[Resource Topic] 2019/972: Noninteractive Zero Knowledge Proof System for NP from Ring LWE

Welcome to the resource topic for 2019/972

Title:
Noninteractive Zero Knowledge Proof System for NP from Ring LWE

Authors: Wenping MA

Abstract:

A hash function family is called correlation intractable if for all sparse relations, it hard to find, given a random function from the family, an input output pair that satisfies the relation. Correlation intractability (CI) captures a strong Random Oracle like property of hash functions. In particular, when security holds for all sparse relations, CI suffices for guaranteeing the soundness of the Fiat-Shamir transformation from any constant round, statistically sound interactive proof to a non-interactive argument. In this paper, based on the method proposed by Chris Peikert and Sina Shiehian, we construct a hash family that is computationally correlation intractable for any polynomially bounded size circuits based on Learning with Errors Over Rings (RLWE) with polynomial approximation factors and Short Integer Solution problem over modules (MSIS), and a hash family that is somewhere statistically intractable for any polynomially bounded size circuits based on RLWE. Similarly, our construction combines two novel ingredients: a correlation intractable hash family for log depth circuits based on RLWE, and a bootstrapping transform that uses leveled fully homomorphic encryption (FHE) to promote correlation intractability for the FHE decryption circuit on arbitrary circuits. Our construction can also be instantiated in two possible modes, yielding a NIZK that is either computationally sound and statistically zero knowledge in the common random string model, or vice-versa in common reference string model. The proposed scheme is much more efficient.

ePrint: https://eprint.iacr.org/2019/972

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 .