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 $x$\u27\u27 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 $f(x,v)=1$,\u27\u27 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 constribution 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 tranformation that tranforms the query of Boolean circuit into a query of combined operations on related sets, which may be of independent interest

Relaxed Lattice-Based Signatures with Short Zero-Knowledge Proofs

Higher-level cryptographic privacy-enhancing protocols such as anonymous credentials, voting schemes, and e-cash are often constructed by suitably combining signature, commitment, and encryption schemes with zero-knowledge proofs. Indeed, a large body of protocols have been constructed in that manner from Camenisch-Lysyanskaya signatures and generalized Schnorr proofs. In this paper, we build a similar framework for lattice-based schemes by presenting a signature and commitment scheme that are compatible with Lyubashevsky\u27s Fiat-Shamir proofs with abort, currently the most efficient zero-knowledge proofs for lattices. To cope with the relaxed soundness guarantees of these proofs, we define corresponding notions of relaxed signature and commitment schemes. We demonstrate the flexibility and efficiency of our new primitives by constructing a new lattice-based anonymous attribute token scheme and providing concrete parameters to securely instantiate this scheme