The Walsh Spectrum Property of Resilient Boolean Functions

The Walsh spectrum of m-resilient Boolean function at any point is divisible by 2m+2. This property is proved by two new methods in this work, which differ from the known method presented by Maitra. The first method is to compute the Walsh spectrum of resilient Boolean function, which is straightforward compared to the Maitra´s method. The second method is to induce the number of variables and the Hamming weight of any point, which is simpler than the Maitra´s method. Furthermore, this paper discusses the cryptographic properties of Multi-output resilient functions and establishes the relationship among difference, Walsh spectrum and the order of multi-output resilient functions.