Construction of Boolean Functions and Multi-Output Boolean Functions Satisfying the k Degree Propagation Criterion

The construction of Boolean functions requires considering various properties to enhance their applicability in cryptographic systems, and the propagation criterion is one of the important properties, it describes how the output of a Boolean function changes when the input changes. In this paper, by modifying the Maiorana-McFarland construction, we obtained a class of plateaued functions that satisfies 1-resilient, high nonlinearity and good global avalanche characteristics, at the same time, they also satisfy the k degree propagation criterion (PC(k)). Moreover, we extend the construction method to construct multiple output functions. Then a class of balanced multi-output Boolean functions satisfying PC(k) is obtained.