Frequency Analysis Attack

Frequency Analysis is a technique used to break classical ciphers, particularly substitution ciphers, by examining the frequency with which letters or combinations of letters appear in the ciphertext.

It exploits the fact that, in any given language, certain letters and letter combinations occur more often than others.

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1. The Underlying Principle

Natural language text does not use all characters with equal probability. This statistical pattern provides a major vulnerability.

English Language Statistics

• Most Frequent Letters: E, T, A, O, I, N, S, H, R.
• Least Frequent Letters: Q, J, Z, X.

2. Attack Steps

1. Calculate Ciphertext Frequency: Count the occurrence of every letter in the given ciphertext to determine its percentage frequency.
2. Compare and Map:
   • Map the most frequent letter in the ciphertext (e.g., X) to the most frequent letter in the standard language (e.g., E).
   • Continue this mapping process for the second, third, and subsequent most frequent letters.
3. Refine with Patterns: Look for common short words and patterns (e.g., single-letter words like 'A' or 'I'; common three-letter words like 'THE' or 'AND') to verify and refine the assumed key mappings.

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3. Vulnerable Ciphers and Defenses

① Vulnerable Ciphers

• Monoalphabetic Ciphers: Caesar Cipher, Simple Substitution Ciphers.
  • Reason: Because every letter is always replaced by the same corresponding cipher letter, the statistical frequency of the plaintext is directly preserved in the ciphertext.

② Defense (Modern Cryptography)

• Polyalphabetic Ciphers: Vigenère Cipher.
  • Reason: The same plaintext letter ('E') can be mapped to many different ciphertext letters ('X', 'Y', 'Z'), thereby flattening the statistical frequency distribution and rendering simple frequency analysis ineffective.
• Modern Block Ciphers (AES): These ciphers completely obscure the relationship between the plaintext and the ciphertext, making statistical attacks impossible.