Computing Almost Exact Probabilities of Differential Hash Collision Paths by Applying Appropriate Stochastic Methods
Generally speaking, the probability of a differential path determines an upper bound for the expected workload and thus for the true risk potential of a differential attack. In particular, if the expected workload seems to be in a borderline region between practical feasibility and non-feasibility it is desirable to know the path probability as exact as possible. We present a generally applicable approach to determine at least almost exact probabilities of differential paths where we focus on (near-)collision paths for Merkle-Damgard-type hash functions. Our results show both that the number of bit conditions provides only a rough estimate for the true path probability and that the IV may have significant impact on the path probability. For MD5 we verified the effectivity of our approach experimentally. An abbreviated version [GIS4], which in particular omits proofs, technical details and several examples, will appear in the proceedings of the security conference 'Sicherheit 2008'.