Quantum Differential Meet-In-The-Middle Attack and Some Applications to Lightweight Ciphers

At CRYPTO 2023, Boura et al. proposed a new cryptanalysis technique, differential meet-in-the-middle (MITM) attack. They used MITM technique to make the key recovery step of a differential attack more efficient. In this study, a quantum differential meet-in-the-middle attack is proposed by using nested quantum search algorithm, which can achieve up to a quadratic speed-up compared to the classical version. Besides, the time complexity of the attack can be reduced by at least a factor of $2^{(\left(k_{in}\cup k_{out}\right)-n)/2}$ ($\left(k_{in}\cup k_{out}\right)$ is the guessed key length and $n$ is the block size) compared to the first quantum differential attack proposed by Kaplan et al. at ToSC 2016. Finally, to demonstrate the efficiency of our attack, it is applied to two reduced-round lightweight block ciphers, PIPO and SIMON, to evaluate their post-quantum security. When attacking the same number of rounds, the time complexity of our attack is significantly lower than that of classical attacks. For the 8-round PIPO-128, the attack significantly improves efficiency, reducing the time complexity from $2^{64}+2^{60.94}$ to $2^{60.48}$, cutting down the required qRAM size by a factor of $2^{14}$ and obtaining the data complexity $2^{57}$ instead of $2^{64}$ compared to the best quantum attack proposed by Schrottenloher at CRYPTO 2023. For the 19-round SIMON-32-64, the time complexity here will be $2^{31.68}$ instead of $2^{33.39}$ compared to the other quantum attack, and the attack can target more rounds than using Grover-meets-Simon technique.