Construction and Counting of 1-Resilient Rotation Symmetric Boolean Functions on pq Variables

Abstract

In this letter, a property of the characteristic matrix of the Rotation Symmetric Boolean Functions (RSBFs) is characterized, and a sufficient and necessary condition for RSBFs being 1st correlation-immune (1-CI for simplicity) is obtained. This property is applied to construct resilient RSBFs of order 1 (1-resilient for simplicity) on pq variables, where p and q are both prime consistently in this letter. The results show that construction and counting of 1-resilient RSBFs on pq variables are equivalent to solving an equation system and counting the solutions. At last, the counting of all 1-resilient RSBFs on pq variables is also proposed.