## Abstract

We establish barriers on the efficiency of succinct arguments in the random oracle model. We give evidence that, under standard complexity assumptions, there do not exist succinct arguments where the argument verifier makes a small number of queries to the random oracle. The new barriers follow from new insights into how probabilistic proofs play a fundamental role in constructing succinct arguments in the random oracle model. IOPs are necessary for succinctness. We prove that any succinct argument in the random oracle model can be transformed into a corresponding interactive oracle proof (IOP). The query complexity of the IOP is related to the succinctness of the argument.Algorithms for IOPs. We prove that if a language has an IOP with good soundness relative to query complexity, then it can be decided via a fast algorithm with small space complexity. By combining these results we obtain barriers for a large class of deterministic and non-deterministic languages. For example, a succinct argument for 3 SAT with few verifier queries implies an IOP with good parameters, which in turn implies a fast algorithm for 3 SAT that contradicts the Exponential-Time Hypothesis. We additionally present results that shed light on the necessity of several features of probabilistic proofs that are typically used to construct succinct arguments, such as holography and state restoration soundness. Our results collectively provide an explanation for “why” known constructions of succinct arguments have a certain structure.

Original language | English |
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Title of host publication | Theory of Cryptography - 18th International Conference, TCC 2020, Proceedings |

Editors | Rafael Pass, Krzysztof Pietrzak |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 47-76 |

Number of pages | 30 |

ISBN (Print) | 9783030643775 |

DOIs | |

State | Published - 2020 |

Externally published | Yes |

Event | 18th International Conference on Theory of Cryptography, TCCC 2020 - Durham, United States Duration: 16 Nov 2020 → 19 Nov 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12551 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 18th International Conference on Theory of Cryptography, TCCC 2020 |
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Country/Territory | United States |

City | Durham |

Period | 16/11/20 → 19/11/20 |

### Bibliographical note

Funding Information:Alessandro Chiesa is funded by the Ethereum Foundation and Eylon Yogev is funded by the ISF grants 484/18, 1789/19, Len Blavatnik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University. This work was done (in part) while the second author was visiting the Simons Institute for the Theory of Computing.

Funding Information:

We thank Amey Bhangale, Karthik C. S., and Inbal Livni Navon for fruitful discussions regarding PCPs and the sliding scale conjecture. Alessandro Chiesa is funded by the Ethereum Foundation and Eylon Yogev is funded by the ISF grants 484/18, 1789/19, Len Blavatnik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University. This work was done (in part) while the second author was visiting the Simons Institute for the Theory of Computing.

Publisher Copyright:

© International Association for Cryptologic Research 2020.

## Keywords

- Interactive oracle proofs
- Succinct arguments