David Kahn notes in The Codebreakers that modern cryptology originated among the Arabs, the first people to systematically document cryptanalytic methods.[15] Al-Khalil (717ā786) wrote the Book of Cryptographic Messages, which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.[16]
The invention of the frequency analysis technique for breaking monoalphabetic substitution ciphers, by Al-Kindi, an Arab mathematician,[17][18] sometime around AD 800, proved to be the single most significant cryptanalytic advance until World War II. Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which he described the first cryptanalytic techniques, including some for polyalphabetic ciphers, cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis.[19] He also covered methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic.[20][21] An important contribution of Ibn Adlan (1187ā1268) was on sample size for use of frequency analysis.[16]
Ahmad al-Qalqashandi (AD 1355ā1418) wrote the Subh al-a 'sha, a 14-volume encyclopedia which included a section on cryptology. This information was attributed to Ibn al-Durayhim who lived from AD 1312 to 1361, but whose writings on cryptography have been lost. The list of ciphers in this work included both substitution and transposition, and for the first time, a polyalphabetic cipher[23] with multiple substitutions for each plaintext letter (later called homophonic substitution). Also traced to Ibn al-Durayhim is an exposition on and a worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which cannot occur together in one word.