The Code Book: The Secret History of Codes and Code-breaking. Simon Singh

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 Ab

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 Uthm

n, 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 Ab

Bakr in 632 to the death of the fourth caliph, Al

, 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 civilisation. 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 lexicon of modern science such as algebra, alkaline and zenith.

      The richness of Islamic culture was to a 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 organised 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 many administrative manuals, such as the tenth-century Adab al-Kutt

b (‘The Secretaries’ Manual’), which include sections devoted to cryptography.

      The administrators usually employed a cipher alphabet which 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 either letters or 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 cryptanalysts succeeded in finding a method for breaking the monoalphabetic substitution cipher, a cipher that had remained invulnerable for several centuries.

      Cryptanalysis could not be invented until a civilisation had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics and linguistics. The Muslim civilisation provided an ideal cradle 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 fulfil their duty. They endeavoured to acquire the knowledge of previous civilisations by obtaining Egyptian, Babylonian, Indian, Chinese, Farsi, Syriac, Armenian, Hebrew and Roman texts and translating them into Arabic. In 815, the Caliph al-Ma’m

n established in Baghdad the Bait al-Hikmah (‘House of Wisdom’), a library and centre for translation.

      At the same time as acquiring knowledge, the Islamic civilisation was able to disperse it, because it had procured the art of paper-making from the Chinese. The manufacture of paper gave rise to the profession of warraq

n, or ‘those who handle paper’, human photocopying machines who copied manuscripts and supplied the burgeoning publishing industry. At its peak, tens of thousands of books were published every year, and in just one suburb of Baghdad there were over a hundred bookshops. As well as such classics as Tales from the Thousand and One Nights, these bookshops also sold textbooks on every imaginable subject, and helped to support the most literate and learned society in the world.

      In addition to a greater understanding of secular subjects, the invention of cryptanalysis also depended on the growth of religious scholarship. Major theological schools were established in Basra, Kufa and Baghdad, where theologians scrutinised 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 Had

th, 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 scrutiny at the level of words. They also analysed 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 innocuous observation would lead to the first great breakthrough in cryptanalysis.

      Although it is not known who first realised that the variation in the frequencies of letters could be exploited in order to break ciphers, the earliest known description of the technique is by the ninth-century scientist Ab

Y

s

fYa’q

b ibn Is-h

q ibn as-Sabb

h ibn ‘omr

n ibn Isma

l al-Kind

. Known as ‘the philosopher of the Arabs’, al-Kind

was the author of 290 books on medicine, astronomy, mathematics, linguistics and music. His greatest treatise, which was rediscovered only in 1987 in the Sulaimaniyyah Ottoman Archive in Istanbul, is entitled A Manuscript on Deciphering Cryptographic Messages; the first page is shown in Figure 6. Although it contains detailed discussions on statistics, Arabic phonetics and Arabic syntax, al-Kind

’s revolutionary system of cryptanalysis is encapsulated in two short paragraphs:

      One way to solve an encrypted message, if