Also known as: letter-frequency analysis
Frequency analysis breaks a substitution cipher by exploiting the fact that letters and symbols of a natural language occur with characteristic, uneven frequencies that survive a simple letter-for-letter substitution.1 Attributed to the 9th-century scholar al-Kindi, it is the oldest systematic method of cryptanalysis.
How it works
In a monoalphabetic substitution cipher each plaintext letter is consistently replaced by one ciphertext symbol. The substitution hides which symbol stands for which letter, but it does not change how often each appears: if the most common ciphertext symbol shows up about as often as the most common letter does in the plaintext language, those two probably match. The analyst tabulates symbol frequencies, aligns them with known language statistics (in English, E, T, A, O dominate; Q and Z are rare), and confirms guesses using common pairs (digrams like TH, ER), doublets (LL, SS), and short words. Because it needs only intercepted ciphertext, it is the archetypal ciphertext-only attack.
Variants
Polyalphabetic ciphers such as Vigenère were designed to defeat the single-alphabet form by rotating among several substitution alphabets, flattening the visible frequencies. They are still broken by a two-step refinement: first estimate the key length — the number of alphabets in rotation — using the index of coincidence or Kasiski examination, then split the ciphertext into that many interleaved streams, each of which is monoalphabetic and yields to ordinary frequency analysis.2 The same idea generalises beyond letters: any encoding that maps symbols one-to-one, at any alphabet size, leaks its mapping through the symbol-count histogram.
In practice
Modern ciphers are built specifically to defeat this. Strong diffusion and confusion spread each plaintext symbol’s influence across the whole output, so a fixed S-box used inside many rounds — rather than as a single standalone substitution — flattens the output statistics. A one-time pad defeats frequency analysis completely: its output is uniform by construction. The histogram therefore doubles as a diagnostic: a flat one signals a well-diffused (or keyed) construction, while a spiky one betrays a simple substitution still waiting to be unpicked.
Relevance to SDR
Frequency analysis does not apply to the encrypted voice GopherTrunk encounters — keyed AES and DES produce statistically flat output by design. Its relevance is to obfuscation, not encryption. When reverse-engineering an unknown, keyless transform clean-room (as in the talker-alias work, issue #773), counting how often each byte value appears is one of the first diagnostics: a non-flat distribution betrays a simple substitution and helps recover a fixed lookup table, whereas a flat distribution suggests a stronger construction. The technique is a tool for understanding unkeyed encodings, not for breaking real encryption.
Sources
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Frequency analysis — Wikipedia, for the ciphertext-only attack on substitution ciphers and the use of language letter statistics. ↩
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Index of coincidence — Wikipedia, for estimating polyalphabetic key length before reducing to monoalphabetic analysis. ↩