A heuristic for finding compatible differential paths with application to HAS-160

The question of compatibility of differential paths plays a central role in second order collision attacks on hash functions. In this context, attacks typically proceed by starting from the middle and constructing the middle-steps quartet in which the two paths are enforced on the respec- tive faces of the quartet structure. Finding paths that can fit in such a quartet structure has been a major challenge and the currently known compatible paths extend over a suboptimal number of steps for hash functions such as SHA-2 and HAS-160. In this paper, we investigate a heuristic that searches for compatible differential paths. The application of the heuristic in case of HAS-160 yields a practical second order collision over all of the function steps, which is the first practical result that covers all of the HAS-160 steps. An example of a colliding quartet is provide

The Boomerang Attacks on BLAKE and BLAKE2

n this paper, we study the security margins of hash functions BLAKE and BLAKE2 against the boomerang attack. We launch boomerang attacks on all four members of BLAKE and BLAKE2, and compare their complexities. We propose 8.5-round boomerang attacks on both BLAKE-512 and BLAKE2b with complexities $2^{464}$ and $2^{474}$ respectively. We also propose 8-round attacks on BLAKE-256 with complexity $2^{198}$ and 7.5-round attacks on BLAKE2s with complexity $2^{184}$. We verify the correctness of our analysis by giving practical 6.5-round Type I boomerang quartets for each member of BLAKE and BLAKE2. According to our analysis, some tweaks introduced by BLAKE2 have increased its resistance against boomerang attacks to a certain extent. But on the whole, BLAKE still has higher a secure margin than BLAKE2