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

are represented by O and X. They are probably e and a, the two most popular vowels in the English language, but does O = e and X = a, or does O = a and X = e? An interesting feature in the ciphertext is that the combination OO appears twice, whereas XX does not appear at all. Since the letters ee appear far more often than aa in plaintext English, it is likely that O = e and X = a.

      At this point, we have confidently identified two of the letters in the ciphertext. Our conclusion that X = a is supported by the fact that X appears on its own in the ciphertext, and a is one of only two English words that consist of a single letter. The only other letter that appears on its own in the ciphertext is Y, and it seems highly likely that this represents the only other one-letter English word, which is i. Focusing on words with only one letter is a standard cryptanalytic trick, and I have included it among a list of cryptanalytic tips in Appendix B. This particular trick works only because this ciphertext still has spaces between the words. Often, a cryptographer will remove all the spaces to make it harder for an enemy interceptor to unscramble the message.

      Although we have spaces between words, the following trick would also work where the ciphertext has been merged into a single string of characters. The trick allows us to spot the letter h, once we have already identified the letter e. In the English language, the letter h frequently goes before the letter e (as in the, then, they, etc.), but rarely after e. The table below shows how frequently the O, which we think represents e, goes before and after all the other letters in the ciphertext. The table suggests that B represents h, because it appears before O on 9 occasions, but it never goes after it. No other letter in the table has such an asymmetric relationship with O.

      Each letter in the English language has its own unique personality, which includes its frequency and its relation to other letters. It is this personality that allows us to establish the true identity of a letter, even when it has been disguised by monoalphabetic substitution.

      We have now confidently established four letters, O = e, X = a, Y = i and B = h, and we can begin to replace some of the letters in the ciphertext with their plaintext equivalents. I shall stick to the convention of keeping ciphertext letters in upper case, while putting plaintext letters in lower case. This will help to distinguish between those letters we still have to identify, and those that have already been established.

      PCQ VMJiPD LhiK LiSe KhahJaWaV haV ZCJPe EiPD KhahJiUaJ LhJee KCPK. CP Lhe LhCMKaPV aPV liJKL PiDhL, QheP Khe haV ePVeV Lhe LaRe CI Sa’aJMI, Khe JCKe aPV EiKKev Lhe DJCMPV ZelCJe hiS, KaUiPD: ‘DJeaL EiPD, ICJ a LhCMKaPV aPV CPe PiDhLK i haNe ZeeP JeACMPLiPD LC UCM Lhe IaZReK CI FaKI aDeK aPV Lhe ReDePVK CI aPAiePL EiPDK. SaU i SaEe KC ZCRV aK LC AJaNe a IaNCMJ CI UCMJ SaGeKLU?’

      eFiRCDMe, LaReK IJCS Lhe LhCMKaPV aPV CPe PiDhLK

      This simple step helps us to identify several other letters, because we can guess some of the words in the ciphertext. For example, the most common three-letter words in English are the and and, and these are relatively easy to spot – Lhe, which appears six times, and aPV, which appears five times. Hence, L probably represents t, P probably represents n, and V probably represents d. We can now replace these letters in the ciphertext with their true values:

      nCQ dMJinD thiK tiSe KhahJaWad had ZCJne EinD KhahJiUaJ thJee KCnK. Cn the thCMKand and LiJKt niDht, Qhen Khe had ended the taRe CI Sa’aJMI, Khe JCKe and EiKKed the DJCMnd ZeICJe hiS, KaUinD: ‘DJeat EinD, ICJ a thCMKand and Cne niDhtK i haNe Zeen JeACMntinD tC UCM the IaZReK CI FaKt aDeK and the ReDendK CI anAient EinDK. SaU i SaEe KC ZCRd aK tC AJaNe a IaNCMJ ICI UCMJ SaGeKtU?’

      eFiRCDMe, taReK IJCS the thCMKand and Cne niDhtK

      Once a few letters have been established, cryptanalysis progresses very rapidly. For example, the word at the beginning of the second sentence is Cn. Every word has a vowel in it, so C must be a vowel. There are only two vowels that remain to be identified, u and o; u does not fit, so C must represent o. We also have the word Khe, which implies that K represents either t or s. But we already know that L = t, so it becomes clear that K = s. Having identified these two letters, we insert them into the ciphertext, and there appears the phrase thoMsand and one niDhts. A sensible guess for this would be thousand and one nights, and it seems likely that the final line is telling us that this is a passage from Tales from the Thousand and One Nights. This implies that M = u, I = f, J = r, D = g, R = I, and S = m.

      We could continue trying to establish other letters by guessing other words, but instead let us have a look at what we know about the plain alphabet and cipher alphabet. These two alphabets form the key, and they were used by the cryptographer in order to perform the substitution that scrambled the message. Already, by identifying the true values of letters in the ciphertext, we have effectively been working out the details of the cipher alphabet. A summary of our achievements, so far, is given in the plain and cipher alphabets below.

      Plain alphabet a b c d e f g h i j k l m n o p q r s t u v w x y z

      Cipher alphabet X - - V O I D B Y - - R S P C - - J K L M - - - - -

      By examining the partial cipher alphabet, we can complete the cryptanalysis. The sequence VOIDBY in the cipher alphabet suggests that the cryptographer has chosen a keyphrase as the basis for the key. Some guesswork is enough to suggest the keyphrase might be A VOID BY GEORGES PEREC, which is reduced to AVOIDBYGERSPC after removing spaces and repetitions. Thereafter, the letters continue in alphabetical order, omitting any that have already appeared in the keyphrase. In this particular case, the cryptographer took the unusual step of not starting the keyphrase at the beginning of the cipher alphabet, but rather starting it three letters in. This is possibly because the keyphrase begins with the letter A, and the cryptographer wanted to avoid encrypting a as A. At last, having established the complete cipher alphabet, we can unscramble the entire ciphertext, and the cryptanalysis is complete.

      Plain alphabet a b c d e f g h i j k l m n o p q r s t u v w x y z

      Cipher alphabet X Z A V O I D B Y G E R S P C F H J K L M N Q T U W

      Now during this time Shahrazad had borne King Shahriyar three sons. On the thousand and first night, when she had ended the tale of Ma’aruf, she rose and kissed the ground before him, saying: ‘Great King, for a thousand and one nights I have been recounting to you the fables of past ages and the legends of ancient kings. May I make so bold as to crave a favour of your majesty?’

      Epilogue, Tales from the Thousand and One Nights

      Renaissance in the West

      Between AD 800 and 1200 Arab scholars enjoyed a vigorous period of intellectual achievement. At the same time, Europe was firmly stuck in the Dark Ages. While al-Kind

was describing the invention of cryptanalysis, Europeans were still struggling with the basics of cryptography. The only European institutions to encourage the study of secret writing were the monasteries, where monks would study the Bible in search of hidden meanings, a fascination that has persisted through to modern times (see Appendix C).

      Medieval monks were intrigued by the fact that the Old Testament contained deliberate and obvious examples of cryptography. For example, the Old Testament includes pieces of text encrypted with atbash, a traditional form of Hebrew substitution cipher. Atbash involves taking each letter, noting the number of places it is from the beginning of the alphabet, and replacing it with a letter that is an equal number of places from the end of the alphabet. In English this would mean that a, at the beginning of the alphabet, is replaced by Z, at the end of the alphabet, b is replaced by Y, and so on. The term atbash itself hints at the substitution it describes, because it consists of the first letter of the Hebrew alphabet, aleph, followed by the last letter taw, and then there is the second letter, beth, followed by the second to last letter shin. An example of atbash appears in Jeremiah 25: 26 and 51: 41, where ‘Babel’ is replaced by the word ‘Sheshach’; the first letter of Babel is beth, the second letter of the Hebrew alphabet, and this is replaced by shin, the second-to-last letter the second letter of Babel is also beth, and so it too is replaced by shin; and the last letter of Babel is lamed, the twelfth letter of the Hebrew alphabet, and this is replaced by kaph,