2005 | OriginalPaper | Chapter
Reducing Complexity Assumptions for Statistically-Hiding Commitment
Authors : Iftach Haitner, Omer Horvitz, Jonathan Katz, Chiu-Yuen Koo, Ruggero Morselli, Ronen Shaltiel
Published in: Advances in Cryptology – EUROCRYPT 2005
Publisher: Springer Berlin Heidelberg
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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.