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 commutat...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.展开更多
基金Supported by the Anhui Provincial Key Natural Science Foundation of Universities and Colleges (Grant No.KJ2007A127ZC)
文摘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.
