4 1. HISTORICAL INTRODUCTION Table 1.1. The Polybius checkerboard. 1 2 3 4 5 1 a b c d e 2 f g h ij k 3 l m n o p 4 q r s t u 5 v w x y z do is look in the appropriate table entry to get the letter (remembering, of course, that 24 can be either an i or a j). For example, 22, 42, 15, 15, 43, 25, 11, 42, 15, 13, 34, 32, 24, 33, 22 decodes to either “Greeks are coming” or “Greeks are comjng” it’s clear from context that the first phrase is what’s meant. A cipher is a method of concealment in which the primary unit is a let- ter. Letters in a message are replaced by other letters, numbers, or symbols, or they are moved around to hide the order of the letters. The word cipher is derived from the Arabic sifr, meaning nothing, and it dates back to the seventh century BCE. We also use the word code, often interchangeably with cipher, though there are differences. A code, from the Latin codex, is a method of concealment that uses words, numbers, or syllables to replace original words or phases. Codes were not used until much later. As the Arabic culture spread throughout much of the western world during this time, mathematics flourished and so too did secret writing and decryption. This is when frequency analysis was first used to break ciphers (messages). Frequency analysis uses the frequency of letters in an alphabet as a way of guessing what the cipher is. For example, e and t are the two most com- monly used letters in English, whereas a and k are the two most commonly used letters in Arabic. Thus, “native language” makes a difference. Chap- ters 4 and 5 include many examples of how frequency analysis can decrypt messages. Abu Yusef Ya’qab ibn ’Ishaq as-Sabbah al-Kindi (Alkindus to contem- porary Europeans) was a Muslim mathematician, who lived in what is now modern day Iraq between 801 and 873 AD. He was a prolific philosopher and mathematician and was known by his contemporaries as “the Second Teacher”, the first one being Aristotle [55]. An early introduction to work at the House of Wisdom, the intellectual hub of the Golden Age of Islam, brought him into contact with thousands of historical documents that were to be translated into Arabic, setting him on a path of scientific inquiry few were exposed to in that time [46]. Al-Kindi was the first known mathematician to develop and utilize the frequency attack, a way of decrypting messages based on the relative rarity of letters in a given language. The total of his work in this field was published in his work On Deciphering Cryptographic Messages in 750 AD,
Previous Page Next Page