International Association for Cryptologic Research

International Association
for Cryptologic Research


A Note on Non-Interactive Zero-Knowledge from CDH

Geoffroy Couteau , CNRS, IRIF, Université Paris-Cité
Abhishek Jain , Johns Hopkins University
Zhengzhong Jin , MIT
Willy Quach , Northeastern University
DOI: 10.1007/978-3-031-38551-3_23 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2023
Abstract: We build non-interactive zero-knowledge (NIZK) and ZAP arguments for all NP where soundness holds for infinitely-many security parameters, and against uniform adversaries, assuming the subexponential hardness of the Computational Diffie-Hellman (CDH) assumption. We additionally prove the existence of NIZK arguments with these same properties assuming the polynomial hardness of both CDH and the Learning Parity with Noise (LPN) assumption. In both cases, the CDH assumption does not require a group equipped with a pairing. Infinitely-often uniform security is a standard byproduct of commonly used non-black-box techniques that build on disjunction arguments on the (in)security of some primitive. In the course of proving our results, we develop a new variant of this non-black-box technique that yields improved guarantees: we obtain explicit constructions (previous works generally only obtained existential results) where security holds for a relatively dense set of security parameters (as opposed to an arbitrary infinite set of security parameters). We demonstrate that our techniques can have applications beyond our main results.
  title={A Note on Non-Interactive Zero-Knowledge from CDH},
  author={Geoffroy Couteau and Abhishek Jain and Zhengzhong Jin and Willy Quach},