Concrete constructions of 2-resilient rotation symmetric Boolean functions with 7 variables

Abstract

Based on the properties of the 2-tuples distribution matrix of the rotation symmetric orbits, all 7-variable 2-resilient rotation symmetric Boolean functions were constructed concretely.The results show that there are only 280 nonlinear 2-resilient rotation symmetric Boolean functions over F 2 7 .Furthermore, there are at least 280 nonlinear 2-resilient rotation symmetric Boolean functions over F 2 7k for any odd number k.

Keywords

• cryptography;rotation symmetric function;resilient function;support matrix;2-tuples distribution matrix