Finding collisions in interactive protocols - A tight lower bound on the round complexity of statistically-hiding commitments

Iftach Haitner*, Jonathan J. Hoch, Omer Reingold, Gil Segev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

49 Scopus citations

Abstract

We study the round complexity of various cryptographic protocols. Our main result is a tight lower bound on the round complexity of any fully-black-box construction of a statistically-hiding commitment scheme from oneway permutations, and even from trapdoor permutations. This lower bound matches the round complexity of the statistically-hiding commitment scheme due to Naor, Ostrovsky, Venkatesan and Yung (CRYPTO '92). As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees statistical security for one of the parties. Our techniques extend the collision-finding oracle due to Simon (EUROCRYPT '98) to the setting of interactive protocols (our extension also implies an alternative proof for the main property of the original oracle). In addition, we substantially extend the reconstruction paradigm of Gennaro and Trevisan (FOCS '00). In both cases, our extensions are quite delicate and may be found useful in proving additional black-box separation results.

Original languageAmerican English
Title of host publicationProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007
Pages669-679
Number of pages11
DOIs
StatePublished - 2007
Externally publishedYes
Event48th Annual Symposium on Foundations of Computer Science, FOCS 2007 - Providence, RI, United States
Duration: 20 Oct 200723 Oct 2007

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference48th Annual Symposium on Foundations of Computer Science, FOCS 2007
Country/TerritoryUnited States
CityProvidence, RI
Period20/10/0723/10/07

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