## Abstract

Collision resistant hashing is a fundamental concept that is the basis for many of the important cryptographic primitives and protocols. Collision resistant hashing is a family of compressing functions such that no efficient adversary can find any collision given a random function in the family. In this work we study a relaxation of collision resistance called distributional collision resistance, introduced by Dubrov and Ishai (STOC ’06). This relaxation of collision resistance only guarantees that no efficient adversary, given a random function in the family, can sample a pair (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. Our first result shows that distributional collision resistance can be based on the existence of multi-collision resistance hash (with no additional assumptions). Multi-collision resistance is another relaxation of collision resistance which guarantees that an efficient adversary cannot find any tuple of (formula presented) inputs that collide relative to a random function in the family. The construction is non-explicit, non-black-box, and yields an infinitely-often secure family. This partially resolves a question of Berman et al. (EUROCRYPT ’18). We further observe that in a black-box model such an implication (from multi-collision resistance to distributional collision resistance) does not exist. Our second result is a construction of a distributional collision resistant hash from the average-case hardness of SZK. Previously, this assumption was not known to imply any form of collision resistance (other than the ones implied by one-way functions).

Original language | English |
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Title of host publication | Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings |

Editors | Alexandra Boldyreva, Hovav Shacham |

Publisher | Springer Verlag |

Pages | 303-327 |

Number of pages | 25 |

ISBN (Print) | 9783319968803 |

DOIs | |

State | Published - 2018 |

Externally published | Yes |

Event | 38th Annual International Cryptology Conference, CRYPTO 2018 - Santa Barbara, United States Duration: 19 Aug 2018 → 23 Aug 2018 |

### 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 | 10992 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 38th Annual International Cryptology Conference, CRYPTO 2018 |
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Country/Territory | United States |

City | Santa Barbara |

Period | 19/08/18 → 23/08/18 |

### Bibliographical note

Publisher Copyright:© 2018, International Association for Cryptologic Research.

### Funding

I. Komargodski—Supported in part by a Packard Foundation Fellowship and by an AFOSR grant FA9550-15-1-0262. E. Yogev—Supported in part by a grant from the Israel Science Foundation (no. 950/16).

Funders | Funder number |
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David and Lucile Packard Foundation | |

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

Israel Science Foundation | 950/16 |