Efficient Verifiable Range and Closest Point Queries in Zero-Knowledge

Abstract

Abstract:We present an efficient method for answering one-dimensional range and closest-point queries in a verifiable and privacy-preserving manner. We consider a model where a data owner outsources a dataset of keyvalue pairs to a server, who answers range and closestpoint queries issued by a client and provides proofs of the answers. The client verifies the correctness of the answers while learning nothing about the dataset besides the answers to the current and previous queries. Our work yields for the first time a zero-knowledge privacy assurance to authenticated range and closest-point queries. Previous work leaked the size of the dataset and used an inefficient proof protocol. Our construction is based on hierarchical identity-based encryption. We prove its security and analyze its efficiency both theoretically and with experiments on synthetic and real data (Enron email and Boston taxi datasets).

Zero-Knowledge Elementary Databases with More Expressive Queries

“…We also mention a large body of work devoted to authenticated data structures [26,32,30,29,27,12]. We insist that these result address a different problem than ours as they stand in the three party setting.…”

“…For this reason, we focus on the two-party setting which is usually more challenging and results in less efficient schemes. Our protocols are indeed less efficient than the range queries of Ghosh et al [12] -which, to our knowledge, is the best size-hiding construction handling range queries in the three-party setting -but they do not assume a trusted committer.…”

“…We recall the complete subtree method proposed by Naor, Naor and Lotspiech [25], which is one of the algorithms in the subsetcover framework. This technique is also used by Ghosh et al [12] to obtain onedimensional range queries in the three party setting. This work, on the other hand, is in the two party setting which is more challenging to realize.…”

Privacy-preserving protocols from lattice cryptography

“…Existing proposals in the literature all require weakening the notion of privacy to achieve range queries. In a three-party setting with trusted data owner, called a committer, and a third party who acts as the prover, a solution for zero-knowledge one-dimensional range queries was proposed by Ghosh et al [90]. Alternatively, if we allow a polynomial-sized upper bound on the database size to be revealed, Ostrovsky et al [166] showed that efficient zero-knowledge d-dimensional orthogonal range queries (d ≥ 1) is possible.…”

“…We recall the notion of canonical coverings from Ghosh et al [90], who used it to achieve zero-knowledge range queries in the three-party setting. For some set of leaves…”