Do identical plaintext map to identical cipher text of a letter frequency analysis attact against a substitution cipher
In the realm of classical cryptography, particularly when analyzing substitution ciphers, the question of whether identical plaintext maps to identical ciphertext is important to understanding the efficacy and vulnerability of these cryptographic methods. A substitution cipher is a method of encoding by which units of plaintext are replaced with ciphertext, according to a fixed system. The units may be single letters (the most common), pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver decodes the text by performing the inverse substitution.
To address the core of the question: in a substitution cipher, identical plaintext units will indeed map to identical ciphertext units. This characteristic is inherent to the design of substitution ciphers and is one of the primary reasons why they are susceptible to letter frequency analysis attacks.
Substitution Ciphers and Their Mechanism
Substitution ciphers can be categorized into two primary types: monoalphabetic and polyalphabetic.
1. Monoalphabetic Substitution Ciphers: In this type of cipher, each letter of the plaintext is replaced by a corresponding letter of the ciphertext alphabet. The relationship between plaintext and ciphertext is fixed throughout the message. For example, if 'A' is substituted with 'D', 'B' with 'E', and so on, the substitution pattern remains consistent for the entire message. Consequently, if the plaintext contains multiple occurrences of the letter 'A', each instance will be encrypted to 'D'.
2. Polyalphabetic Substitution Ciphers: These ciphers use multiple substitution alphabets to encrypt the plaintext. A common example is the Vigenère cipher, where the substitution pattern changes based on the position of the letter and a keyword. Despite this complexity, within a single substitution alphabet, identical plaintext units still map to identical ciphertext units.
Letter Frequency Analysis Attack
A letter frequency analysis attack exploits the predictable nature of monoalphabetic substitution ciphers. In any given language, certain letters appear more frequently than others. For instance, in English, the letter 'E' is the most common letter, followed by 'T', 'A', 'O', 'I', 'N', etc. When a substitution cipher is used, these frequency patterns are preserved in the ciphertext.
Example of Frequency Analysis:
Consider a simple monoalphabetic substitution cipher where:
– Plaintext: HELLO WORLD
– Ciphertext: KHOOR ZRUOG
Here, the substitution pattern might be:
– H -> K
– E -> H
– L -> O
– O -> R
– W -> Z
– R -> U
– D -> G
If an attacker intercepts the ciphertext "KHOOR ZRUOG", they can perform frequency analysis by counting the occurrences of each letter. Suppose the intercepted ciphertext is sufficiently long; the attacker will notice that 'O' appears more frequently, which might suggest that 'O' corresponds to a common letter in the plaintext, such as 'L'. By comparing the frequency distribution of the ciphertext to the known frequency distribution of the plaintext language, the attacker can make educated guesses about the substitutions.
Example Scenario:
Assume an intercepted ciphertext: "XLMW MW XLMRO XLMW MW XLMRO".
By counting the frequency of each letter, we might find:
– X: 6 times
– L: 6 times
– M: 6 times
– W: 6 times
– I: 3 times
– R: 3 times
– O: 3 times
Given the repetition, an analyst might infer that "XLMW" is a common word. If we suspect "XLMW" represents "THIS", we can start mapping:
– X -> T
– L -> H
– M -> I
– W -> S
Using this partial key, we can decrypt parts of the ciphertext and refine our guesses until the entire message is decrypted.
Vulnerability and Defense Mechanisms
The primary vulnerability of monoalphabetic substitution ciphers lies in their deterministic nature, where each plaintext letter maps to a fixed ciphertext letter. This predictability makes them susceptible to frequency analysis attacks.
To mitigate this vulnerability, cryptographers developed polyalphabetic ciphers, which use multiple substitution alphabets to confuse frequency analysis. The Vigenère cipher, for example, uses a keyword to determine which substitution alphabet to use, thereby altering the mapping of plaintext letters to ciphertext letters at different positions in the text.
Example of Polyalphabetic Cipher:
Consider the Vigenère cipher with the keyword "KEY":
– Plaintext: ATTACK AT DAWN
– Keyword: KEYKEY KEYKEY
– Ciphertext: KXEYQK KY DQYN
Here, the letter 'A' in plaintext is encrypted differently depending on its position:
– First 'A' (with 'K' from the keyword) -> K
– Second 'A' (with 'E' from the keyword) -> X
– Third 'A' (with 'Y' from the keyword) -> E
Even though the same plaintext letter 'A' appears multiple times, it maps to different ciphertext letters (K, X, E) based on the keyword. This variability complicates frequency analysis, making the cipher more secure.
In classical cryptography, substitution ciphers are fundamental yet vulnerable to frequency analysis attacks due to their deterministic nature. Identical plaintext units map to identical ciphertext units in monoalphabetic substitution ciphers, making them susceptible to such attacks. Polyalphabetic ciphers, while more secure, still follow the principle that within a single substitution alphabet, identical plaintext units map to identical ciphertext units. Understanding these principles is important for appreciating the evolution of cryptographic techniques and the ongoing efforts to enhance security.
Other recent questions and answers regarding EITC/IS/CCF Classical Cryptography Fundamentals:
- Is cryptography considered a part of cryptology and cryptanalysis?
- Will a shift cipher with a key equal to 4 replace the letter d with the letter h in ciphertext?
- Does the ECB mode breaks large input plaintext into subsequent blocks
- What is EEA ?
- Are brute force attack always an exhausive key search?
- In RSA cipher, does Alice need Bob’s public key to encrypt a message to Bob?
- Can we use a block cipher to build a hash function or MAC?
- What are initialization vectors?
- How many part does a public and private key has in RSA cipher
- Can OFB mode be used as keystream generators?
View more questions and answers in EITC/IS/CCF Classical Cryptography Fundamentals