Improved (Pseudo) Preimage Attacks on Reduced-Round GOST and Grøstl-256 and Studies on Several Truncation Patterns for AES-like Compression Functions

In this paper, we present improved preimage attacks on the reduced-round GOST hash function family, which serves as the new Russian hash standard, with the aid of techniques such as the rebound attack, the Meet-in-the-Middle preimage attack and the multicollisions. Firstly, the preimage attack on 5-round GOST-256 is proposed which is the first preimage attack for GOST-256 at the hash function level. Then we extend the (previous) attacks on 5-round GOST-256 and 6-round GOST-512 to 6.5 and 7.5 rounds respectively by exploiting the involution property of the GOST transposition operation. Secondly, inspired by the preimage attack on GOST-256, we also study the impacts of four representative truncation patterns on the resistance of the Meet-in-the-Middle preimage attack against AES-like compression functions, and propose two stronger truncation patterns which make it more difficult to launch this type of attack. Based on our investigations, we are able to slightly improve the previous pseudo preimage attacks on reduced-round Grøstl-256.