## Abstract

Zero-knowledge proofs allow a prover to convince a verifier of a statement without revealing anything besides its validity. A major bottleneck in scaling sub-linear zero-knowledge proofs is the high space requirement of the prover, even for NP relations that can be verified in a small space. In this work, we ask whether there exist complexity-preserving (i.e. overhead w.r.t time and space are minimal) succinct zero-knowledge arguments of knowledge with minimal assumptions while making only black-box access to the underlying primitives. We design the first such zero-knowledge system with sublinear communication complexity (when the underlying NP relation uses non-trivial space) and provide evidence why existing techniques are unlikely to improve the communication complexity in this setting. Namely, for every NP relation that can be verified in time T and space S by a RAM program, we construct a public-coin zero-knowledge argument system that is black-box based on collision-resistant hash-functions (CRH) where the prover runs in time O~ (T) and space O~ (S), the verifier runs in time O~ (T/ S+ S) and space O~ (1 ) and the communication is O~ (T/ S), where O~ () ignores polynomial factors in log T and κ is the security parameter. As our construction is public-coin, we can apply the Fiat-Shamir heuristic to make it non-interactive with sample communication/computation complexities. Furthermore, we give evidence that reducing the proof length below O~ (T/ S) will be hard using existing symmetric-key based techniques by arguing the space-complexity of constant-distance error correcting codes.

Original language | English |
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Title of host publication | Theory of Cryptography - 20th International Conference, TCC 2022, Proceedings |

Editors | Eike Kiltz, Vinod Vaikuntanathan |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 417-446 |

Number of pages | 30 |

ISBN (Print) | 9783031223174 |

DOIs | |

State | Published - 2022 |

Event | 20th Theory of Cryptography Conference, TCC 2022 - Chicago, United States Duration: 7 Nov 2022 → 10 Nov 2022 |

### 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 | 13747 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 20th Theory of Cryptography Conference, TCC 2022 |
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Country/Territory | United States |

City | Chicago |

Period | 7/11/22 → 10/11/22 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

### Funding

Acknowledgements. We thank the anonymous TCC‘22 reviewers for their helpful comments. The first author conducted research during her internship at JP Morgan. The second and third authors are supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office and ISF grant No. 1316/18. The third and fourth authors are supported by DARPA under Contract No. HR001120C0087. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

Funders | Funder number |
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Israel National Cyber Bureau in the Prime Minister’s Office | |

Defense Advanced Research Projects Agency | HR001120C0087 |

Israel Science Foundation | 1316/18 |