Quantum Attacks without Superposition Queries: the Offline Bernstein-Vazirani Meets Grover Algorithm

Block cryptanalysis has a major breakthrough in the model of superposition queries. For instance, Simon’s algorithm can efficiently break various constructions. In practice, Bernstein-Vaziran’s algorithm can also realize the periodic search of the vector function. Moreover, in some cases, it can have more advantages than the Simon’s algorithm.In the context of this study, we present an algorithm that combines Grover’s and Bernstein-Vazirani’s quantum algorithms. This algorithm empowers us to carry out key recovery attacks on Feistel structures. on Feistel structures, FX construction and Even Mansour construction. We exploit cryptosystems’ algebraic structure to launch successful key recovery attacks, considering that quantum attackers can only make classical queries. Through comparison, it can be concluded that this algorithm has stronger practicability in attacking block ciphers.