Improved Quantum Linear Attacks and Application to CAST

This paper studies quantum linear key-recovery attacks on block ciphers. The first such attacks were last-rounds attacks proposed by Kaplan et al. (ToSC 2016), which combine a linear distinguisher with a guess of a partial key. However, the most efficient classical attacks use the framework proposed by Collard et al. (ICISC 2007), which computes experimental correlations using the Fast Walsh-Hadamard Transform. Recently, Schrottenloher (CRYPTO 2023) proposed a quantum version of this technique, in which one uses the available data to create a quantum correlation state, which is a superposition of subkey candidates where the amplitudes are the corresponding correlations. A limitation is that the good subkey is not marked in this state, and cannot be found easily.In this paper, we combine the correlation state with another distinguisher. From here, we can use Amplitude Amplification to recover the right key. We apply this idea to Feistel ciphers and exemplify different attack strategies on LOKI91 before applying our idea on the CAST-128 and CAST-256 ciphers. We demonstrate the approach with two kinds of distinguishers, quantum distinguishers based on Simon’s algorithm and linear distinguishers. The resulting attacks outperform the previous Grover-meet-Simon attacks.