Secure distributed computing made (nearly) optimal

Merav Parter, Eylon Yogev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

In this paper, we study secure distributed algorithms that are nearly optimal, with respect to running time, for the given input graph G. Roughly speaking, an algorithm is secure if the nodes learn only their final output while gaining no information on the input (or output) of other nodes. A graph theoretic framework for secure distributed computation was recently introduced by the authors (SODA 2019). This framework is quite general and it is based on a new combinatorial structure called private neighborhood trees : a collection of n trees T(u1), , T(un) such that each tree T(ui) spans the neighbors of ui without going through ui. Intuitively, each tree T(ui) allows all neighbors of ui to exchange a secret that is hidden from ui. The efficiency of the framework depends on two key parameters of these trees: their depth and the amount of overlap. In a (d,c)-private neighborhood trees each tree T(ui) has depth O(d) and each edge e G appears in at most O(c) different trees. An existentially optimal construction of private neighborhood trees with d=O(Δ D) and c= (D) was presented therein. We make two key contributions: Universally Optimal Private Trees: We show a combinatorial construction of nearly (universally) optimal (d,c)-private neighborhood trees with d + c= (OPT(G)) for any input graph G. Perhaps surprisingly, we show that OPT(G) is equal to the best depth possible for these trees even without the congestion constraint. We also present efficient distributed constructions of these private trees. Optimal Secure Computation: Using the optimal constructions above, we get a secure compiler for distributed algorithms where the overhead for each round is (poly(Δ) OPT(G)). As our second key contribution, we design an optimal compiler with an overhead of merely (OPT(G)) per round for a class of "simple" algorithms. This class includes many standard distributed algorithms such as Luby-MIS, the standard logarithmic-round algorithms for matching and Δ + 1-coloring, as well as the computation of aggregate functions.

Original languageEnglish
Title of host publicationPODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages107-116
Number of pages10
ISBN (Electronic)9781450362177
DOIs
StatePublished - 16 Jul 2019
Externally publishedYes
Event38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada
Duration: 29 Jul 20192 Aug 2019

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference38th ACM Symposium on Principles of Distributed Computing, PODC 2019
Country/TerritoryCanada
CityToronto
Period29/07/192/08/19

Bibliographical note

Publisher Copyright:
© 2019 ACM.

Keywords

  • Distributed algorithms
  • Multi-party computation
  • Private neighborhood trees
  • Secure computation

Fingerprint

Dive into the research topics of 'Secure distributed computing made (nearly) optimal'. Together they form a unique fingerprint.

Cite this