Finding collisions in interactive protocols - Tight lower bounds on the round and communication complexities of statistically hiding commitments

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

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations and from trapdoor permutations. 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 [Advances in Cryptology - EUROCRYPT '98, Lecture Notes in Comput. Sci. 1403, Springer, Berlin, 1998, pp. 334-345] to the setting of interactive protocols and the reconstruction paradigm of Gennaro and Trevisan [Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS), IEEE Press, Piscataway, NJ, 2000, pp. 305-313].

Original languageAmerican English
Pages (from-to)193-242
Number of pages50
JournalSIAM Journal on Computing
Volume44
Issue number1
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.

Keywords

  • Black-box impossibility results
  • One-way functions
  • Private information retrieval
  • Statistically hiding commitments

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