Practical Near-Collisions on the Compression Function of BMW

Blue Midnight Wish (BMW) is one of the fastest SHA-3 candidates in the second round of the competition. In this paper we study the compression function of BMW and we obtain practical partial collisions in the case of BMW-256: we show a pair of inputs so that 300 pre-specified bits of the outputs collide (out of 512 bits). Our attack requires about 2 evaluations of the compression function. The attack can also be considered as a near-collision attack: we give an input pair with only 122 active bits in the output, while generic algorithm would require 2 operations for the same result. A similar attack can be developed for BMW-512, which will gives message pairs with around 600 colliding bits for a cost of 2. This analysis does not affect the security of the iterated hash function, but it shows that the compression function is far from ideal. We also describe some tools for the analysis of systems of additions and rotations, which are used in our attack, and which can be useful for the analysis of other systems.