# Higher order universal one-way hash functions from the subset sum assumption

Steinfeld, Ron, Pieprzyk, Josef, & Wang, Huaxiong
(2006)
Higher order universal one-way hash functions from the subset sum assumption.
*Lecture Notes in Computer Science : Public Key Cryptography - PKC 2006*, *3958*, pp. 157-173.

## Abstract

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs.

We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log m). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with ‘extension factor’ k+1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k+1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

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ID Code: | 73456 |
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Item Type: | Journal Article |

Refereed: | Yes |

Additional Information: | Paper presented in the 9th International Conference on Theory and Practice in Public-Key Cryptography, New York, NY, USA, April 24-26, 2006.Print ISBN 978-3-540-33851-2 |

DOI: | 10.1007/11745853_11 |

ISBN: | 978-3-540-33852-9 |

ISSN: | 1611-3349 |

Divisions: | Current > QUT Faculties and Divisions > Science & Engineering Faculty |

Deposited On: | 07 Jul 2014 23:14 |

Last Modified: | 15 Jul 2014 02:44 |

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