On the Number Counting of Polynomial Functions
Received:August 06, 2007  Revised:January 05, 2009
Key Words: polynomial functions   permutation polynomials   finite commutative rings   counting formula.  
Fund Project:Supported by the Anhui Provincial Key Natural Science Foundation of Universities and Colleges (Grant No.KJ2007A127ZC).
Author NameAffiliation
Jian Jun JIANG Department of Mathematics and Computer Science, Tongling University, Anhui 244000, P. R. China 
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      Polynomial functions (in particular, permutation polynomials) play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let $A$ be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over $A$ is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.
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