Easy and hard functions for the Boolean hidden shift problem

16 Apr 2013Andrew M. ChildsRobin KothariMaris OzolsMartin Roetteler

We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent... (read more)

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