The first three centuries of Islamic civilization focused on the acquiring of knowledge and learning from other civilizations, past and present, through copious book acquisition and translation. From 700-1000 AD works were gathered from all over the known world (the art of paper making came to Baghdad at about this time from the Chinese via Indian trade-routes1) - books usually were taken by a) force through conquest, b) stealth through well funded bibliophile thieves, c) greed through offered wealth, whether real or promised, d) co-operation through scholarly exchange or e) dumb luck (books and their owners tended to wander during this period, as learned men were simultaneously politically dangerous yet much in demand- so stumbling across new folks with new books wasn't unusual, despite cultural divides). Subjects of particular fascination for the Islamic scholars included philosophy, astronomy, mathematics, physics, history and poetry.
    One huge problem the translation effort encountered through as that many of the languages encountered in the books, as they flooded via the Caliph's agents around the world, were completely unknown in Arabia, or dead languages nobody could remember. The were in essence ciphertext (in the argot of crypto) and so with their knowledge of mathematics (borrowed at first from India, where concepts such as the zero, decimal, algorithm, algebra and statistical analysis were already well-known, though they would not reach Europe for another six centuries) the Arab scholars began setting down rules for textual decryption.2
    The pivotal work of Arabic cryptology was written by ibn ad-Duraihim (1312-1361) entitled Miftãh al-Kunuz fî Idah al marmûz (The Treasured Key for Clarifying Ciphers), which was reprinted recently in Arabic and awaits translation into English (it appears in a compilation, Origins of Arab Cryptography and Cryptanalysis3, which itself is an elaboration of an older text written by Abu al-Khalîl (718-786), the Kitab al Mu'ammã (The Messenger of the Caliph?) which has only ever been mentioned in later works and is considered a lost book, likely a victim of time. al-Khalîl was trained primarily as a linguist, but as the unknown languages, scripts and dialects flooded into his study by order of the Caliphate, he developed the idea of the dictionary and an index of coincidence for tracking letter frequency and combinations for various languages. Then came Al-Khwãrrizmi (750-847), who was of particular significant to the West in somuch as it was his works (translated in Cordoba into Latin by the Englishman Robert of Chester (12th c.) under the title Algebra et Almucaba) which gave Europe the zero and decimal system, and the means to finally replace Roman numerals with the arabic numeral (which, as you can imagine, would make complex math even more of a drag). Finally, Abu Yûsûf al-Kindï, head librarian at the Bait al-Hikmah wrote a treatise on statistical cryptanalysis using letter frequency entitled Risalah fí Istikhraj al-Mu'amma, which was unearthed in the 1980s in the Sulaimaniyyah Ottoman Archive in Istambul.
Notes:
1. At this point, papyrus and parchment were the only written media for most of the Mediterranean world. Before that it had been clay tablets & sticks (Babylon) or public monuments (Code of Hammurabi).
2. The other part of the necessity for this was that some attempts at enciphering were already known, like straight-forward substitution or the Caesar cipher, and used by certain sects: the Magi (left over Zoroastrian priests on the run from suspicion and persecution) and scholars of controversial theology, alchemy or sorcery. By writing their texts in a code, however rough, they could keep dangerous knowledge out of the hands of their enemies.
3. Full title as it appears in Library of Congress -- `Ilm al-ta`miyah wa-istikhr¯aj al-mu`ammá `inda al-`Arab / dir¯asat wa-tahq¯iq Muhammad Mar¯ay¯at¯i, Yahyá M¯ir `Alam, Muhammad Hass¯an al-Tayy¯an ; taqd¯im Sh¯akir al-Fahh¯am. Damascus : Majma` al-Lughah al-`Arab¯iyah bi-Dimashq, 1987?-

Sources:
1. Al -Kadi, "Origins of Cryptology", from Selections from Cryptologia (1998), pp. 93-123
2. Kahn, The Code Breakers : the story of secret writing (NY : 1967)
3. Badeau, The Genius of Arab Civilization : Source of the Renaissance (Cambridge : MIT, 1983)

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