International Association for Cryptologic Research

International Association
for Cryptologic Research


Your Reputation's Safe with Me: Framing-Free Distributed Zero-Knowledge Proofs

Carmit Hazay , Bar-Ilan University
Muthuramakrishnan Venkitasubramaniam , Georgetown University
Mor Weiss , Bar-Ilan University
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Presentation: Slides
Conference: TCC 2023
Abstract: {\em Distributed Zero-Knowledge (dZK) proofs}, recently introduced by Boneh et al. (CYPTO`19), allow a prover $\prover$ to prove NP statements on an input $x$ which is {\em distributed} between $k$ verifiers $\verifier_1,\ldots,\verifier_k$, where each $\verifier_i$ holds only a piece of $x$. As in standard ZK proofs, dZK proofs guarantee {\em Completeness} when all parties are honest; {\em Soundness} against a malicious prover colluding with $t$ verifiers; and {\em Zero Knowledge} against a subset of $t$ malicious verifiers, in the sense that they learn nothing about the NP witness and the input pieces of the honest verifiers. Unfortunately, dZK proofs provide no correctness guarantee for an honest prover against a subset of maliciously corrupted verifiers. In particular, such verifiers might be able to ``frame'' the prover, causing honest verifiers to reject a true claim. This is a significant limitation, since such scenarios arise naturally in dZK applications, e.g., for proving honest behavior, and such attacks are indeed possible in existing dZKs (Boneh et al., CRYPTO`19). We put forth and study the notion of {\em strong completeness} for dZKs, guaranteeing that true claims are accepted even when $t$ verifiers are maliciously corrupted. We then design strongly-complete dZK proofs using the ``MPC-in-the-head'' paradigm of Ishai et al. (STOC`07), providing a novel analysis that exploits the unique properties of the distributed setting. To demonstrate the usefulness of strong completeness, we present several applications in which it is instrumental in obtaining security. First, we construct a certifiable version of Verifiable Secret Sharing (VSS), which is a VSS in which the dealer additionally proves that the shared secret satisfies a given NP relation. Our construction withstands a constant fraction of corruptions, whereas a previous construction of Ishai et al. (TCC`14) required $k=\poly\left(t\right)$. We also design a {\em reusable} version of certifiable VSS that we introduce, in which the dealer can prove an {\em unlimited} number of predicates on the {\em same} shared secret. Finally, we extend a compiler of Boneh et al. (CRYPTO`19), who used dZKs to transform a class of ``natural'' semi-honest protocols in the honest-majority setting into maliciously secure ones with abort. Our compiler uses {\em strongly-complete} dZKs to obtain {\em identifiable} abort.
  title={Your Reputation's Safe with Me: Framing-Free Distributed Zero-Knowledge Proofs},
  author={Carmit Hazay and Muthuramakrishnan Venkitasubramaniam and Mor Weiss},