Friday, March 5, 2021 - 1:00pm to 2:30pm

Location:

Please email dlehto@mit.edu for Zoom Link

Speaker:

Alex Lombardi

Seminar group:

Abstract: We construct hash functions that, assuming the hardness of LWE, securely realize the Fiat-Shamir transform (in the standard model) for the following rich classes of protocols:

- The parallel repetition of any ``commit-and-open'' protocol (such as the seminal Goldreich-Micali-Wigderson protocol for 3-coloring), using a natural choice of commitment scheme. Commit-and-open protocols are a ubiquitous paradigm for constructing general purpose public-coin zero knowledge proofs.

- The parallel repetition of any base protocol that (1) satisfies a stronger notion of soundness called round-by-round soundness, and (2) has an efficient procedure, using a suitable trapdoor, for recognizing ``bad verifier randomness'' that would allow the prover to cheat.

- The parallel repetition of any base protocol that (1) satisfies a stronger notion of soundness called round-by-round soundness, and (2) has an efficient procedure, using a suitable trapdoor, for recognizing ``bad verifier randomness'' that would allow the prover to cheat.

This results in non-interactive variants of all such protocols, and -- for the HVZK proof systems -- proves that assuming LWE, the original interactive protocols cannot be zero knowledge. This leverages a connection due to Dwork-Naor-Reingold-Stockmeyer (FOCS '99) and resolves long-standing open questions about protocols such as GMW.

Our results are obtained by establishing a new connection between the Fiat-Shamir transform and list-recoverable codes. In contrast to the usual focus in coding theory, we focus on a parameter regime in which the input lists are extremely large, but the rate can be small. We give a (probabilistic) construction based on Parvaresh-Vardy codes (FOCS '05) that suffices for our applications.

Based on joint work with Justin Holmgren and Ron Rothblum.