Redei rational functions as permutation functions and an algorithm to compute redei rational functions

Permutation polynomials have received significantly wider attention because of their potential applications in cryptosystems and various combinatorial designs. A polynomial f(x) ε F_q[x] of positive degree is called a permutation polynomial if and only if f(x) induces a bijection from F_q onto itself. The rational functions over F_q[x] that yield permutations of F_q are called permutation functions. In the process of the study of necessary and sufficentt conditions for a polynomial to be permutation polynomial a special kind of polynomials gn(a; x) called Dickson polynomials are introduced by Dickson and the study of Dickson polynomials lead to the introduction of the special class of the special class of functions called Redei rational functions to be permutation functions are presented and an algorithm to compute the Redei rational functions is given which is useful in cryptosystems with Redei rational functions as trapdoor functions.