Paper 2023/970

A Note on Non-Interactive Zero-Knowledge from CDH

Geoffroy Couteau, Université Paris Cité, CNRS, IRIF
Abhishek Jain, Johns Hopkins University
Zhengzhong Jin, Massachusetts Institute of Technology
Willy Quach, Northeastern University

We build non-interactive zero-knowledge (NIZK) and ZAP arguments for all $\mathsf{NP}$ 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 technique can have applications beyond our main results.

Available format(s)
Publication info
A minor revision of an IACR publication in CRYPTO 2023
Non-Interactive Zero-KnowledgeCDH
Contact author(s)
couteau @ irif fr
abhishek @ cs jhu edu
zzjin @ mit edu
quach w @ northeastern edu
2023-06-21: approved
2023-06-20: received
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      author = {Geoffroy Couteau and Abhishek Jain and Zhengzhong Jin and Willy Quach},
      title = {A Note on Non-Interactive Zero-Knowledge from CDH},
      howpublished = {Cryptology ePrint Archive, Paper 2023/970},
      year = {2023},
      note = {\url{}},
      url = {}
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