Substitution ciphers are a cornerstone of classical cryptography and have been used for thousands of years to encrypt and decrypt messages.
The first ever published description of how to crack simple substitution ciphers was given by Al-Kindi in A Manuscript on Deciphering Cryptographic Messages written around 850 CE. The method he described is now known as frequency analysis (Wikipedia).
A substitution cipher is a method of encryption where units of plaintext are replaced with ciphertext in a defined manner, with the help of a key. The units may be single letters, pairs of letters, triplets of letters, mixtures of the above, and so forth. In a substitution cipher, the units of the plaintext are retained in the same sequence in the ciphertext, but the units themselves are altered.
There are different types of substitution ciphers, such as simple substitution cipher and polyalphabetic cipher. A monoalphabetic cipher uses fixed substitution over the entire message, whereas a polyalphabetic cipher uses a number of substitutions at different positions in the message, with each letter of the plaintext being potentially replaced by multiple different letters or symbols.
Types of Substitution Ciphers
Substitution ciphers are a method of encryption where each letter in the plaintext is replaced by another letter or symbol. They are one of the simplest forms of encryption and form a significant part of the history and evolution of classical cryptography. There are primarily two types of substitution ciphers: monoalphabetic substitution ciphers and polyalphabetic substitution ciphers.
Monoalphabetic Substitution Ciphers
In a monoalphabetic substitution cipher, each letter in the plaintext is replaced by only one other letter throughout the entire text. This implies that the same plaintext letter always gets replaced by the same ciphertext letter, and vice versa.
For example, if ‘A’ is replaced by ‘D’, every ‘A’ in the plaintext will be replaced by ‘D’ in the ciphertext. This type of cipher uses a fixed substitution over the entire message.
Some popular examples of monoalphabetic substitution ciphers include:
- Atbash Cipher: Mirrors the alphabet for letter replacement.
- Caesar Cipher: Shifts letters a fixed number of positions.
- Affine Cipher: Applies a mathematical operation (shift and multiply) for substitution.
- Baconian Cipher: Converts letters into binary sequences.
- Pigpen Cipher: Replaces letters with symbols.
- Playfair cipher: Substitutes letter pairs (digraphs) instead of individual letters.
Polyalphabetic Substitution Ciphers
On the other hand, polyalphabetic substitution ciphers use multiple cipher alphabets. With this type of cipher, each letter of the plaintext is potentially replaced by multiple different letters or symbols depending on its position in the text.
This means that the same plaintext letter can be replaced by different ciphertext letters at different positions in the message. This increases the complexity of the cipher and makes it more resistant to frequency analysis, a common technique for breaking substitution ciphers.
Examples of polyalphabetic substitution ciphers include:
- Vigenère cipher: Utilizes a keyword to dictate letter shifts, creating a more complex code.
- Autokey cipher: Employs the message itself as a key for letter shifts.
- Beaufort cipher: A variant of the Vigenère cipher with an additional keyword layer.
- Gronsfeld Cipher: Involves a key and a lookup table for substitution
Other Notable Ciphers:
- ADFGVX Cipher (German Field Cipher): Uses a bigram table for substitution during World War I.
- Bifid Cipher (Delastelle’s): Separates letters into two alphabets for independent substitutions.
- Trifid Cipher (Delastelle’s): Similar to Bifid, but uses three alphabets.
- Homophonic Substitution Cipher: Assigns multiple letters to the same ciphertext symbol.
- One-Time Pad: The only theoretically unbreakable cipher, requiring a key as long as the message. (Not truly a substitution cipher in the strictest sense, but often included in discussions)
Famous Substitution Ciphers
The Caesar Cipher
One of the earliest known substitution ciphers is the Caesar Cipher, named after Julius Caesar who used it to communicate with his officials. The operation of the Caesar Cipher is incredibly simple. Each letter in the plaintext is shifted a certain number of positions down the alphabet. For instance, with a shift of 3, ‘A’ would be encrypted as ‘D’, ‘B’ as ‘E’, and so on. Despite its simplicity, the Caesar Cipher marked the inception of coded communication, a concept that would evolve and become essential in various fields, including military, diplomacy, and modern computing. Learn more about the Caesar Cipher here.
The Vigenère Cipher
Building on the principles of the Caesar Cipher, the Vigenère Cipher adds a layer of complexity by using a series of different Caesar ciphers based on a keyword. For example, if the keyword is ‘KEY’, the first letter of the plaintext is shifted according to ‘K’, the second according to ‘E’, the third according to ‘Y’, and then the cycle repeats. This method of multiple substitutions makes the Vigenère Cipher more secure against frequency analysis, a common method of cracking substitution ciphers. Discover more about the Vigenère Cipher here.
The Enigma Machine
The Enigma Machine, used during World War II, stands as a testament to the sophistication that substitution ciphers can achieve. Unlike the Caesar and Vigenère Ciphers, the Enigma Machine used rotating disks and plugboards to perform a series of substitutions, making it a highly secure system at the time. The complexity of the Enigma Machine and the crucial role it played in wartime communication highlight the power of substitution ciphers in cryptography.
Cryptanalysis of Substitution Ciphers
Cryptanalysis, the art of deciphering encoded messages without the key, involves different techniques when it comes to substitution ciphers. Two common methods used are frequency analysis and keyword analysis.
Frequency Analysis
Frequency analysis is a common method used to crack substitution ciphers. This technique involves statistically analyzing the frequency of occurrence of different characters in the cipher text and matching them to the frequency of letters in the plain text language (Source).
The earliest known description of frequency analysis dates back to around 850 CE, where Al-Kindi detailed the method in A Manuscript on Deciphering Cryptographic Messages. This method is particularly effective against simple substitution ciphers, which are a type of monoalphabetic cipher.
Frequency analysis operates on the fact that in any written language, certain letters and combinations of letters occur with predictable frequencies. For instance, in the English language, the letters E, T, A and O are the most frequently used. By comparing these frequency patterns, a cryptanalyst can make educated guesses about the likely plaintext substitutions of the cipher text characters.
Keyword Analysis
Keyword analysis is another technique used in the cryptanalysis of substitution ciphers. This method involves the use of a keyword to generate a substitution alphabet. The traditional keyword method for creating a mixed substitution alphabet is simple but has a disadvantage that the last letters of the alphabet (which are mostly low frequency) tend to stay at the end. A stronger way of constructing a mixed alphabet is to generate the substitution alphabet completely randomly.
This method is often used in deciphering polyalphabetic ciphers, which use multiple substitution alphabets in the encoding process. By identifying the keyword, a cryptanalyst can reverse-engineer the substitution alphabets used, making it possible to decode the cipher text.
Strengths and Weaknesses of Substitution Ciphers
Advantages of Substitution Ciphers
One of the key advantages of substitution ciphers is their simplicity. This type of cipher is a straightforward cryptographic algorithm that replaces each letter in the plaintext with a different letter or symbol (Source). This makes substitution ciphers relatively easy to implement and understand.
In comparison to transposition ciphers, where the units of the plaintext are rearranged in a complex order, substitution ciphers retain the units of the plaintext in the same sequence in the ciphertext, albeit altered. This can make the encryption and decryption processes more straightforward.
Disadvantages of Substitution Ciphers
Despite their simplicity, substitution ciphers have significant limitations. One of the main weaknesses is their vulnerability to frequency analysis. This method involves analyzing the most commonly used letters and patterns in the ciphertext and matching them to the most common letters and patterns in the plaintext. Given enough text, a substitution cipher can be broken with relative ease.
Furthermore, substitution ciphers do not offer any significant cryptographic advantages in the modern age. They are mainly used for recreational purposes, such as in puzzles or games. In the face of modern computational power and advanced cryptographic algorithms, the security offered by substitution ciphers is negligible.