Draft:Aristocrat Cipher

The Aristocrat Cipher is a type of monoalphabetic substitution cipher in which plaintext is replaced with ciphertext and encoded into assorted letters, numbers, and symbols based on a keyword. The formatting of these ciphers generally includes a title, letter frequency, keyword indicators, and the encoders nom de plume. The predecessor to these ciphers stems from the Caesar Cipher around 100. The Aristocrat Cipher also used a transposition of letters to encrypt a message.

History
Coined in 1929 by a group of friends, a part of the American Cryptogram Association (ACA), the Aristocrat Cipher's name was a play on words intended to show the organization as high class and intellectual. The Aristocrat Cipher was termed the "Aristocrat of Puzzles" and was a change in the paradigm of cryptography.

Substitution Ciphers and the Aristocrat Cipher are still used in many ways today including storage encryption, password encryption, cyber security, etc. The most common of these is data encryption, where using the Encryption Algorithms you convert plaintext to ciphertext, allowing your data to be stored without easy exfiltration.

History
Monoalphabetic substitution ciphers originated from a man named Leon Battista Alberti, who was born February 14, 1404 in Genoa, Italy. Alberti was the illegitimate son of Lorenzo Alberti, and at the age of 10, learnt Latin and studied mathematics. Alberti got a degree in law from the University of Bologna, however, he soon realized that he favored the arts and sciences. In 1432, he became the Papal Chancery, and in 1434, at a visit to Florence in the papal secretariat, he discovered an interest for cryptography. Alberti became friends with Leonardo Dati, who instructed him on the art of cryptology.

In 1467, Alberti conceived of a disk which held 24 equal segments called cells that contained letters, and a movable inner circle which contained ciphertext symbols. This became known as the Alberti Disk and was the very first polyalphabetic cipher in history. Alberti's disk also helped develop the monoalphabetic ciphers, by compartmentalizing plaintext and ciphertext.

Types of Aristocrat Ciphers
The Aristocrat Ciphers have four main types: K1, K2, K3, and K4.

K1 Aristocrat Cipher - Being the most popular cipher, it uses a keyed plaintext to encrypt a message.

K2 Aristocrat Cipher - This type uses a keyed ciphertext in order to encrypt the message (Example in Encryption Section).

K3 Aristocrat Cipher - This type uses both a keyed plaintext and a keyed ciphertext, but the keys are the same for both.

K4 Aristocrat Cipher - This type also uses a keyed plaintext and ciphertext, but the keys are not the same for both.

These types allow cryptographers to diversify their encryption techniques and help prevent decryption of the message. Under the ACA guidelines, "No letter can map to itself".

Homophones
Cite Reference: Substitution Ciphers

A homophone is a type of cipher in which each plaintext character translates to some ciphertext letters or symbols. Ciphers that use this method are called homophonic ciphers, some of these ciphers are the Hill Cipher and Playfair Cipher. Homophonic ciphers can be decrypted to multiple messages. Ciphers that include multiple messages are called High-Order Homophonic. High-order ciphers outline multiple keys for encryption and decryption, this means that depending on your key you'd receive a different message.

K2 Aristocrat Cipher Encryption
K2 Aristocrat would be the message "The quick brown fox jumped over the lazy dog", using the keyword "jumping".

The plaintext to ciphertext would translate to the letters in the box below, since you're inputting your keyword at the beginning and retyping the alphabet, but omitting the letters being used in your keyword. Also, if letters overlap at the end of the alphabets, so Z-Z or X-X, then move them to the front in order to make it more secure and follow ACA guidelines.

Security
The cypher can be broken using cryptanalysis methods, especially when using a keyword. If keywords were excluded, it would make the puzzle more secure, but there still are ways around the encryption. The most known way is frequency analysis, this uses the distribution of letters throughout texts to infer what the ciphertext would be. The method creates a chain-reaction when a letter is decrypted, this means that after decrypting a word, the letters of that word can be used to decrypt other words.

Depending on the type of cipher, a brute force attack method can be used, which attempts to use all possible keys for the encryption. David Kahn states in The Codebreakers, "If a cryptanalyst tried one of these (403,291,461,126,605,635,584,000,000 possible keys) every second, he or she would need 1.2788 x 109 years to run through them all."

Frequency Analysis
There are many ways to decode these ciphers, the most common being frequency analysis. The process of frequency analysis can be complicated, and it uses educated analysis of the frequency of letters in texts to declassify the key. By calculating the frequency distribution for the K2 Aristocrat and comparing it to the English Distribution, the translation can be estimated. This can be compared to the English Language Allocation Map. The most likely correlation would be toward Z or C for the letter E, since they have the highest frequencies.