Quantum algorithm to check Resiliency of a Boolean function ( Extended

In this paper, for the first time, we present quantum algorithms to check the order of resiliency of a Boolean function. We first show that the DeutschJozsa algorithm can be directly used for this purpose. We also point out how the quadratic improvement in query complexity over the Deutsch-Jozsa algorithm can be obtained using the well known Grover’s algorithm. While the worst case quantum query complexity to check the resiliency order is exponential, we can cleverly devise a strategy so that the number of measurements are polynomial in number of input variables of the Boolean function. We also point out a subset of n-variable Boolean functions for which the algorithm works in polynomial many steps, i.e., we achieve exponential speed-up over best known classical algorithms.