Verifiable Set Operations Over Outsourced Databases

We study the problem of verifiable delegation of computation over outsourced data, whereby a powerful worker maintains a large data structure for a weak client in a verifiable way. Compared to the well-studied problem of verifiable computation, this setting imposes additional difficulties since the verifier also needs to check the consistency of updates succinctly and without maintaining large state. 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. 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 (involving O(1) modular operations per update). Our construction extends that of [Papamanthou et al., CRYPTO 2011] and relies on a modified version of the extractable collision-resistant hash function (ECRH) construction, introduced in [Bitansky et al., ITCS 2012] that can be used to succinctly hash univariate polynomials.