TY - GEN

T1 - Broadcast CONGEST Algorithms Against Eavesdroppers

AU - Hitron, Yael

AU - Parter, Merav

AU - Yogev, Eylon

N1 - Publisher Copyright:
© Yael Hitron, Merav Parter, and Eylon Yogev.

PY - 2022/10/1

Y1 - 2022/10/1

N2 - An eavesdropper is a passive adversary that aims at extracting private information on the input and output values of the network's participants, by listening to the traffic exchanged over a subset of edges in the graph. We consider secure congest algorithms for the basic broadcast task, in the presence of eavesdropper (edge) adversaries. For D-diameter n-vertex graphs with edge connectivity Θ(f), we present f-secure broadcast algorithms that run in Õ(D + √fn) rounds. These algorithms transmit some broadcast message m∗ to all the vertices in the graph, in a way that is information-theoretically secure against an eavesdropper controlling any subset of at most f edges in the graph. While our algorithms are heavily based on network coding (secret sharing), we also show that this is essential. For the basic problem of secure unicast we demonstrate a network coding gap of Ω(n) rounds. In the presence of vertex adversaries, known as semi-honest, we introduce the Forbidden-Set Broadcast problem: In this problem, the vertices of the graph are partitioned into two sets, trusted and untrusted, denoted as R, F ⊆ V, respectively, such that G[R] is connected. It is then desired to exchange a secret message m∗ between all the trusted vertices while leaking no information to the untrusted set F. Our algorithm works in Õ(D + √|R|) rounds and its security guarantees hold even when all the untrusted vertices F are controlled by a (centralized) adversary.

AB - An eavesdropper is a passive adversary that aims at extracting private information on the input and output values of the network's participants, by listening to the traffic exchanged over a subset of edges in the graph. We consider secure congest algorithms for the basic broadcast task, in the presence of eavesdropper (edge) adversaries. For D-diameter n-vertex graphs with edge connectivity Θ(f), we present f-secure broadcast algorithms that run in Õ(D + √fn) rounds. These algorithms transmit some broadcast message m∗ to all the vertices in the graph, in a way that is information-theoretically secure against an eavesdropper controlling any subset of at most f edges in the graph. While our algorithms are heavily based on network coding (secret sharing), we also show that this is essential. For the basic problem of secure unicast we demonstrate a network coding gap of Ω(n) rounds. In the presence of vertex adversaries, known as semi-honest, we introduce the Forbidden-Set Broadcast problem: In this problem, the vertices of the graph are partitioned into two sets, trusted and untrusted, denoted as R, F ⊆ V, respectively, such that G[R] is connected. It is then desired to exchange a secret message m∗ between all the trusted vertices while leaking no information to the untrusted set F. Our algorithm works in Õ(D + √|R|) rounds and its security guarantees hold even when all the untrusted vertices F are controlled by a (centralized) adversary.

KW - congest

KW - edge-connectivity

KW - secret sharing

UR - http://www.scopus.com/inward/record.url?scp=85140928406&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.DISC.2022.27

DO - 10.4230/LIPIcs.DISC.2022.27

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AN - SCOPUS:85140928406

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 36th International Symposium on Distributed Computing, DISC 2022

A2 - Scheideler, Christian

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 36th International Symposium on Distributed Computing, DISC 2022

Y2 - 25 October 2022 through 27 October 2022

ER -