Quantum Algorithms for the Resiliency of Vectorial Boolean Functions

Abstract

Recently, Cui and Guo (Quantum Inform. Process. 18, 182, 2019) gave some quantum testing algorithms of multi-output Boolean functions, one of them was for resiliency testing. However, through the algorithm, we cannot get the probability distribution of a Boolean function. Improving the algorithm there, we present quantum algorithms for this problem. Under the condition of non-resiliency, we obtain not only the conclusion that the function F(x) is statistically dependent of which t variables but also the distance of the probability distribution from the uniform distribution.