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Journal of Cryptology

, Volume 22, Issue 3, pp 283–310 | Cite as

Reducing Complexity Assumptions for Statistically-Hiding Commitment

  • Iftach Haitner
  • Omer Horvitz
  • Jonathan Katz
  • Chiu-Yuen Koo
  • Ruggero Morselli
  • Ronen Shaltiel
Article

Abstract

We revisit the following question: what are the minimal assumptions needed to construct statistically-hiding commitment schemes? Naor et al. show how to construct such schemes based on any one-way permutation. We improve upon this by showing a construction based on any approximable preimage-size one-way function. These are one-way functions for which it is possible to efficiently approximate the number of pre-images of a given output. A special case is the class of regular one-way functions where all points in the image of the function have the same (known) number of pre-images.

We also prove two additional results related to statistically-hiding commitment. First, we prove a (folklore) parallel composition theorem showing, roughly speaking, that the statistical hiding property of any such commitment scheme is amplified exponentially when multiple independent parallel executions of the scheme are carried out. Second, we show a compiler which transforms any commitment scheme which is statistically hiding against an honest-but-curious receiver into one which is statistically hiding even against a malicious receiver.

Keywords

Bit commitment Statistical hiding Regular one way functions 

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Copyright information

© International Association for Cryptologic Research 2007

Authors and Affiliations

  • Iftach Haitner
    • 1
  • Omer Horvitz
    • 2
  • Jonathan Katz
    • 2
  • Chiu-Yuen Koo
    • 2
  • Ruggero Morselli
    • 2
  • Ronen Shaltiel
    • 3
  1. 1.Department of Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  3. 3.Department of Computer ScienceUniversity of HaifaHaifaIsrael

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