| 具有最大代数免疫度函数的研究 |
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| 引用本文： | 谯通旭,王运兵,谢上明,董新锋,张文政.具有最大代数免疫度函数的研究[J].通信技术,2013(11):86-89. |
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| 作者姓名： | 谯通旭 王运兵 谢上明 董新锋 张文政 |
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| 作者单位： | [1]中国电子科技集团公司第三十研究所,四川成都610041 [2]保密通信重点实验室,四川成都610041 |
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| 基金项目： | 国家自然科学基金（No.61309034）资助,受四川省科技厅青年科学基金项目、中国电子科技集团创新人才项目资助 |
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| 摘 要： | 代数免疫度是私钥密码学中的重要概念。具有高代数免疫度的函数能抵抗新型攻击——代数攻击。CARLET Claude和FENG Keqin构造了具有最大代数免疫度的平衡函数及其线性等价函数，根据CARLET和FENG的构造，首先证明这类最大代数免疫度函数的数目，然后给出曹浩等人给出的定理6的简化证明，最后说明没有矩阵满足曹浩等人给出的定理7的条件（即不能用曹浩等人的方法构造具有最大代数免疫度的1阶弹性函数）．
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| 关 键 词： | 最大代数免疫度 本原元 矩阵 弹性函数 |
Study on Functions with Optimum Algebraic Immunity |
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| QIAO Tong-xu,WANG Yun-bing,XIE Shang-ming,DONG Xin-feng,ZHANG Wen-zheng.Study on Functions with Optimum Algebraic Immunity[J].Communications Technology,2013(11):86-89. |
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| Authors: | QIAO Tong-xu WANG Yun-bing XIE Shang-ming DONG Xin-feng ZHANG Wen-zheng |
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| Affiliation: | 1. No. 30 Institute of China Electronics Technology Group Corporation, Chengdu Sichuan 610041, China; 2. Key Laboratory for Secure Communications, Chengdu Sichuan 610041, China) |
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| Abstract: | Algebraic immunity is an important notion in private-key cryptography . Functions with high al- gebraic immunity can successfully resist the new-type attack algebraic attack. CARLET Claude and FENG Keqin construct the balanced functions with optimum algebraic immunity and their linearly equiva- lent functions. In accordance with CARLET and FENG＇ s construction, the number of functions with opti- mum algebraic immunity is determined first, and then the simplified proof of theorem 6 by CAO Hao et al. is presented, finally it is pointed that there in no existence of the matrix which could satisfy the condition of theorem 7 given by CAO Hao et al.. This means that the first order resilient function with optimum alge- braic immunity couldn＇ t be usually constructed with CAO＇ s method. |
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| Keywords: | optimum algebraic immunity primitive element matrix resilient function |
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