| 关于多项式函数的计数 |
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| 引用本文： | 蒋剑军.关于多项式函数的计数[J].数学研究及应用,2010,30(2):241-248. |
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| 作者姓名： | 蒋剑军 |
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| 作者单位： | 铜陵学院数学与计算机科学系, 安徽 铜陵 244000 |
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| 基金项目： | 安徽高校省级自然科学研究重点项目(Grant No.KJ2007A127ZC). |
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| 摘 要： | 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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| 关 键 词： | 多项式函数 有限交换环 计数 置换多项式 密码系统 数量计算 局部环 环数 |
| 收稿时间： | 8/6/2007 12:00:00 AM |
| 修稿时间： | 1/5/2009 12:00:00 AM |
On the Number Counting of Polynomial Functions |
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| Jian Jun JIANG.On the Number Counting of Polynomial Functions[J].Journal of Mathematical Research with Applications,2010,30(2):241-248. |
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| Authors: | Jian Jun JIANG |
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| Institution: | Department of Mathematics and Computer Science,Tongling University,Anhui 244000,P.R.China |
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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. |
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| Keywords: | polynomial functions permutation polynomials finite commutative rings counting formula |
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