A Graph Theoretic Approach for Resilient Distributed Algorithms

Projektinformationen

DISTRES

ID Finanzhilfevereinbarung: 949083

DOI

10.3030/949083

EK-Unterschriftsdatum 12 Oktober 2020

Startdatum 1 November 2020

Enddatum 31 Oktober 2026

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten

€ 1 450 085,00

EU-Beitrag

€ 1 450 085,00

Koordiniert durch

WEIZMANN INSTITUTE OF SCIENCE
Israel

Periodic Reporting for period 3 - DISTRES (A Graph Theoretic Approach for Resilient Distributed Algorithms)

Berichtszeitraum: 2023-11-01 bis 2025-04-30

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

Following the immense recent advances in distributed networks, the explosive growth of the Internet, and our increased dependency on these infrastructures, guaranteeing the uninterrupted operation of communication networks has become a major objective in network algorithms. The modern instantiations of distributed networks, such as the Bitcoin network and cloud computing, introduce new security challenges that deserve urgent attention in both theory and practice.

The project is aimed at providing a unified framework for obtaining fast, resilient and secure distributed algorithms for fundamental graph problems. Our approach is based on a graph-theoretic perspective in which common notions of resilient requirements are translated into suitably tailored combinatorial graph structures. Our algorithms provide perfect notions of security which holds against unbounded adversaries that hold full information on the network topology.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

Our developments can be described along the following three lines of research:

1. Designing distributed algorithms that can handle various adversarial settings, such as, node crashes and Byzantine attacks. We will mainly provide general compilation schemes that are based on exploiting the high-connectivity of the graph. Our key focus will be on the efficiency of the resilient algorithms in terms of the number of communication rounds.

2. Initiating and establishing the theoretical exploration of security in distributed graph algorithms. Such a notion has been addressed before mainly in the context of secure multi-party computation (MPC). The heart of our approach is to develop new graph theoretical infrastructures to provide graphical secure channels between nodes in a communication network of an arbitrary topology. Our algorithms are based on strengthening the connections between the areas of fault tolerant network design, distributed graph algorithms and information theoretic security.

3. Designing fault-tolerant graph structures and algorithms, such as fast algorithms for fault-tolerant graph structures, succinct fault-tolerant labeling schemes against edge and vertex failures, and routing schemes.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

In a very recent work, we present an improved framework for secure computation which can handle efficiently a large coalition of semi-honest adversaries. This work is based on
combining two independent lines of research: secure computation and distributed universal optimality.

Another breakthrough result provides a new technique for handling node failure in the network where the complexity measures of the algorithms (in terms of time and space) do not depend on the degree of the corrupted nodes. These graph theoretic foundations lie the basis for providing secure and resilient algorithms against various adversarial settings.