Devil's Night

How many different simple substitution ciphers exists? We can count them by enumerating all the possible values of each single plain-text letter. First we assign a to one of the 26 possible cipher text letters from A to Z, then assign b to the rest 25 cause one of the letter in cipher alphabet has been occupied by letter a; then there are 26*25 = 650 possible ways to assign a and b. Thus the total number of ways to assign 26 plain-text letters to 26 cipher-text letters by using each cipher-text once, is

26*25*24*23…*3*2*1 = 26! = 403291461126605635584000000

there are more than 10 ²⁶ possibilities for a code-breaker, those who were attempting crack the substitution cipher. if they just simply test each possible keys. If a code-breaker is able to check one million keys per second, it takes him/her 10¹³ years to finish all jobs. It’s even longer than the life of universe. So, is there an efficient way to break it?

Many ancient scholar thought that substitution ciphers are unbreakable. And for centuries it seemed to be true. But remember

Your opponent always uses her or his best strategy to defeat you, not the strategy that you want her or him to use. Thus the security of an encryption system depends on the best known method to break it. As new and improved methods are developed. the level of security can only get worse, never better

So code-breakers will eventually find a shortcut to discover the correct key instead of spending billions of years on testing each possible key. The shortcut could reveal the message in a matter of few minutes. The breakthrough occurred in the east, and required a brilliant combinations of linguistics, statistics and religious devotion.

The mono-alphabet substitution cipher(each plain-letter matches only one cipher letter) was destroyed by Arab scholars, who invented cryptanalysis, the science of unscrambling a message without knowledge of the key. Arab cryptanalysts succeeded in finding a method for breaking the mono-alphabet substitution cipher, a cipher that had remained invulnerable for several centuries.

Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics and linguistics. The Muslim civilization provided a ideal cradle for cryptanalysis. Because Islam demands justice in all spheres of human activity. To achieve this, knowledge or ilm is required. Every Muslim is obliged to pursue knowledge in all its forms, and the economic success of the Abbasid caliphate meant that scholar had the time, money and material required to fulfill their duty. They endeavored to acquire the knowledge of previous civilizations by obtaining Egyptian, Babylonian, Indian, Chinese, Farsi, Syrian, Armenian, Hebrew and Roman texts and translating them into Arabic. In 815, the Caliph Al-Ma’mun established in Baghdad the Bait al-Hikmah (‘House of Wisdom’), a library and center for translation.

If you are very good at scramble game. It is not difficult to find some specific rules behind each English words. For example, letter O always appears in pairs, and letter q is always followed by letter u. Some useful letters such as e and t show up way frequently than those uncommon letters like x or z. So does Arabic scholars, in particular they found that some letters are more common than others. The letter a and l are the most common in Arabic, partly because of the definite article al-. This apparently innocuous observation would lead to the first great breakthrough in cryptanalysis.