We present a scheme for verifiable evaluation of hierarchical set operations (unions, intersections and set-differences) applied to a collection of dynamically changing sets of elements from a given domain. That is, we consider two types of queries issued by the client: updates (insertions and deletions) and data queries, which consist of ``circuits'' of unions, intersections, and set-differences on the current collection of sets. This type of queries comes up in database queries, keyword search and numerous other applications, and indeed our scheme can be effectively used in such scenarios. The verification cost incurred is proportional only to the size of the final outcome set and to the size of the query, and is independent of the cardinalities of the involved sets. The cost of updates is optimal ($O(1)$ modular operations per update).
Our construction extends that of [Papamanthou et al., Crypto 2011] and relies on a modified version of the \emph{extractable collision-resistant hash function} (ECRH) construction, introduced in [Bitansky et al., ITCS 2012] that can be used to succinctly hash univariate polynomials.
Category / Keywords: secure data outsourcing; verifiable computation; knowledge accumulators; extractable collision-resistant hash functions; secure set operations; authenticated query processing; authenticated data structures Date: received 4 Nov 2013 Contact author: dipapado at bu edu Available format(s): PDF | BibTeX Citation Version: 20131107:054629 (All versions of this report) Short URL: ia.cr/2013/724 Discussion forum: Show discussion | Start new discussion