International Association
for Cryptologic Research

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 provided