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Reducing Complexity Assumptions for Statistically-Hiding Commitment

  • Iftach Haitner
  • Omer Horvitz
  • Jonathan Katz
  • Chiu-Yuen Koo
  • Ruggero Morselli
  • Ronen Shaltiel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3494)

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.

Keywords

Function Family Output Distribution Commitment Scheme Pseudorandom Generator Minimal Assumption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

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 Science 
  2. 2.Department of Computer ScienceUniversity of Maryland 
  3. 3.Department of Computer ScienceUniversity of Haifa 

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