Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables

Construction and count of 1-resilient Rotation symmetric Boolean functions (RSBFs) on $p^{r}$ variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on $p^{r}$ variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on $p^{r}$ variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.