Byzantine-Resilient Counting in Networks

04/25/2022
by   Soumyottam Chatterjee, et al.
0

We present two distributed algorithms for the Byzantine counting problem, which is concerned with estimating the size of a network in the presence of a large number of Byzantine nodes. In an n-node network (n is unknown), our first algorithm, which is deterministic, finishes in O(logn) rounds and is time-optimal. This algorithm can tolerate up to O(n^1 - γ) arbitrarily (adversarially) placed Byzantine nodes for any arbitrarily small (but fixed) positive constant γ. It outputs a (fixed) constant factor estimate of logn that would be known to all but o(1) fraction of the good nodes. This algorithm works for any bounded degree expander network. However, this algorithms assumes that good nodes can send arbitrarily large-sized messages in a round. Our second algorithm is randomized and most good nodes send only small-sized messages (Throughout this paper, a small-sized message is defined to be one that contains O(logn) bits in addition to at most a constant number of node IDs.). This algorithm works in almost all d-regular graphs. It tolerates up to B(n) = n^1/2 - ξ (note that n and B(n) are unknown to the algorithm) arbitrarily (adversarially) placed Byzantine nodes, where ξ is any arbitrarily small (but fixed) positive constant. This algorithm takes O(B(n)log^2n) rounds and outputs a (fixed) constant factor estimate of logn with probability at least 1 - o(1). The said estimate is known to most nodes, i.e., ≥ (1 - β)n nodes for any arbitrarily small (but fixed) positive constant β. To complement our algorithms, we also present an impossibility result that shows that it is impossible to estimate the network size with any reasonable approximation with any non-trivial probability of success if the network does not have sufficient vertex expansion.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/18/2021

Network Size Estimation in Small-World Networks under Byzantine Faults

We study the fundamental problem of counting the number of nodes in a sp...
research
04/14/2020

Round-Efficient Distributed Byzantine Computation

We present the first round efficient algorithms for several fundamental ...
research
07/12/2023

Sublinear Message Bounds of Authenticated Implicit Byzantine Agreement

This paper studies the message complexity of authenticated Byzantine agr...
research
10/12/2022

Self-stabilization and byzantine tolerance for maximal independt setb ELF-STABILIZATION

We analyze the impact of transient and Byzantine faults on the construct...
research
11/16/2021

Self-Stabilization and Byzantine Tolerance for Maximal Independent Set

We analyze the impact of transient and Byzantine faults on the construct...
research
02/15/2021

Byzantine Dispersion on Graphs

This paper considers the problem of Byzantine dispersion and extends pre...
research
01/23/2018

Byzantine Gathering in Polynomial Time

We study the task of Byzantine gathering in a network modeled as a graph...

Please sign up or login with your details

Forgot password? Click here to reset