Statistically Hiding Sets

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 zero-knowledge sets, but providing an information theoretic hiding guarantee, rather than one based on efficient simulation. This is comparable to relaxing zero-knowledge proofs to witness independent proofs. More precisely, we continue to use the simulation paradigm for our definition, but do not require the simulator (nor the distinguisher) to be efficient. 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 zero-knowledge set constructions so far. This not only provides efficien...

• Type: Conference
• Year: 2009
• Where: CTRSA
• Authors: Manoj Prabhakaran, Rui Xue
• Keywords: Cryptology, CTRSA 2009, Zero-knowledge Proofs, Zero-knowledge Set, Zero-knowledge Set Constructions