Improved MITM Cryptanalysis on Streebog

At ASIACRYPT 2012, Sasaki et al. introduced the guess-and-determine approach to extend the meet-in-the-middle (MITM) preimage attack. At CRYPTO 2021, Dong et al. proposed a technique to derive the solution spaces of nonlinear constrained neutral words in the MITM preimage attack. In this paper, we try to combine these two techniques to further improve the MITM preimage attacks. Based on the previous MILP-based automatic tools for MITM attacks, we introduce new constraints due to the combination of guess-and-determine and nonlinearly constrained neutral words to build a new automatic model. As a proof of work, we apply it to the Russian national standard hash function Streebog, which is also an ISO standard. We find the first 8.5-round preimage attack on Streebog-512 compression function and the first 7.5-round preimage attack on Streebog-256 compression function. In addition, we give the 8.5-round preimage attack on Streebog-512 hash function. Our attacks extend the best previous attacks by one round. We also improve the time complexity of the 7.5-round preimage attack on Streebog-512 hash function and 6.5-round preimage attack on Streebog-256 hash function.