Statistically hiding sets

Manoj Prabhakaran, Rui Xue

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Zero-knowledge set is a primitive introduced by Micali, Rabin, and Kilian (FOCS 2003) which enables a prover to commit a set to a verifier, without revealing even the size of the set. Later the prover can give zero-knowledge proofs to convince the verifier of membership/nonmembership of elements in/not in the committed set. We present a new primitive called Statistically Hiding Sets (SHS), similar to zeroknowledge sets, but providing an information theoretic hiding guarantee, rather than one based on efficient simulation. Then we present a new scheme for statistically hiding sets, which does not fit into the "Merkletree/ mercurial-commitment" paradigm that has been used for all zeroknowledge set constructions so far. This not only provides efficiency gains compared to the best schemes in that paradigm, but also lets us provide statistical hiding; previous approaches required the prover to maintain growing amounts of state with each new proof for such a statistical security. Our construction is based on an algebraic tool called trapdoor DDH groups (TDG), introduced recently by Dent and Galbraith (ANTS 2006). However the specific hardness assumptions we associate with TDG are different, and of a strong nature - strong RSA and a knowledge-ofexponent assumption. Our new knowledge-of-exponent assumption may be of independent interest.We prove this assumption in the generic group model.

Original languageEnglish (US)
Title of host publicationTopics in Cryptology - CT-RSA 2009 - The Cryptographers' Track at the RSA Conference 2009, Proceedings
Number of pages17
StatePublished - 2009
Externally publishedYes
EventCryptographers' Track at the RSA Conference, CT-RSA 2009 - San Francisco, CA, United States
Duration: Apr 20 2009Apr 24 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


OtherCryptographers' Track at the RSA Conference, CT-RSA 2009
Country/TerritoryUnited States
CitySan Francisco, CA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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