Quantum Meet-in-the-Middle Attack on Feistel Construction
This work addresses cryptanalysis for security researchers by providing a more practical quantum attack model, though it is incremental as it builds on prior classical and quantum methods.
The paper tackles the problem of reducing time complexity in attacking Feistel constructions by proposing a new quantum meet-in-the-middle attack, achieving a total time complexity of O(2^{2n/3+(r-7)n/4}) for r-round Feistel with r ≥ 7, which is less than classical and quantum attacks.
Inspired by Hosoyamada et al.'s work [14], we propose a new quantum meet-in-the-middle (QMITM) attack on $r$-round ($r \ge 7$) Feistel construction to reduce the time complexity. Similar to Hosoyamada et al.'s work, our attack on 7-round Feistel is also based on Guo et al.'s classical meet-in-the-middle (MITM) attack [13]. The classic MITM attack consumes a lot of time mainly in three aspects: construct the lookup table, query data and find a match. Therefore, parallel Grover search processors are used to reduce the time of constructing the lookup table. And we adjust the truncated differentials of the 5-round distinguisher proposed by Guo et al. to balance the complexities between constructing the lookup table and querying data. Finally, we introduce a quantum claw finding algorithm to find a match for reducing time. The subkeys can be recovered by this match. Furthermore, for $r$-round ($r > 7$) Feistel construction, we treat the above attack on the first 7 rounds as an inner loop and use Grover's algorithm to search the last $r-7$ rounds of subkeys as an outer loop. In summary, the total time complexity of our attack on $r$-round ($r \ge 7$) is only $O(2^{2n/3+(r-7)n/4})$ less than classical and quantum attacks. Moreover, our attack belongs to Q1 model and is more practical than other quantum attacks.