[Resource Topic] 2023/970: A Note on Non-Interactive Zero-Knowledge from CDH

Welcome to the resource topic for 2023/970

A Note on Non-Interactive Zero-Knowledge from CDH

Authors: Geoffroy Couteau, Abhishek Jain, Zhengzhong Jin, Willy Quach


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.

ePrint: https://eprint.iacr.org/2023/970

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .