Designated-Verifier Pseudorandom Generators, and Their Applications

Geoffroy Couteau (1) , Dennis Hofheinz

1 DI-ENS - Département d'informatique - ENS Paris

We provide a generic construction of non-interactive zero-knowledge (NIZK) schemes. Our construction is a refinement of Dwork and Naor's (FOCS 2000) implementation of the hidden bits model using verifiable pseudorandom generators (VPRGs). Our refinement simplifies their construction and relaxes the necessary assumptions considerably. As a result of this conceptual improvement, we obtain interesting new instantiations:-A designated-verifier NIZK (with unbounded soundness) based on the computational Diffie-Hellman (CDH) problem. If a pairing is available, this NIZK becomes publicly verifiable. This constitutes the first fully secure CDH-based designated-verifier NIZKs (and more generally, the first fully secure designated-verifier NIZK from a non-generic assumption which does not already imply publicly-verifiable NIZKs), and it answers an open problem recently raised by Kim and Wu (CRYPTO 2018).-A NIZK based on the learning with errors (LWE) assumption, and assuming a noninteractive witness-indistinguishable (NIWI) proof system for bounded distance decoding (BDD). This simplifies and improves upon a recent NIZK from LWE that assumes a NIZK for BDD (Rothblum et al., PKC 2019).

Mots clés: non-interactive zero-knowledge; computational Diffie-Hellman; learning with errors; verifiable pseudorandom generators

Domaines: Cryptographie et sécurité [cs.CR]

Geoffroy Couteau, Dennis Hofheinz. Designated-Verifier Pseudorandom Generators, and Their Applications. EUROCRYPT 2019 - Annual International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2019, Darmstadt, Germany. pp.562-592, ⟨10.1007/978-3-030-17656-3_20⟩. ⟨hal-03373101⟩