| 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.
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| Fund Project:Supported by the Anhui Provincial Key Natural Science Foundation of Universities and Colleges (Grant No.KJ2007A127ZC). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.02.006 |
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