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Codes & LettersCiphers, scripts, symbols — every code humans write, taken apart.

Definition

Frequency Fingerprint

Updated

A frequency fingerprint is the statistical profile a text makes through how often each letter, or more generally each grapheme, appears in it. Each language has a characteristic distribution of letters that stays roughly the same from one long sample of the language to the next, and that pattern of high and low counts is the fingerprint. In the three English novels counted on this site's Letter Frequency page, e makes up 12.52% of the letters, about one in eight, and its share moves by 0.63 points across the three books. In three German novels it is 15.97%, close to one in six.

A borrowed term

Frequency fingerprint is a term already used in cryptography teaching. Codes & Letters did not coin it and uses it in that existing sense.

When the fingerprint survives

In a single-alphabet substitution cipher that replaces each letter with one fixed letter, such as the Caesar cipher, the fingerprint survives encryption. Move each letter three places along the alphabet and the profile moves with it, its shape unchanged: the 12.52% that belonged to e in those English novels now belongs to h, still the tallest spike. If the ciphertext is long enough and typical of ordinary English, the most frequent cipher letter is therefore a strong first candidate for e, which leads the English count ahead of t at 9.03%.

That is a candidate, not an answer. Before trusting it, test it against word shapes, such as whether a guessed the lands where short common words should be, and against counts of letter pairs and triplets.

When it does not apply

  • Short ciphertexts. Helen Fouché Gaines's 1939 textbook Elementary Cryptanalysis warns that single letters, especially in short texts, "may vary greatly from their normal percentages." Cut the same three English novels into 100-letter blocks, and e is the most common letter in 63.1% of them, with ties split evenly. A short ciphertext may not represent the full letter distribution, which makes frequency analysis harder.
  • Polyalphabetic ciphers. These use several cipher alphabets, so a plaintext letter can be replaced by more than one cipher letter. Polyalphabetic substitution was one of the schemes devised to defeat frequency analysis of simple substitution. On the Vigenère cipher page, the keyword BELLASO turns a plain e in the same English novels into f, i, p, e, w or s. The tallest cipher letter, s, reaches only 7.64%.
  • Homophonic substitution. This gives some or all plaintext letters more than one cipher symbol, with extra symbols for the most frequent letters. Gaines bases her method for attacking these ciphers on the assumption that the encipherer can "conceal the true frequencies of his high-frequency letters" but can do little to hide the rare ones.

How counts and ciphertexts on the site are checked: About Codes & Letters. Other terms used on the site: the eye's thumb on the scale and letter debt.

Sources