Aborting Random Oracles: How to Build Them, How to Use Them

In this work, we initiate the study of aborting hash functions, i.e., hash functions that may abort on a non-negligible fraction of inputs. We introduce the aborting random oracle model (aROM), an idealized framework that extends the standard random oracle model (ROM) to account for aborts. Within this model, we derive bounds for various security notions and establish generic indifferentiability results demonstrating how to construct aborting random oracles from standard ones. Consequently, the derived bounds ultimately hold in the standard ROM. In this way, the aROM and its associated bounds provide a convenient and easy-to-use framework for analyzing cryptographic constructions that rely on potentially aborting hash functions.

To illustrate the utility of our framework, we apply our techniques to two settings: (1) the analysis of SNARK-friendly incomparable hypercube encodings, a core primitive in hash-based signature schemes, and (2) the analysis of grinding in Fiat–Shamir-based non-interactive arguments. Through our generic indifferentiability results, we can easily translate these analyses into concrete security bounds in the standard (non-aborting) random oracle model.