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| 摘要: |
| Sumanta Sarkar等人给出了一类具有最大代数免疫阶的旋转对称布尔函数,但对给出的旋转对称布尔函数仅研究了该函数的非线性度而对其他密码学性质未加以研究.因此,研究了上面给出的旋转对称布尔函数的其他密码学性质:代数次数、线性结构、扩散性、相关免疫性等.研究结果显示,虽然这类布尔函数的代数免疫阶达到最大,但是其他的密码学性质并不好.因此,此类布尔函数并不能直接应用在密码系统中. |
| 关键词: 布尔函数 对称布尔函数 旋转对称布尔函数 代数免疫阶 代数次数 |
| DOI： |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60673068 (国家自然科学基金); the Fundamental Research Funds for the Central Universities of China under Grant No.2009B27414 (中央高校基本科研业务费专项资金); the Natural Science Foundation of Hohai University of China under Grant No.2084/409270 (河海大学自然科学基金) |
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| Cryptographic Properties of Several Classes of Rotation Symmetric Boolean Functions |
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SUN Guang-Hong, WU Chuan-Kun
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| Abstract: |
| Sumanta Sarkar, et al. give a class of rotation symmetric Boolean functions with maximum algebraic immunity, but only consider the nonlinearity of the functions and did not study other cryptographic properties. In this paper, other cryptographic properties of the class of Boolean functions are studied, such as, algebraic degree, linear structure, propagation, correlation immunity etc. The results, unfortunately, show that their other cryptographic properties are not good even though their algebraic immunity is optimum. Hence, the class of Boolean functions cannot be applied in cryptography. |
| Key words: Boolean function symmetric Boolean function rotation symmetric Boolean function algebraic immunity algebraic degree |
