Sometimes You Can’t Distribute Random-Oracle-Based Proofs

Abstract. In this talk, we discuss the conditions under which straight-line extractable non-interactive zero knowledge proofs (NIZKs) in the random oracle model (i.e. without a common reference string) permit threshold realizations that are black-box in the same random oracle. We show that even in the semi-honest setting, any secure protocol to compute such a NIZK cannot make black-box use of the random oracle or a hash function instantiating it if security against all-but-one corruptions is desired, unless the size of the NIZK grows with the number of parties. This presents a fundamental barrier to constructing efficient protocols to securely distribute the computation of NIZKs (and signatures) based on MPC-in-the-head, PCPs/IOPs, and sigma protocols compiled with transformations due to Fischlin, Pass, or Unruh. When the adversary is restricted to corrupt only a constant fraction of parties, we give a positive result by means of a tailored construction, which demonstrates that our impossibility does not extend to weaker corruption models in general.The paper on which this talk is based is available online at https://eprint.iacr.org/2023/1381

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