### Abstract

We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing. We also give a quantum algorithm for finding collisions in an arbitrary function. For the sponge construction, the algorithm complexity asymptotically matches the complexity implied by collision resistance.

Language | English |
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Title of host publication | Post-Quantum Cryptography - 9th International Conference, PQCrypto 2018, Proceedings |

Publisher | Springer |

Pages | 185-204 |

Number of pages | 20 |

ISBN (Print) | 9783319790626 |

DOIs | |

State | Published - 1 Jan 2018 |

Event | 9th International Conference on Post-Quantum Cryptography (PQCrypto 2018) - Fort Lauderdale, United States Duration: 9 Apr 2018 → 11 Apr 2018 Conference number: 9 |

### 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 | 10786 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 9th International Conference on Post-Quantum Cryptography (PQCrypto 2018) |
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Abbreviated title | PQCrypto 2018 |

Country | United States |

City | Fort Lauderdale |

Period | 9/04/18 → 11/04/18 |

### Fingerprint

### Keywords

- Collapsing
- Collision resistance
- QROM
- Quantum algorithms
- Sponge construction

### Cite this

*Post-Quantum Cryptography - 9th International Conference, PQCrypto 2018, Proceedings*(pp. 185-204). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10786 LNCS). Springer. DOI: 10.1007/978-3-319-79063-3_9

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*Post-Quantum Cryptography - 9th International Conference, PQCrypto 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10786 LNCS, Springer, pp. 185-204, 9th International Conference on Post-Quantum Cryptography (PQCrypto 2018), Fort Lauderdale, United States, 9/04/18. DOI: 10.1007/978-3-319-79063-3_9

**Post-quantum security of the sponge construction.** / Czajkowski, Jan; Groot Bruinderink, Leon; Hülsing, Andreas; Schaffner, Christian; Unruh, Dominique.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Post-quantum security of the sponge construction

AU - Czajkowski,Jan

AU - Groot Bruinderink,Leon

AU - Hülsing,Andreas

AU - Schaffner,Christian

AU - Unruh,Dominique

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing. We also give a quantum algorithm for finding collisions in an arbitrary function. For the sponge construction, the algorithm complexity asymptotically matches the complexity implied by collision resistance.

AB - We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing. We also give a quantum algorithm for finding collisions in an arbitrary function. For the sponge construction, the algorithm complexity asymptotically matches the complexity implied by collision resistance.

KW - Collapsing

KW - Collision resistance

KW - QROM

KW - Quantum algorithms

KW - Sponge construction

UR - http://www.scopus.com/inward/record.url?scp=85045403878&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-79063-3_9

DO - 10.1007/978-3-319-79063-3_9

M3 - Conference contribution

SN - 9783319790626

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 185

EP - 204

BT - Post-Quantum Cryptography - 9th International Conference, PQCrypto 2018, Proceedings

PB - Springer

ER -