  Traditional cryptography is facing great challenges with the development of
quantum computing. Not only public-key cryptography, the applications of
quantum algorithms to symmetric cryptanalysis has also drawn more and more
attention. In this paper, we apply quantum algorithms to the miss-in-the-middle
technique and propose a quantum algorithm for finding impossible differentials
of general block ciphers. We prove that, as long as the attacked block cipher
satisfies certain algebraic conditions, the outputs of the quantum algorithm
will be impossible differentials of it except for a negligible probability. The
proposed quantum algorithm has polynomial quantum complexity and does not
require any quantum or classical query to the encryption oracle of the block
cipher. Compared with traditional miss-in-the-middle technique, which is
difficult to find impossible differentials as the number of rounds increases,
the quantum version of miss-in-the-middle technique proposed in this paper is
more conducive to find impossible differentials when the block cipher has a
large number of rounds.
