Better Than Advertised: Improved Collision-Resistance Guarantees for MD-Based Hash Functions

The MD transform that underlies the MD and SHA families iterates a compression function h to get a hash function H. The question we ask is, what property X of h guarantees collision resistance (CR) of H? The classical answer is that X itself be CR. We show that weaker conditions X, in particular forms of what we call constrained-CR, suffice. This reduces demands on compression functions, to the benefit of security, and also, forensically, explains why collisionfinding attacks on compression functions have not, historically, lead to immediate breaks of the corresponding hash functions. We obtain our results via a definitional framework called RS security, and a parameterized treatment of MD, that also serve to unify prior work and variants of the transform.