## Abstract

Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions. Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions, and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC ’09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions. A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class SZK (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.

Original language | English |
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Title of host publication | Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Editors | Yuval Ishai, Vincent Rijmen |

Publisher | Springer Verlag |

Pages | 667-695 |

Number of pages | 29 |

ISBN (Print) | 9783030176587 |

DOIs | |

State | Published - 2019 |

Event | 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 - Darmstadt, Germany Duration: 19 May 2019 → 23 May 2019 |

### 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 | 11478 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 |
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Country/Territory | Germany |

City | Darmstadt |

Period | 19/05/19 → 23/05/19 |

### Funding

Funders | Funder number |
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Alon Young Faculty Fellowship | |

European Union’s Horizon 2020 research and innovation program | 742754 |

Air Force Office of Scientific Research | FA9550-15-1-0262 |

Horizon 2020 Framework Programme | |

Blavatnik Family Foundation | |

Iowa Science Foundation | |

European Research Council | 638121 |

Israel Science Foundation | 18/484 |

Horizon 2020 |