Constructions of resilient rotation symmetric boolean functions on given number of variables
Constructions of resilient rotation symmetric boolean functions on given number of variables
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DOI：
10.1049/iet-ifs.2013.0090
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
Jiao Du;Q. Wen;Jie Zhang;S. Pang
中科院分区：
文献类型：
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作者：
Jiao Du;Q. Wen;Jie Zhang;S. Pang
研究了旋转对称布尔函数支撑表的性质，得到了旋转对称布尔函数1-弹性和2-弹性的两个充分必要条件.基于弹性函数与正交表之间的关系，借助于RSBF的支撑表的性质，证明了在给定的变量个数上构造1-弹性RSBF等价于求解一个方程组，且函数的个数等于方程组的解的个数.此外，类似的结果也得到了2-弹性RSBF。最后，给出了一个简单的例子来说明我们的方法.结果表明，构造n元1-弹性RSBF等价于研究关于2的分圆陪集Cs模2 n − 1。
In this study, the properties of the support tables of rotation symmetric Boolean functions (RSBFs for simplicity) are studied, and two sufficient and necessary conditions for RSBFs being 1- and 2-resilient are obtained, respectively. Based on the relations between resilient functions and orthogonal arrays, with the help of the properties about the support tables of RSBFs, it is shown that the constructions of 1-resilient RSBFs on given number of variables are equivalent to solving an equation system, and the number of functions is equal to the number of solutions of the equation system. Moreover, similar results are also obtained for 2-resilient RSBFs. Lastly, a simple example is given to demonstrate our method. The results indicate that the constructions of n-variable 1-resilient RSBFs are equivalent to studying the cyclotomic cosets Cs modulo 2 n − 1 with respect to 2.