  Due to the powerful computing capability of quantum computers, cryptographic
researchers have applied quantum algorithms to cryptanalysis and obtained many
interesting results in recent years. In this paper, we study related-key attack
in the quantum setting, and proposed a specific related-key attack which can
recover the key of block ciphers efficiently, as long as the attacked block
ciphers satisfy certain conditions. The attack algorithm employs
Bernstein-Vazirani algorithm as a subroutine and requires the attacker to query
the encryption oracle with quantum superpositions. Afterwards, we rigorously
demonstrate the validity of the attack and analyze its complexity. Our work
shows that related-key attack is quite powerful when combined with quantum
algorithms, and provides some guidance for the design of block ciphers that are
secure against quantum adversaries.
