| 摘要: |
| 本文提出了GF(q)上(n,k)置换多项式的概念，建立了它与函数相关免疫性之间的联系，并研究了它们的性质．得到了GF(q)(q＞2)上一些特殊类型的函数是ｍ阶和所有二次多项式是最大阶相关免疫的充分必要条件．证明了在GF(q)(q＞4)上存在非线性的具有最大阶相关免疫阶的函数，也给出了一种由低次数具有特定相关免疫阶的函数构造非线性次数高的同阶相关免疫函数的有效方法. |
| 关键词: 置换多项式 相关免疫 流密码 组合序列 滚动密钥生成器 |
| DOI： |
| 分类号: |
| 基金项目:本文研究得到国家自然科学基金资助. |
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| PERMUTATION POLYNOMIALS AND CORRELATION IMMUNITY OF FUNCTIONS OVER GF（q） |
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Long Yonghong
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| Abstract: |
| The concept of (n,k) permutation polynomial over GF(q) is first introduced.The properties of (n,k) permutation polynomials and the relation to kth order correlationimmune functions have been studied. Sufficient and necessary conditions are proved forsome special n-ary functions to be mth(m＜n) order correlation immune and all functions with degree no greater than 2 to be (n－1)thorder correlation immune. The results show that over GF(q)(q＞4) are there nonlinear functions of highest possible correlation immunity order. An efficient method is put forward to construct functions of high nonlinearityfrom those of lower nonlinearity with the same correlation immunity order. |
| Key words: Permutation polynomial correlation immunity stream cipher combinationsequence RKG （running key generator）. |
