## Abstract

Determining the minimal assumptions needed to construct various cryptographic building blocks has been a focal point of research in theoretical cryptography. Here, we revisit the following question: what are the minimal assumptions needed to construct statistically-hiding commitment schemes'? Previously, it was known how to construct such schemes based on one-way permutations. We improve upon this by constructing statistically-hiding commitment schemes based on approximable-preimage-size one-way functions. These are one-way functions for which there is an efficient way to approximate the number of preimages of a given output. A special case (for which we show a somewhat simpler construction) is that of regular one-way functions where all outputs have the same number of preimages. We utilize two different approaches in constructing statistically-hiding commitment schemes. Our first approach proceeds by showing that the scheme of Naor et al. can be implemented using any one-way function having an output distribution which is "sufficiently similar" to uniform. We then construct one-way functions with this property from approximable-preimage-size one-way functions. Our second approach begins by constructing a commitment scheme which is statistically hiding against an honest-but-curious receiver. We then demonstrate a compiler which transforms any such commitment scheme into one which is statistically hiding even against a malicious receiver. This compiler and its analysis may be of independent interest.

Original language | English |
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Pages (from-to) | 58-77 |

Number of pages | 20 |

Journal | Lecture Notes in Computer Science |

Volume | 3494 |

DOIs | |

State | Published - 2005 |

Event | 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology - EUROCRYPT 2005 - Aarhus, Denmark Duration: 22 May 2005 → 26 May 2005 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science