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Concept
Frequency analysis
Summary
In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies. Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language. For instance, given a section of English language, , , and are the most common, while , , and are rare. Likewise, , , , and are the most common pairs of letters (termed bigrams or digraphs), and , , , and are the most common repeats. The nonsense phrase "ETAOIN SHRDLU" represents the 12 most frequent letters in typical English language text.
In some ciphers, such properties of the natural language plaintext are preserved in the ciphertext, and these patterns have the potential to be exploited in a ciphertext-only attack.
In a simple substitution cipher, each letter of the plaintext is replaced with another, and any particular letter in the plaintext will always be transformed into the same letter in the ciphertext. For instance, if all occurrences of the letter turn into the letter , a ciphertext message containing numerous instances of the letter would suggest to a cryptanalyst that represents .
The basic use of frequency analysis is to first count the frequency of ciphertext letters and then associate guessed plaintext letters with them. More s in the ciphertext than anything else suggests that corresponds to in the plaintext, but this is not certain; and are also very common in English, so might be either of them also. It is unlikely to be a plaintext or which are less common. Thus the cryptanalyst may need to try several combinations of mappings between ciphertext and plaintext letters.
More complex use of statistics can be conceived, such as considering counts of pairs of letters (bigrams), triplets (trigrams), and so on.
Official source
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