Devil's Night

Much of modern cryptography is built on the foundation of linear algebra and number theory. At the most basic level, Number theory is the study of natural numbers

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a simple exlorering…

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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?

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The alternative of transposition is substitution. One of the earliest description of encryption by substitution can be dated back to first century B.C. During Gallic Wars, the great emperor Julius Caesar, invented the famous Caesar’s Cypher.

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