed alphabet calculation.

So, ATTACK encrypted with the keyword ROYAL using the Beaufort Cipher would yield RVFAJH as the ciphertext.

The Autokey Cipher, invented by Blaise de Vigenère in the 16th century, is a form of polyalphabetic substitution cipher that improves on the traditional Vigenère cipher by incorporating the plaintext itself into the key. This cipher was designed to strengthen encryption by reducing repetitive patterns in the key, making it more resistant to frequency analysis. The concept of the Autokey Cipher builds on Vigenère's previous work and is part of what’s sometimes called the Vigenère family of ciphers. It gained popularity due to its enhanced complexity and its ability to make cryptanalysis more difficult compared to earlier ciphers.

In the Autokey Cipher, the encryption key is generated by appending part of the plaintext to the initial keyword. For example, if the keyword is short, the plaintext itself effectively extends the key, which prevents repeating patterns in the encryption. This method creates a unique and shifting key for each character of the plaintext, ensuring that identical characters in the plaintext do not correspond to the same characters in the ciphertext.

To encrypt a message, the Autokey Cipher uses a Vigenère table or a Caesar shift for each character in the plaintext, with shifts determined by the characters in the key (which is composed of both the keyword and the plaintext). This makes it harder for attackers to detect regularities that could reveal the key or plaintext.

Example

Let’s say the keyword is "KING" and we want to encrypt the plaintext "DEFEND".

1. Initial Key: KING + DEFEND (plaintext appended).
2. Resulting Key Sequence: KINGDEF.

Now, encrypt each letter of the plaintext "DEFEND" using the corresponding character in the key sequence.

So, "DEFEND" encrypted with the keyword "KING" using the Autokey Cipher would yield "NMSKQH" as the ciphertext.

The Alberti cipher, created by Leon Battista Alberti in the 15th century, is recognized as one of the earliest examples of a polyalphabetic substitution cipher. Alberti, an Italian Renaissance polymath, developed this cipher as a response to the need for stronger, more secure encryption methods that could withstand frequency analysis, a technique that had become effective against simpler monoalphabetic ciphers. The Alberti cipher represents a significant advancement in cryptography, as it was among the first to use multiple alphabets to encode a single message.

Alberti invented a cipher disk, known as the Alberti Cipher Disk, which consisted of two rotating rings: an outer ring containing the plaintext alphabet in uppercase letters and an inner ring with a shifted or scrambled alphabet in lowercase. The outer disk would remain stationary, while the inner disk could rotate to change the substitution relationship between plaintext and ciphertext characters. This enabled the use of multiple alphabets throughout the message, significantly increasing encryption strength.

The key innovation of the Alberti cipher was the ability to change the substitution alphabet during encryption. This process is known as polyalphabetic substitution, where a keyword or special signal letter in the message would prompt the encoder to rotate the inner disk, thereby switching the alphabet used for substitution. By frequently changing the alphabet, the alberti cipher made it challenging for unauthorized parties to decipher the text by frequency analysis, as the same plaintext character would not always correspond to the same ciphertext character.

Suppose we want to encrypt the message "SECRET" using an Alberti cipher disk. We can set the inner disk so that it initially aligns with the letter A on the outer disk corresponding to a lowercase letter on the inner disk. Each time we encounter a special signal, we rotate the inner disk by a predetermined increment.

1. Initial Alignment: Outer disk A aligns with inner disk d.
2. First Letter: S (outer disk) → encrypted as d.
3. Rotate Inner Disk by One.
4. Second Letter: E (outer disk) → encrypted as w.

Repeat this for each letter in "SECRET," rotating the inner disk based on a predefined rule or keyword.

Since the Alberti cipher employs a polyalphabetic approach, a full substitution table would not apply as each rotation modifies the substitution dynamically.