Using Bernstein-Vazirani Algorithm to Attack Block Ciphers

We study applications of BV algorithm and present several new attacks for block ciphers based on it. Specifically, we propose new quantum distinguishers for the 3-round Feistel scheme and a quantum algorithm to recover partial key of Even-Mansour construction. Afterwards, by observing that a linear structure of a encryption function can induce a high probability differential, we propose two quantum algorithms which can be applied in differential cryptanalysis and impossible differential cryptanalysis respectively. Based on the fact that our algorithms find differentials of a vector function by searching for the differentials of its component functions respectively, we propose a new kind of differential cryptanalysis, called small probability differential cryptanalysis. The efficiencies and success probabilities of all attacks are analyzed rigorously.