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Fully Local Succinct Distributed Arguments

Authors Eden Aldema Tshuva , Rotem Oshman

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Author Details

Eden Aldema Tshuva
  • Tel Aviv University, Israel
Rotem Oshman
  • Tel Aviv University, Israel

Funding

  • Aldema Tshuva, Eden: Supported in part by AFOSR Award FA9550-23-1-0312, and an Algorand Foundation grant.
  • Oshman, Rotem: Research funded by the Israel Science Foundation, Grant No. 2801/20, and also supported by Len Blavatnik and the Blavatnik Family Foundation.

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Eden Aldema Tshuva and Rotem Oshman. Fully Local Succinct Distributed Arguments. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.1

Abstract

Distributed certification is a proof system for detecting illegal network states or improper execution of distributed algorithms. A certification scheme consists of a proving algorithm, which assigns a certificate to each node, and a verification algorithm where nodes use these certificates to decide whether to accept or reject. The system must ensure that all nodes accept if and only if the network is in a legal state, adhering to the principles of completeness and soundness. The main goal is to design a scheme where the verification process is local and the certificates are succinct, while using as efficient as possible proving algorithm. In cryptographic proof systems, the soundness requirement is often relaxed to computational soundness, where soundness is guaranteed only against computationally bounded adversaries. Computationally sound proof systems are called arguments. Recently, Aldema Tshuva, Boyle, Cohen, Moran, and Oshman (TCC 2023) showed that succinct distributed arguments can be used to enable any polynomially bounded distributed algorithm to certify its execution with polylogarithmic-length certificates. However, their approach required a global communication phase, adding O(D) communication rounds in networks of diameter D, which limits its applicability to local algorithms. In this work, we give the first construction of a fully local succinct distributed argument system, where the prover and the verifier are both local. We show that a distributed algorithm that runs in R rounds, has polynomial local computation, and messages of B bits each can be compiled into a self-certifying algorithm that runs in R + polylog(n) rounds and sends messages of size B + polylog(n), with certificates of length polylog(n). This construction has several applications, including self-certification for local algorithms, ongoing certification of long-lived algorithms, and efficient local mending of the certificates when the network changes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • distributed certification
  • proof labeling schemes
  • SNARG

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