Constructions of resilient rotation symmetric boolean functions on given number of variables

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 C_s modulo 2ⁿ- 1 with respect to 2.