General method of combining Grover and Simon for attacking block ciphers

The compatibility of different quantum algorithms should be considered when these algorithms are combined. In this paper, the method of combining Grover and Simon is studied for the first time, under some preconditions or assumptions. First, we give two preconditions of applying Grover's algorithm, which ensure that the success probability of finding the marked element is close to 1. Then, based on these two preconditions, it is found out that the success probability of the quantum algorithm for FX-construction is far less than 1. Furthermore, we give the design method of the Oracle function, and then present the general method of combining Grover and Simon algorithm for attacking block ciphers, with success probability close to 1.