On nonlinear resilient functions

Abstract

This paper studies resilient functions which have applications in fault-tolerant distributed computing, quantum cryptographic key distribution and random sequence generation for stream ciphers. We present a number of methods for synthesizing resilient functions. An interesting aspect of these methods is that they are applicable both to linear and to nonlinear resilient functions. Our second major contribution is to show that every linear resilient function can be transformed into a large number of nonlinear resilient functions with the same parameters. As a result, we obtain resilient functions that are highly nonlinear and have a high algebraic degree.