New Constructions of Statistical NIZKs: Dual-Mode DV-NIZKs and More.

Non-interactive zero-knowledge proofs (NIZKs) are important primitives in cryptography. A major challenge since the early works on NIZKs has been to construct NIZKs with a statistical zero-knowledge guarantee against unbounded verifiers. In the common reference string (CRS) model, such “statistical NIZK arguments” are currently known from \\(k\\text {-}\\mathsf {Lin} \\) in a pairing-group and from \\(\\mathsf {LWE}\\). In the (reusable) designated-verifier model (DV-NIZK), where a trusted setup algorithm generates a reusable verification key for checking proofs, we also have a construction from \\(\\mathsf {DCR}\\). If we relax our requirements to computational zero-knowledge, we additionally have NIZKs from factoring and \\(\\mathsf {CDH}\\) in a pairing group in the CRS model, and from nearly all assumptions that imply public-key encryption (e.g., \\(\\mathsf {CDH}\\), \\(\\mathsf {LPN}\\), \\(\\mathsf {LWE}\\)) in the designated-verifier model. Thus, there still remains a gap in our understanding of statistical NIZKs in both the CRS and the designated-verifier models.