Symmetric

A Digraph Cipher is a cryptographic technique that operates on pairs of letters (digraphs) rather than individual letters. It is a substitution cipher where each digraph in the plaintext is replaced by a corresponding digraph in the ciphertext according to a predefined rule or key.

Here's a general overview of how a Digraph Cipher works:

• Key Generation: The sender and receiver agree on a specific encryption rule or key that determines the mapping between digraphs in the plaintext and the corresponding digraphs in the ciphertext.
• Splitting into Digraphs: The plaintext is divided into pairs of letters (digraphs). If the plaintext contains an odd number of letters, a padding character (such as X) may be added at the end to form a complete digraph.
• Encryption: Each digraph in the plaintext is replaced by the corresponding digraph in the ciphertext according to the encryption rule or key.
• Decryption: The receiver uses the same encryption rule or key to decipher the ciphertext. Each digraph in the ciphertext is replaced by the corresponding digraph in the plaintext.

The encryption and decryption rules in a Digraph Cipher can vary depending on the specific algorithm or key chosen. Some common approaches include:

• Digraph Substitution: Each digraph is replaced with a different digraph based on a substitution table or matrix. For example, the digraph AB in the plaintext might be replaced by the digraph XY in the ciphertext.
• Digraph Transposition: The order of the digraphs in the plaintext is rearranged according to a specific transposition rule or permutation. This rearrangement can be based on the positions of the letters within the digraphs or other predetermined patterns.
• Digraph Combination: The encryption process may involve a combination of substitution and transposition techniques, where digraphs are both substituted and rearranged.

The security of a Digraph Cipher depends on the complexity and randomness of the encryption rule or key. It is important to use a sufficiently large set of possible digraph mappings to ensure resistance against cryptanalysis techniques such as frequency analysis.

Digraph Ciphers have been used historically as a way to enhance the security of simple substitution ciphers by introducing an additional layer of complexity. However, they are generally considered relatively weak compared to more modern and sophisticated encryption methods.

It's worth noting that while the concept of Digraph Ciphers provides an interesting perspective on encryption, they are not commonly used in modern cryptography. Instead, more advanced algorithms, such as symmetric key ciphers (e.g., AES) or public-key ciphers (e.g., RSA), are employed to ensure stronger security.

A Digraph Cipher is a type of substitution cipher that encrypts pairs of letters (digraphs) from the plaintext, rather than single letters as in simpler substitution ciphers. The Playfair cipher is one well-known example of a digraph cipher.

Below is an example of a Playfair Cipher table (which is a type of Digraph Cipher) using the keyword "CIPHER." The table is constructed by placing the keyword at the start and filling the rest of the 5x5 grid with the remaining letters of the alphabet (I and J are typically treated as the same letter in Playfair).

Step 1: Construct the Playfair Table

Keyword: CIPHER

1. Remove duplicate letters from the keyword.
• CIPHER → C, I, P, H, E, R
2. Fill the table with the keyword first, followed by the remaining letters of the alphabet (excluding J, or combining I/J):

Playfair Cipher Table Example:

Step 2: Encrypting with the Digraph Cipher

To encrypt with the Playfair cipher, you follow these basic rules:

1. Pair the letters of the plaintext into digraphs (groups of 2). If a digraph contains the same letter twice (e.g., "LL"), insert an "X" between them.
2. Locate the letters of each digraph in the table.
• If both letters appear on the same row, replace them with the letters immediately to their right (wrapping around if needed).
• If both letters appear in the same column, replace them with the letters immediately below them (wrapping around if needed).
• If the letters form a rectangle, replace them with the letters at the other corners of the rectangle.

Example

Suppose we want to encrypt the word "HELLO":

1. Convert to digraphs: "HE LL O"
• "LL" becomes "LX" (to break the repeated letters)
• So, now we have the pairs: "HE", "LX", "LO"
2. Use the Playfair table to find and replace each digraph:

• "HE": H and E are in the same row. The letter to the right of H is E, and the letter to the right of E is C. So, "HE" becomes "EC".
• "LX": L and X form a rectangle. Replace L with X and X with L, so "LX" becomes "PX".
• "LO": L and O form a rectangle. Replace L with G and O with R, so "LO" becomes "GR".

3. The final encrypted message is: "EC PX GR"

This is how a Digraph Cipher using the Playfair cipher works with a simple table and a keyword.

A Dice Cipher, also known as a Dice Cryptography or a Book Cipher, is a cryptographic technique that uses dice as a randomization tool to generate a series of numbers that correspond to words or characters in a pre-selected reference book. It is a form of polyalphabetic substitution cipher.

Here's a general overview of how a Dice Cipher works:

1. Key Generation: The sender and receiver agree on a specific reference book, such as a novel, dictionary, or any other published text. This book serves as the key for encryption and decryption.
2. Dice Rolling: The sender rolls a set of dice and records the numbers that come up. Each roll corresponds to a specific word or character in the reference book. For example, if a roll produces the numbers 3, 1, and 5, the third word on the first page of the book might be chosen.
3. Encoding: The sender uses the selected words or characters from the reference book to encode their plaintext message. Each word or character is assigned a specific number or code based on its position in the book. The numbers generated by the dice rolls determine which words or characters to select.
4. Transmission: The sender transmits the encoded message to the receiver.
5. Decoding: The receiver uses the same reference book and dice rolls to decipher the encoded message. By matching the received numbers with the corresponding words or characters in the book, the original plaintext is recovered.

The security of a Dice Cipher depends on the randomness and fairness of the dice rolls, as well as the secrecy of the chosen reference book. It is essential to use fair dice and ensure that the rolls are truly random to avoid any biases that could compromise the encryption. Additionally, the reference book should be kept secret to prevent attackers from gaining access to the key.

One advantage of the Dice Cipher is that it does not require complex mathematical operations or algorithms. However, it does rely heavily on the randomness of the dice rolls and the secrecy of the book, making it more suitable for personal or low-security communications rather than high-stakes cryptography.

Dice Ciphers have a long history and have been used in various forms throughout the centuries. They offer an interesting and unconventional approach to encryption, often evoking a sense of intrigue and adventure.

The Columnar cipher is a transposition cipher that rearranges the characters of a message by writing them in a grid format and then reading them column by column in a specific order. It does not change the actual characters but alters their order to create the ciphertext.

Here's how the Columnar cipher works:

1. Choose a keyword or passphrase that will determine the order in which the columns are read.
2. Write the plaintext message in rows underneath the keyword, filling up the grid.
3. Read the columns of the grid in the order specified by the keyword.
4. Concatenate the characters from each column to form the ciphertext.

Let's illustrate this process with an example:

Plaintext: HELLO COLUMNAR CIPHER Keyword: CODE

Step 1: Prepare the grid based on the keyword CODE.

C O D E

H E L L 
O C O 
L U M N 
A R C I 
P H E R

Step 2: Read the columns in the order determined by the keyword CODE.

C O D E

L O C A 
E U M P 
L R H E 
L I R 
O P

Step 3: Concatenate the characters column-wise to obtain the ciphertext.

CIPHERCOLURMNELO

So, the plaintext HELLO COLUMNAR CIPHER encrypted with the Columnar cipher using the keyword CODE yields the ciphertext CIPHERCOLURMNELO.

To decrypt the ciphertext, you follow the same steps in reverse:

1. Use the keyword to determine the column order.
2. Write the ciphertext characters in the grid column by column.
3. Read the rows of the grid in the original order to obtain the plaintext.

The Columnar cipher relies on the secrecy of the keyword for its security. It is a form of transposition cipher and does not substitute or change the characters themselves. Instead, it rearranges the order of the characters to achieve encryption.

The Chaocipher is a cipher system invented by John Francis Byrne in 1918. Byrne, an American author and cryptologist, created this cipher with the hope of presenting a complex and supposedly "unbreakable" encryption system that could be used in the military and for diplomatic purposes. However, unlike many other historical ciphers, the Chaocipher remained a mystery for a long time, as Byrne kept the details of its inner workings a secret, even after presenting it to various cryptographic experts of his time. He demonstrated the cipher's security by sending encrypted messages to prominent cryptographers, challenging them to decode it without revealing the method.

For decades, the Chaocipher intrigued cryptologists because Byrne never disclosed the mechanism, and he even included it as an unsolved challenge in his autobiography. The inner mechanics of the cipher were finally revealed only in 2010, almost a century later, when Byrne's family donated his notes to the National Cryptologic Museum.

The Chaocipher works using two rotating alphabets, which change positions after encrypting each character, making it a polyalphabetic substitution cipher. The two alphabets interact in a way that makes each letter dependent on all previous letters in the message, resulting in a complex, interwoven encryption. Unlike other polyalphabetic ciphers where a keyword guides encryption, the Chaocipher relies on systematic rotations of the alphabets, which vary with every letter in the plaintext, creating a different substitution for each character.

Here’s a simplified example to illustrate the general process of the Chaocipher's mechanism. Note that a complete example is difficult without knowing the exact rotation rules and positions, as they are unique to the Chaocipher’s design.

Suppose we want to encrypt the word HELLO with the Chaocipher. We start with two wheels of alphabets:

1. Left Wheel (Plaintext Alphabet)
2. Right Wheel (Ciphertext Alphabet)

Each letter is encrypted by matching it from the Left Wheel to the corresponding letter in the Right Wheel. After each letter, both wheels are rotated in a specific way that changes the subsequent mappings, making each letter encrypted differently based on the evolving positions of the alphabets.

For example:

Each step would result in new configurations for the wheels, which makes reconstructing the encryption or decryption without knowing the rotations virtually impossible. This complexity was the essence of the Chaocipher’s mystery and its reputed security.

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.