Analysis of the Kupyna-256 Hash Function

The hash function Kupyna was recently published as the Ukrainian standard DSTU 7564:2014. It is structurally very similar to the SHA-3 finalist Grøstl, but differs in details of the round transformations. Most notably, some of the round constants are added with a modular addition, rather than bitwise xor. This change prevents a straightforward application of some recent attacks, in particular of the rebound attacks on the compression function of similar AES-like hash constructions. However, we show that it is actually possible to mount rebound attacks, despite the presence of modular constant additions. More specifically, we describe collision attacks on the compression function for 6 (out of 10) rounds of Kupyna-256 with an attack complexity of 2, and for 7 rounds with complexity 2. In addition, we have been able to use the rebound attack for creating collisions for the round-reduced hash function itself. This is possible for 4 rounds of Kupyna-256 with complexity 2 and for 5 rounds with complexity 2.