Frequency analysis
Letter frequencies in French, a cryptogram's histogram, breaking a Caesar by its peak, the index of coincidence and why Vigenère flattens the histogram.
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Frequency analysis: what is it?
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An attack that counts the letters of a cryptogram and matches their frequencies to those of the plaintext language to guess the key.
It works against any monoalphabetic substitution: encryption changes letters' identity, not how often they appear.
A message encrypted by substitution is only 8 letters long. Why is frequency analysis unreliable on it?
- Too few letters to approach the language's frequencies
- Substitution changes the frequencies of a short message
- Frequency analysis only works against Caesar
- You need at least 26 letters, one per letter of the alphabet
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Too few letters to approach the language's frequencies
A language's average frequencies only show up on long texts: on 8 letters, any letter can dominate. You generally need at least a few dozen letters, ideally a few hundred.
In French, the most frequent letter is …; the letters W, K and Y are among the ….
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In French, the most frequent letter is E; the letters W, K and Y are among the rarest.
E alone accounts for over 10% of ordinary French text, well ahead of any other letter. A ciphertext letter that dominates like this is the natural candidate for E.
Letter frequency: what is it?
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The share of each letter in a text; in French, E dominates, far ahead of the others, and W and K are very rare.
This profile is fairly stable from one French text to another from a few hundred letters on, which lets you recognise E in a cryptogram.