Abstract: Permutation is different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation used in the pattern analysis, Databases and data mining, simulation, accumulation of electronic communication data, Homeland security, wireless networks. Bottom-Up, Lexicography, Johnson-Trotter, Back-tracking, Heap algorithm, Brute-Force are of the most popular permutation algorithms that emerged during the past decades. Lexicography used in graph colouring. Backtracking are used in Sudoku. A performance analysis in terms of time complexity is done by implementing algorithms in different programming languages on different platforms. In cryptography, cipher text is the result of encryption performed on plain text using an algorithm called cipher which is used in client-server application.

Keywords: Permutation, Time complexity, Pseudo Random generator, Authentication, Passkey.