## Cryptology ePrint Archive: Report 2000/053

A Construction of Resilient Functions with High Nonlinearity

Thomas Johansson and Enes Pasalic

Abstract: The relationship between nonlinearity and resiliency for a function $F:\mathbb{F}_2^n \mapsto \mathbb{F}_2^m$ is considered. We give a construction of resilient functions with high nonlinearity. The construction leads to the problem of finding a set of linear codes with a fixed minimum distance, having the property that the intersection between any two codes is the all zero codeword only. This problem is considered, and existence results are provided. The constructed functions obtain a nonlinearity superior to previous construction methods.

Category / Keywords: boolean function;resilient function;S-box;nonintersecting codes