Low Congestion Cycle Covers and Their Applications

Parter, Merav; Yogev, Eylon

doi:10.1137/1.9781611975482.101

Cited by 11 publications

(21 citation statements)

References 45 publications

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“…In [PY19a] and [PY19b] we implemented this GBRS methodology for several adversarial settings (e.g., eavesdropper, Byzantine and semi-honest adversaries) in which at most one edge or vertex are corrupted. Extending this scheme to support multiple corruptions, calls for providing new combinatorial graph structures that exploit the high connectivity of the graph, as discussed in Sect.…”

Section: Graph-based Resilient Simulationmentioning

confidence: 99%

Invited Talk: Resilient Distributed Algorithms

Parter

2021

SOFSEM 2021: Theory and Practice of Computer Science

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Following the immense recent advances in distributed networks, the explosive growth of the Internet, and our increased dependence 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 in addition, new security challenges that deserve urgent attention in both theory and practice.This extended abstract describes our initial steps towards developing a unified framework for obtaining fast, resilient and secure distributed algorithms for fundamental graph problems. We will be focusing on two main objectives:-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. -Developing efficient distributed algorithms against various adversarial settings, such as, node crashes and Byzantine attacks. The main novelty in addressing these objectives is in our approach, which is based on taking a graph theoretic perspective where common notions of resilience requirements will be translated into suitably tailored combinatorial graph structures. We believe that the proposed perspective will deepen the theoretical foundations for resilient distributed computation, strengthen the connections with the areas of fault tolerant network design and information theoretic security, and provide a refreshing perspective on extensively-studied graph theoretical concepts.

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Section: Graph-based Resilient Simulationmentioning

confidence: 99%

Invited Talk: Resilient Distributed Algorithms

Parter

2021

SOFSEM 2021: Theory and Practice of Computer Science

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“…Finally, we note that a compiler that works for even a weaker adversary was proposed in [PY18]. In their setting, the adversary can listen to the messages of a single edge where in our setting the adversary listens to all messages received by a single node.…”

Section: Mpc With Locality Constraintsmentioning

confidence: 99%

“…Theorem 3 (Low Congestion Cycle Cover, [PY18]). Every bridgeless graph 3 with diameter D has a (d, c)-cycle cover where d = O(D) and c = O(1).…”

Section: Constructing Private Neighborhood Treesmentioning

confidence: 99%

“…The construction of the private neighborhood trees N consists of = log ∆ phases. In each phase, we compute an (O(D log n), O(log 3 n)) cycle cover in some auxiliary graph using the cycle cover algorithm in [PY18]. We begin by having each node u holding an empty forest F 0 (u) = (Γ(u, G), ∅) consisting only of u's neighbors.…”

Section: Private Neighborhood Treesmentioning

confidence: 99%

“…Using the O(n)-round construction of (d, c) cycle covers with d = O(D) and c = O(1) from [PY18], yields the following: Corollary 1. For every n-vertex graph G = (V, E) with diameter D and maximum degree ∆, one can construct in O(n + ∆ · d) rounds a (d, c) private trees with d = O(D · ∆) and c = O(D).…”

Section: A Distributed Construction Of Private Neighborhood Treesmentioning

confidence: 99%

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Distributed Algorithms Made Secure: A Graph Theoretic Approach

Parter

Yogev

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the area of distributed graph algorithms a number of network's entities with local views solve some computational task by exchanging messages with their neighbors. Quite unfortunately, an inherent property of most existing distributed algorithms is that throughout the course of their execution, the nodes get to learn not only their own output but rather learn quite a lot on the inputs or outputs of many other entities. This leakage of information might be a major obstacle in settings where the output (or input) of network's individual is a private information (e.g., distributed networks of selfish agents, decentralized digital currency such as Bitcoin).While being quite an unfamiliar notion in the classical distributed setting, the notion of secure multi-party computation (MPC) is one of the main themes in the Cryptographic community. The existing secure MPC protocols do not quite fit the framework of classical distributed models in which only messages of bounded size are sent on graph edges in each round. In this paper, we introduce a new framework for secure distributed graph algorithms and provide the first general compiler that takes any "natural" non-secure distributed algorithm that runs in r rounds, and turns it into a secure algorithm that runs in O(r · D · poly(∆)) rounds where ∆ is the maximum degree in the graph and D is its diameter. A "natural" distributed algorithm is one where the local computation at each node can be performed in polynomial time. An interesting advantage of our approach is that it allows one to decouple between the price of locality and the price of security of a given graph function f . The security of the compiled algorithm is information-theoretic but holds only against a semi-honest adversary that controls a single node in the network.This compiler is made possible due to a new combinatorial structure called private neighborhood trees: a collection of n trees T(u 1 ), . . . , T(u n ), one for each vertex u i ∈ V(G), such that each tree T(u i ) spans the neighbors of u i without going through u i . Intuitively, each tree T(u i ) allows all neighbors of u i to exchange a secret that is hidden from u i , which is the basic graph infrastructure of the compiler. In a (d, c)-private neighborhood trees each tree T(u i ) has depth at most d and each edge e ∈ G appears in at most c different trees. We show a construction of private neighborhood trees with d = O(∆ · D) and c = O(D), both these bounds are existentially optimal.

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