The Cracking Code Book. Simon Singh

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      The advantage of building a cipher alphabet in this way is that it is easy to memorize the keyword or keyphrase, and hence the cipher alphabet. This is important, because if the sender has to keep the cipher alphabet on a piece of paper, the enemy can capture the paper, discover the key and read any communications that have been encrypted with it. However, if the key can be committed to memory, it is less likely to fall into enemy hands.

      This simplicity and strength meant that the substitution cipher dominated the art of secret writing throughout the first millennium AD. Codemakers had evolved a system for guaranteeing secure communication, so there was no need for further development – without necessity, there was no need for invention. The onus had fallen upon the codebreakers, those who were attempting to crack the substitution cipher. Was there any way for an enemy interceptor to unravel an encrypted message? Many ancient scholars considered that the substitution cipher was unbreakable, thanks to the gigantic number of possible keys, and for centuries this seemed to be true. However, codebreakers would eventually find a shortcut to the process of exhaustively searching through all the keys. Instead of taking billions of years to crack a cipher, the shortcut could reveal the message in a matter of minutes. The breakthrough occurred in the East and required a brilliant combination of linguistics, statistics and religious devotion.

       THE ARAB CRYPTANALYSTS

      At the age of about forty, Muhammad began regularly visiting an isolated cave on Mount Hira just outside Mecca. This was a retreat, a place for prayer, meditation and contemplation. It was during a period of deep reflection, around AD 610, that he was visited by the archangel Gabriel, who proclaimed that Muhammad was to be the messenger of God. This was the first of a series of revelations that continued until Muhammad died some twenty years later. The revelations were recorded by various scribes during the Prophet’s life, but only as fragments, and it was left to Abū Bakr, the first caliph of Islam, to gather them together into a single text. The work was continued by Umar, the second caliph, and his daughter Hafsa, and was eventually completed by Uthmān, the third caliph. Each revelation became one of the 114 chapters of the Koran.

      The ruling caliph was responsible for carrying on the work of the Prophet, upholding his teachings and spreading his word. Between the appointment of Abū Bakr in 632 and the death of the fourth caliph, Alī, in 661, Islam spread until half of the known world was under Muslim rule. Then, in 750, after a century of consolidation, the start of the Abbasid caliphate (or dynasty) heralded the golden age of Islamic civilization. The arts and sciences flourished in equal measure. Islamic craftsmen bequeathed us magnificent paintings, ornate carvings and the most elaborate textiles in history, while the legacy of Islamic scientists is evident from the number of Arabic words that pepper the language of modern science, such as algebra, alkali and zenith.

      The richness of Islamic culture was in large part the result of a wealthy and peaceful society. The Abbasid caliphs were less interested than their predecessors in conquest, and instead concentrated on establishing an organized and affluent society. Lower taxes encouraged businesses to grow and gave rise to greater commerce and industry, while strict laws reduced corruption and protected the citizens. All of this relied on an effective system of administration, and in turn the administrators relied on secure communication achieved through the use of encryption. As well as encrypting sensitive affairs of state, it is documented that officials protected tax records, demonstrating a widespread and routine use of cryptography. Further evidence comes from the many administrative manuals, such as the tenth-century Adab al-Kuttāb (The Secretaries’ Manual), that include sections devoted to cryptography.

      The administrators usually employed a cipher alphabet that was simply a rearrangement of the plain alphabet, as described earlier, but they also used cipher alphabets that contained other types of symbols. For example, a in the plain alphabet might be replaced by # in the cipher alphabet, b might be replaced by +, and so on. The monoalphabetic substitution cipher is the general name given to any substitution cipher in which the cipher alphabet consists of letters, symbols or a mix of both. All the substitution ciphers that we have met so far come within this general category.

      Had the Arabs merely been familiar with the use of the monoalphabetic substitution cipher, they would not warrant a significant mention in any history of cryptography. However, in addition to employing ciphers, the Arab scholars were also capable of destroying ciphers. They in fact invented cryptanalysis, the science of unscrambling a message without knowledge of the key. While the cryptographer develops new methods of secret writing, it is the cryptanalyst who struggles to find weaknesses in these methods in order to break into secret messages. Arabian cryptanalysis succeeded in finding a method for breaking the monoalphabetic substitution cipher, a cipher that had remained unbreakable for several centuries.

      Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of education in several disciplines, including mathematics, statistics and linguistics. The Muslim civilization provided an ideal birthplace for cryptanalysis, because Islam demands justice in all spheres of human activity, and achieving this requires knowledge, or ilm. Every Muslim is obliged to pursue knowledge in all its forms, and the economic success of the Abbasid caliphate meant that scholars had the time, money and materials required to fulfill their duty. They endeavoured to acquire the knowledge of previous civilizations by obtaining Egyptian, Babylonian, Indian, Chinese, Farsi, Syriac, Armenian, Hebrew and Roman texts and translating them into Arabic. In 815, the Caliph al-Ma‘mūn established in Baghdad the Bait al-Hikmah (House of Wisdom), a library and centre for translation.

      In addition to a greater understanding of secular subjects, the invention of cryptanalysis also depended on the growth of religious education. Major theological schools were established in Basra, Kufa and Baghdad, where theologians studied the revelations of Muhammad as contained in the Koran. The theologians were interested in establishing the chronology of the revelations, which they did by counting the frequencies of words contained in each revelation. The theory was that certain words had evolved relatively recently, and hence if a revelation contained a high number of these newer words, this would indicate that it came later in the chronology. Theologians also studied the Hadīth which consists of the Prophet’s daily utterances. They tried to demonstrate that each statement was indeed attributable to Muhammad. This was done by studying the etymology of words and the structure of sentences, to test whether particular texts were consistent with the linguistic patterns of the Prophet.

      Significantly, the religious scholars did not stop their investigation at the level of words. They also analyzed individual letters, and in particular they discovered that some letters are more common than others. The letters a and I are the most common in Arabic, partly because of the definite article al-, whereas the letter j appears only a tenth as frequently. This apparently minor observation would lead to the first great breakthrough in cryptanalysis.

      The earliest known description of the technique is by the ninth-century scientist Abū Yūsūf Ya‘qūb ibn СКАЧАТЬ