Quantum attacks on some feistel block ciphers

Post-quantum cryptography has attracted much attention from worldwide cryptologists. However, most research works are related to public-key cryptosystem due to Shor's attack on RSA and ECC ciphers. At CRYPTO 2016, Kaplan et al. showed that many secret-key (symmetric) systems could be broken using a quantum period finding algorithm, which encouraged researchers to evaluate symmetric systems against quantum attackers. In this paper, we continue to study symmetric ciphers against quantum attackers. First, we convert the classical advanced slide attacks (introduced by Biryukov and Wagner) to a quantum one, that gains an exponential speed-up in time complexity. Thus, we could break 2/4K-Feistel and 2/4K-DES in polynomial time. Second, we give a new quantum key-recovery attack on full-round GOST, which is a Russian standard, with 2114.8 quantum queries of the encryption process, faster than a quantum brute-force search attack by a factor of 213.2