Abstract
Post-quantum cryptography has drawn considerable attention from cryptologists on a global scale. At Asiacrypt 2017, Leander and May combined Grovers and Simons quantum algorithms to break the FX-based block ciphers, which were introduced by Kilian and Rogaway to strengthen DES. In this study, we investigate the Feistel constructions using Grovers and Simons algorithms to generate new quantum key-recovery attacks on different rounds of Feistel constructions. Our attacksrequire $2^{0.25nr-0.75n}$ quantum queries to break an $r$-round Feistel construction.The time complexity of our attacks is less than that observed for quantum brute-force search by a factor of $2^{0.75n}$. When compared with the best classical attacks, i.e., Dinur et al.s attacks at CRYPTO 2015, the time complexity is reduced by a factor of $2^{0.5n}$ without incurring any memory cost.
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