New collision attacks on SHA-1 based on optimal joint local-collision analysis

The main contributions of this paper are two-fold. Firstly, we present a novel direction in the cryptanalysis of the cryptographic hash function {\SHA}. Our work builds on previous cryptanalytic efforts on {\SHA} based on combinations of local collisions. Due to dependencies, previous approaches used heuristic corrections when combining the success probabilities and message conditions of the individual local collisions. Although this leads to success probabilities that are seemingly sufficient for feasible collision attacks, this approach most often does not lead to the maximum success probability possible as desired. We introduce novel techniques that enable us to determine the theoretical maximum success probability for a given set of (dependent) local collisions, as well as the smallest set of message conditions that attains this probability. We apply our new techniques and present an implemented open-source near-collision attack on {\SHA} with a complexity equivalent to $2^{57.5}$ {\SHA} compressions. Secondly, we present an identical-prefix collision attack and a chosen-prefix collision attack on {\SHA} with complexities equivalent to approximately $2^{61}$ and $2^{77.1}$ {\SHA} compressions, respectively.