Zero-Knowledge Functional Elementary Databases

Zero-knowledge elementary databases (ZK-EDBs) enable a prover to commit a database D of key-value (x, v) pairs and later provide a convincing answer to the query "send me the value D(x) associated with x" without revealing any extra knowledge (including the size of D). After its introduction, several works extended it to allow more expressive queries, but the expressiveness achieved so far is still limited: only a relatively simple queries-range queries over the keys and values- can be handled by known constructions. In this paper we introduce a new notion called zero knowledge functional elementary databases (ZK-FEDBs), which allows the most general functional queries. Roughly speaking, for any Boolean circuit f, ZK-FEDBs allows the ZK-EDB prover to provide convincing answers to the queries of the form "send me all records (x, v) in D satisfying f(x, v) = 1," without revealing any extra knowledge (including the size of D). We present a construction of ZK-FEDBs in the random oracle model and generic group model, whose proof size is only linear in the length of record and the size of query circuit, and is independent of the size of input database D. Our technical contribution is two-fold. Firstly, we introduce a new variant of zero-knowledge sets (ZKS) which supports combined operations on sets, and present a concrete construction that is based on groups with unknown order. Secondly, we develop a transformation that transforms the query of Boolean circuit into a query of combined operations on related sets, which may be of independent interest.