Multi-clients verifiable computation via conditional disclosure of secrets

In this paper, we explore the connection between two-party conditional disclosure of secrets (CDS) and verifiable computation. Here, the integrity mechanism underlying CDS is leveraged to ensure two-clients verifiable computation, where the computation is outsourced to an external server by two clients that share the input to the function. Basing integrity on CDS enjoys several significant advantages such as non-interactivity, constant rate communication complexity, a simple verification procedure, easily batched, and more. In this work, we extend the definition of plain CDS, considering two additional security properties of privacy and obliviousness that respectively capture input and output privacy. We then show that these extended notions of CDS are useful for designing secure two-party protocols in the presence of an untrusted third party. We complement the above with a sequence of new CDS constructions for a class of predicates of interest, including private set-intersection (PSI) and set-union cardinality, comparison, range predicate, and more. Based on these constructions we design new non-interactive constant-rate protocols for comparing two strings based on symmetric-key cryptography, and without requiring bit-decomposition. We additionally design new protocols for PSI cardinality and PSI based on recent work by Le, Ranellucci, and Gordon (CCS 2019) with similar advantages.