On the Impossibility of Probabilistic Proofs in Relativized Worlds

Alessandro Chiesa; Siqi Liu

Paper 2019/1430

On the Impossibility of Probabilistic Proofs in Relativized Worlds

Alessandro Chiesa and Siqi Liu

Abstract

We initiate the systematic study of probabilistic proofs in relativized worlds. The goal is to understand, for a given oracle, if there exist "non-trivial" probabilistic proofs for checking deterministic or nondeterministic computations that make queries to the oracle. This question is intimately related to a recent line of work that builds cryptographic primitives (e.g., hash functions) via constructions that are "friendly" to known probabilistic proofs. This improves the efficiency of probabilistic proofs for computations calling these primitives. We prove that "non-trivial" probabilistic proofs relative to several natural oracles do not exist. Our results provide strong complexity-theoretic evidence that certain functionalities cannot be treated as black boxes, and thus investing effort to instantiate these functionalities via constructions tailored to known probabilistic proofs may be inherent.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Major revision. ITCS 2020
Keywords: probabilistically checkable proofs relativization
Contact author(s): alexch @ berkeley edu
History: 2019-12-10: received
Short URL: https://ia.cr/2019/1430
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1430,
      author = {Alessandro Chiesa and Siqi Liu},
      title = {On the Impossibility of Probabilistic Proofs in Relativized Worlds},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1430},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1430}
}