On the Security of Hash Functions Employing Blockcipher Postprocessing
Analyzing desired generic properties of hash functions is an important current area in cryptography. For example, in Eurocrypt 2009, Dodis, Ristenpart and Shrimpton  introduced the elegant notion of “Preimage Awareness” (PrA) of a hash function HP, and they showed that a PrA hash function followed by an output transformation modeled to be a FIL (fixed input length) random oracle is PRO (pseudorandom oracle) i.e. indifferentiable from a VIL (variable input length) random oracle. We observe that for recent practices in designing hash function (e.g. SHA-3 candidates) most output transformations are based on permutation(s) or blockcipher(s), which are not PRO. Thus, a natural question is how the notion of PrA can be employed directly with these types of more prevalent output transformations? We consider the Davies-Meyer’s type output transformation OT(x) : = E(x) ⊕ x where E is an ideal permutation. We prove that OT(HP(·)) is PRO if HP is PrA, preimage resistant and computable message aware (a related but not redundant notion, needed in the analysis that we introduce in the paper). The similar result is also obtained for 12 PGV output transformations. We also observe that some popular double block length output transformations can not be employed as output transformation.