Frequency analysis

Frequency analysis breaks substitution ciphers by comparing how often ciphertext symbols occur with the characteristic frequencies of letters or other symbols in the plaintext language.

Letter frequency: The rate at which each letter occurs in a text or language. Unequal letter rates let analysts propose which ciphertext symbols stand for common plaintext letters.
Al-Kindi: A ninth-century Arab polymath who wrote an early surviving systematic account of cryptanalysis. His treatise describes using letter-frequency differences to solve substitution ciphers.
Caesar cipher: A substitution cipher that shifts each plaintext letter by a fixed number of positions in the alphabet. Its shifted frequency profile makes the method especially straightforward to demonstrate.
One-time pad: A cipher using a truly random key as long as the message, used only once. Proper use makes ciphertext symbols statistically independent of the plaintext.
Monoalphabetic substitution cipher: A cipher that replaces each plaintext symbol with the same ciphertext symbol throughout a message. Its fixed symbol mapping preserves the frequency pattern that analysis exploits.
Risāla fī istikhrāj al-muʿammā: A treatise by Al-Kindi explaining methods for deciphering encrypted messages. It contains the earliest known detailed exposition of frequency analysis.
Cryptogram: A puzzle in which a message is encoded by substituting one symbol for another. Solvers commonly use letter counts and word patterns to recover its substitution.
Homophonic substitution cipher: A substitution cipher that assigns multiple ciphertext symbols to a plaintext symbol. Distributing common letters across several symbols weakens direct frequency matching.
Ciphertext: Text transformed by encryption so its original message is not directly readable. The observed symbol counts come from this transformed text.
Cryptanalysis: The study and practice of recovering information from ciphers without the intended key. Frequency analysis became one of cryptanalysis’s foundational statistical techniques.

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