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DOI: 10.4230/LIPIcs.ITCS.2024.36

Fraud Detection for Random Walks

Authors: Varsha Dani, Thomas P. Hayes, Seth Pettie, and Jared Saia

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

Traditional fraud detection is often based on finding statistical anomalies in data sets and transaction histories. A sophisticated fraudster, aware of the exact kinds of tests being deployed, might be difficult or impossible to catch. We are interested in paradigms for fraud detection that are provably robust against any adversary, no matter how sophisticated. In other words, the detection strategy should rely on signals in the data that are inherent in the goals the adversary is trying to achieve. Specifically, we consider a fraud detection game centered on a random walk on a graph. We assume this random walk is implemented by having a player at each vertex, who can be honest or not. In particular, when the random walk reaches a vertex owned by an honest player, it proceeds to a uniformly random neighbor at the next timestep. However, when the random walk reaches a dishonest player, it instead proceeds to an arbitrary neighbor chosen by an omniscient Adversary. The game is played between the Adversary and a Referee who sees the trajectory of the random walk. At any point during the random walk, if the Referee determines that a {specific} vertex is controlled by a dishonest player, the Referee accuses that player, and therefore wins the game. The Referee is allowed to make the occasional incorrect accusation, but must follow a policy that makes such mistakes with small probability of error. The goal of the adversary is to make the cover time large, ideally infinite, i.e., the walk should never reach at least one vertex. We consider the following basic question: how much can the omniscient Adversary delay the cover time without getting caught? Our main result is a tight upper bound on this delay factor. We also discuss possible applications of our results to settings such as Rotor Walks, Leader Election, and Sybil Defense.

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Varsha Dani, Thomas P. Hayes, Seth Pettie, and Jared Saia. Fraud Detection for Random Walks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dani_et_al:LIPIcs.ITCS.2024.36,
  author =	{Dani, Varsha and Hayes, Thomas P. and Pettie, Seth and Saia, Jared},
  title =	{{Fraud Detection for Random Walks}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.36},
  URN =		{urn:nbn:de:0030-drops-195645},
  doi =		{10.4230/LIPIcs.ITCS.2024.36},
  annote =	{Keywords: Fraud detection, random processes, Markov chains}
}

Document

DOI: 10.4230/LIPIcs.DISC.2020.31

Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols

Authors: John Augustine, Valerie King, Anisur Rahaman Molla, Gopal Pandurangan, and Jared Saia

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract

The last decade has seen substantial progress on designing Byzantine agreement algorithms which do not require all-to-all communication. However, these protocols do require each node to play a particular role determined by its ID. Motivated by the rise of permissionless systems such as Bitcoin, where nodes can join and leave at will, we extend this research to a more practical model where initially, each node does not know the identity of its neighbors. In particular, a node can send to new destinations only by sending to random (or arbitrary) nodes, or responding to messages received from those destinations. We assume a synchronous and fully-connected network, with a full-information, but static Byzantine adversary. A major drawback of existing Byzantine protocols in this setting is that they have at least Ω(n²) message complexity, where n is the total number of nodes. In particular, the communication cost incurred by the honest nodes is Ω(n²), even when Byzantine node send no messages. In this paper, we design protocols for fundamental problems which are message-competitive, i.e., the total number of bits sent by honest nodes is not significantly more than the total sent by Byzantine nodes. We describe a message-competitive algorithm to solve Byzantine agreement, leader election, and committee election. Our algorithm sends an expected O((T+n)log n) bits and has latency O(polylog(n)) (even in the CONGEST model), where T = O(n²) is the number of bits sent by Byzantine nodes. The algorithm is resilient to (1/4-ε)n Byzantine nodes for any fixed ε > 0, and succeeds with high probability. Our message bounds are essentially optimal up to polylagarithmic factors, for algorithms that run in polylogarithmic rounds in the CONGEST model. We also show lower bounds for message-competitive Byzantine agreement regardless of rounds. We prove that, in general, one cannot hope to design Byzantine protocols that have communication cost that is significantly smaller than the cost of the Byzantine adversary.

Cite as

John Augustine, Valerie King, Anisur Rahaman Molla, Gopal Pandurangan, and Jared Saia. Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{augustine_et_al:LIPIcs.DISC.2020.31,
  author =	{Augustine, John and King, Valerie and Molla, Anisur Rahaman and Pandurangan, Gopal and Saia, Jared},
  title =	{{Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.31},
  URN =		{urn:nbn:de:0030-drops-131093},
  doi =		{10.4230/LIPIcs.DISC.2020.31},
  annote =	{Keywords: Byzantine protocols, Byzantine agreement, Leader election, Committee election, Message-competitive protocol, Randomized protocol}
}

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Documents authored by Saia, Jared

Fraud Detection for Random Walks

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Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols

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