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| 摘要: |
| 本文基于有限域中的伪随机子集，构造了大族Boolean函数并研究了其性质.利用有限域中特征和估计的方法，分析了Boolean函数的非线性，平均灵敏度与稀疏性，给出了估计式.推广并改进了相关领域的已有结果. |
| 关键词: Boolean函数 最大Fourier系数 非线性 平均灵敏度 稀疏性 |
| DOI： |
| 分类号:TN918.1;O156.4 |
| 基金项目:国家自然科学基金资助（11571277）；陕西省青年科技新星项目资助（2014KJXX-61）；陕西省自然科学基金资助（2014JM1007）；陕西省工业科技攻关项目资助（2016GY-080；2016GY-077）. |
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| LARGE FAMILY OF BOOLEAN FUNCTIONS CONSTRUCTED BY USING PSEUDORANDOM SUBSETS |
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LIU Hua-ning,CHEN Xiao-lin
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| Abstract: |
| In this paper, we study the cryptography properties of large families of Boolean functions constructed by the pseudorandom subsets in finite fields. Using bounds on character sums over finite fields, we obtain lower bounds on the nonlinearity, average sensitivity and sparsity, which generalizes the previous results. |
| Key words: Boolean function maximum Fourier coefficient nonlinearity average sensitivity sparsity |
