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**Published in:** LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Consensus enables n processes to agree on a common valid L-bit value, despite t < n/3 processes being faulty and acting arbitrarily. A long line of work has been dedicated to improving the worst-case communication complexity of consensus in partial synchrony. This has recently culminated in the worst-case word complexity of O(n²). However, the worst-case bit complexity of the best solution is still O(n²L + n²κ) (where κ is the security parameter), far from the Ω(nL + n²) lower bound. The gap is significant given the practical use of consensus primitives, where values typically consist of batches of large size (L > n).
This paper shows how to narrow the aforementioned gap. Namely, we present a new algorithm, DARE (Disperse, Agree, REtrieve), that improves upon the O(n²L) term via a novel dispersal primitive. DARE achieves O(n^{1.5}L + n^{2.5}κ) bit complexity, an effective √n-factor improvement over the state-of-the-art (when L > nκ). Moreover, we show that employing heavier cryptographic primitives, namely STARK proofs, allows us to devise DARE-Stark, a version of DARE which achieves the near-optimal bit complexity of O(nL + n²poly(κ)). Both DARE and DARE-Stark achieve optimal O(n) worst-case latency.

Pierre Civit, Seth Gilbert, Rachid Guerraoui, Jovan Komatovic, Matteo Monti, and Manuel Vidigueira. Every Bit Counts in Consensus. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 13:1-13:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{civit_et_al:LIPIcs.DISC.2023.13, author = {Civit, Pierre and Gilbert, Seth and Guerraoui, Rachid and Komatovic, Jovan and Monti, Matteo and Vidigueira, Manuel}, title = {{Every Bit Counts in Consensus}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {13:1--13:26}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-301-0}, ISSN = {1868-8969}, year = {2023}, volume = {281}, editor = {Oshman, Rotem}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.13}, URN = {urn:nbn:de:0030-drops-191399}, doi = {10.4230/LIPIcs.DISC.2023.13}, annote = {Keywords: Byzantine consensus, Bit complexity, Latency} }

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**Published in:** LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Detecting the source of a gossip is a critical issue, related to identifying patient zero in an epidemic, or the origin of a rumor in a social network. Although it is widely acknowledged that random and local gossip communications make source identification difficult, there exists no general quantification of the level of anonymity provided to the source. This paper presents a principled method based on ε-differential privacy to analyze the inherent source anonymity of gossiping for a large class of graphs. First, we quantify the fundamental limit of source anonymity any gossip protocol can guarantee in an arbitrary communication graph. In particular, our result indicates that when the graph has poor connectivity, no gossip protocol can guarantee any meaningful level of differential privacy. This prompted us to further analyze graphs with controlled connectivity. We prove on these graphs that a large class of gossip protocols, namely cobra walks, offers tangible differential privacy guarantees to the source. In doing so, we introduce an original proof technique based on the reduction of a gossip protocol to what we call a random walk with probabilistic die out. This proof technique is of independent interest to the gossip community and readily extends to other protocols inherited from the security community, such as the Dandelion protocol. Interestingly, our tight analysis precisely captures the trade-off between dissemination time of a gossip protocol and its source anonymity.

Rachid Guerraoui, Anne-Marie Kermarrec, Anastasiia Kucherenko, Rafael Pinot, and Sasha Voitovych. On the Inherent Anonymity of Gossiping. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{guerraoui_et_al:LIPIcs.DISC.2023.24, author = {Guerraoui, Rachid and Kermarrec, Anne-Marie and Kucherenko, Anastasiia and Pinot, Rafael and Voitovych, Sasha}, title = {{On the Inherent Anonymity of Gossiping}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {24:1--24:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-301-0}, ISSN = {1868-8969}, year = {2023}, volume = {281}, editor = {Oshman, Rotem}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.24}, URN = {urn:nbn:de:0030-drops-191504}, doi = {10.4230/LIPIcs.DISC.2023.24}, annote = {Keywords: Gossip protocol, Source anonymity, Differential privacy} }

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**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Byzantine Reliable Broadcast (BRB) is a fundamental distributed computing primitive, with applications ranging from notifications to asynchronous payment systems. Motivated by practical consideration, we study Client-Server Byzantine Reliable Broadcast (CSB), a multi-shot variant of BRB whose interface is split between broadcasting clients and delivering servers. We present Draft, an optimally resilient implementation of CSB. Like most implementations of BRB, Draft guarantees both liveness and safety in an asynchronous environment. Under good conditions, however, Draft achieves unparalleled efficiency. In a moment of synchrony, free from Byzantine misbehaviour, and at the limit of infinitely many broadcasting clients, a Draft server delivers a b-bits payload at an asymptotic amortized cost of 0 signature verifications, and (log₂(c) + b) bits exchanged, where c is the number of clients in the system. This is the information-theoretical minimum number of bits required to convey the payload (b bits, assuming it is compressed), along with an identifier for its sender (log₂(c) bits, necessary to enumerate any set of c elements, and optimal if broadcasting frequencies are uniform or unknown). These two achievements have profound practical implications. Real-world BRB implementations are often bottlenecked either by expensive signature verifications, or by communication overhead. For Draft, instead, the network is the limit: a server can deliver payloads as quickly as it would receive them from an infallible oracle.

Martina Camaioni, Rachid Guerraoui, Matteo Monti, and Manuel Vidigueira. Oracular Byzantine Reliable Broadcast. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{camaioni_et_al:LIPIcs.DISC.2022.13, author = {Camaioni, Martina and Guerraoui, Rachid and Monti, Matteo and Vidigueira, Manuel}, title = {{Oracular Byzantine Reliable Broadcast}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {13:1--13:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.13}, URN = {urn:nbn:de:0030-drops-172048}, doi = {10.4230/LIPIcs.DISC.2022.13}, annote = {Keywords: Byzantine reliable broadcast, Good-case complexity, Amortized complexity, Batching} }

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**Published in:** LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic communication complexity in the worst case. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT).
This paper closes the existing gap by introducing SQuad, a partially synchronous Byzantine consensus protocol with quadratic worst-case communication complexity. In addition, SQuad is optimally-resilient and achieves linear worst-case latency complexity. The key technical contribution underlying SQuad lies in the way we solve view synchronization, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present RareSync, a view synchronization protocol with quadratic communication complexity and linear latency complexity, which we utilize in order to obtain SQuad.

Pierre Civit, Muhammad Ayaz Dzulfikar, Seth Gilbert, Vincent Gramoli, Rachid Guerraoui, Jovan Komatovic, and Manuel Vidigueira. Byzantine Consensus Is Θ(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{civit_et_al:LIPIcs.DISC.2022.14, author = {Civit, Pierre and Dzulfikar, Muhammad Ayaz and Gilbert, Seth and Gramoli, Vincent and Guerraoui, Rachid and Komatovic, Jovan and Vidigueira, Manuel}, title = {{Byzantine Consensus Is \Theta(n²): The Dolev-Reischuk Bound Is Tight Even in Partial Synchrony!}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {14:1--14:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-255-6}, ISSN = {1868-8969}, year = {2022}, volume = {246}, editor = {Scheideler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.14}, URN = {urn:nbn:de:0030-drops-172059}, doi = {10.4230/LIPIcs.DISC.2022.14}, annote = {Keywords: Optimal Byzantine consensus, Communication complexity, Latency complexity} }

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**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Traditional techniques for handling Byzantine failures are expensive: digital signatures are too costly, while using 3f+1 replicas is uneconomical (f denotes the maximum number of Byzantine processes). We seek algorithms that reduce the number of replicas to 2f+1 and minimize the number of signatures. While the first goal can be achieved in the message-and-memory model, accomplishing the second goal simultaneously is challenging. We first address this challenge for the problem of broadcasting messages reliably. We study two variants of this problem, Consistent Broadcast and Reliable Broadcast, typically considered very close. Perhaps surprisingly, we establish a separation between them in terms of signatures required. In particular, we show that Consistent Broadcast requires at least 1 signature in some execution, while Reliable Broadcast requires O(n) signatures in some execution. We present matching upper bounds for both primitives within constant factors. We then turn to the problem of consensus and argue that this separation matters for solving consensus with Byzantine failures: we present a practical consensus algorithm that uses Consistent Broadcast as its main communication primitive. This algorithm works for n = 2f+1 and avoids signatures in the common case - properties that have not been simultaneously achieved previously. Overall, our work approaches Byzantine computing in a frugal manner and motivates the use of Consistent Broadcast - rather than Reliable Broadcast - as a key primitive for reaching agreement.

Marcos K. Aguilera, Naama Ben-David, Rachid Guerraoui, Dalia Papuc, Athanasios Xygkis, and Igor Zablotchi. Frugal Byzantine Computing. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{aguilera_et_al:LIPIcs.DISC.2021.3, author = {Aguilera, Marcos K. and Ben-David, Naama and Guerraoui, Rachid and Papuc, Dalia and Xygkis, Athanasios and Zablotchi, Igor}, title = {{Frugal Byzantine Computing}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {3:1--3:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.3}, URN = {urn:nbn:de:0030-drops-148051}, doi = {10.4230/LIPIcs.DISC.2021.3}, annote = {Keywords: Reliable Broadcast, Consistent Broadcast, Consensus, Byzantine Failure, Message-and-memory} }

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**Published in:** LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Modern machine learning architectures distinguish servers and workers. Typically, a d-dimensional model is hosted by a server and trained by n workers, using a distributed stochastic gradient descent (SGD) optimization scheme. At each SGD step, the goal is to estimate the gradient of a cost function. The simplest way to do this is to average the gradients estimated by the workers. However, averaging is not resilient to even one single Byzantine failure of a worker. Many alternative gradient aggregation rules (GARs) have recently been proposed to tolerate a maximum number f of Byzantine workers. These GARs differ according to (1) the complexity of their computation time, (2) the maximal number of Byzantine workers despite which convergence can still be ensured (breakdown point), and (3) their accuracy, which can be captured by (3.1) their angular error, namely the angle with the true gradient, as well as (3.2) their ability to aggregate full gradients. In particular, many are not full gradients for they operate on each dimension separately, which results in a coordinate-wise blended gradient, leading to low accuracy in practical situations where the number (s) of workers that are actually Byzantine in an execution is small (s < < f).
We propose Aksel, a new scalable median-based GAR with optimal time complexity (𝒪(nd)), optimal breakdown point (n > 2f) and the lowest upper bound on the expected angular error (𝒪(√d)) among full gradient approaches. We also study the actual angular error of Aksel when the gradient distribution is normal and show that it only grows in 𝒪(√dlog{n}), which is the first logarithmic upper bound ever proven on the number of workers n assuming an optimal breakdown point. We also report on an empirical evaluation of Aksel on various classification tasks, which we compare to alternative GARs against state-of-the-art attacks. Aksel is the only GAR reaching top accuracy when there is actually none or few Byzantine workers while maintaining a good defense even under the extreme case (s = f). For simplicity of presentation, we consider a scheme with a single server. However, as we explain in the paper, Aksel can also easily be adapted to multi-server architectures that tolerate the Byzantine behavior of a fraction of the servers.

Amine Boussetta, El-Mahdi El-Mhamdi, Rachid Guerraoui, Alexandre Maurer, and Sébastien Rouault. AKSEL: Fast Byzantine SGD. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{boussetta_et_al:LIPIcs.OPODIS.2020.8, author = {Boussetta, Amine and El-Mhamdi, El-Mahdi and Guerraoui, Rachid and Maurer, Alexandre and Rouault, S\'{e}bastien}, title = {{AKSEL: Fast Byzantine SGD}}, booktitle = {24th International Conference on Principles of Distributed Systems (OPODIS 2020)}, pages = {8:1--8:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-176-4}, ISSN = {1868-8969}, year = {2021}, volume = {184}, editor = {Bramas, Quentin and Oshman, Rotem and Romano, Paolo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.8}, URN = {urn:nbn:de:0030-drops-134931}, doi = {10.4230/LIPIcs.OPODIS.2020.8}, annote = {Keywords: Machine learning, Stochastic gradient descent, Byzantine failures} }

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**Published in:** LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Reliable broadcast is a communication primitive guaranteeing, intuitively, that all processes in a distributed system deliver the same set of messages. The reason why this primitive is appealing is twofold: (i) we can implement it deterministically in a completely asynchronous environment, unlike stronger primitives like consensus and total-order broadcast, and yet (ii) reliable broadcast is powerful enough to implement important applications like payment systems.
The problem we tackle in this paper is that of dynamic reliable broadcast, i.e., enabling processes to join or leave the system. This property is desirable for long-lived applications (aiming to be highly available), yet has been precluded in previous asynchronous reliable broadcast protocols. We study this property in a general adversarial (i.e., Byzantine) environment.
We introduce the first specification of a dynamic Byzantine reliable broadcast (dbrb) primitive that is amenable to an asynchronous implementation. We then present an algorithm implementing this specification in an asynchronous network. Our dbrb algorithm ensures that if any correct process in the system broadcasts a message, then every correct process delivers that message unless it leaves the system. Moreover, if a correct process delivers a message, then every correct process that has not expressed its will to leave the system delivers that message. We assume that more than 2/3 of processes in the system are correct at all times, which is tight in our context.
We also show that if only one process in the system can fail - and it can fail only by crashing - then it is impossible to implement a stronger primitive, ensuring that if any correct process in the system broadcasts or delivers a message, then every correct process in the system delivers that message - including those that leave.

Rachid Guerraoui, Jovan Komatovic, Petr Kuznetsov, Yvonne-Anne Pignolet, Dragos-Adrian Seredinschi, and Andrei Tonkikh. Dynamic Byzantine Reliable Broadcast. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{guerraoui_et_al:LIPIcs.OPODIS.2020.23, author = {Guerraoui, Rachid and Komatovic, Jovan and Kuznetsov, Petr and Pignolet, Yvonne-Anne and Seredinschi, Dragos-Adrian and Tonkikh, Andrei}, title = {{Dynamic Byzantine Reliable Broadcast}}, booktitle = {24th International Conference on Principles of Distributed Systems (OPODIS 2020)}, pages = {23:1--23:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-176-4}, ISSN = {1868-8969}, year = {2021}, volume = {184}, editor = {Bramas, Quentin and Oshman, Rotem and Romano, Paolo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.23}, URN = {urn:nbn:de:0030-drops-135087}, doi = {10.4230/LIPIcs.OPODIS.2020.23}, annote = {Keywords: Byzantine reliable broadcast, deterministic distributed algorithms, dynamic distributed systems} }

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

Atomic lock-free multi-word compare-and-swap (MCAS) is a powerful tool for designing concurrent algorithms. Yet, its widespread usage has been limited because lock-free implementations of MCAS make heavy use of expensive compare-and-swap (CAS) instructions. Existing MCAS implementations indeed use at least 2k+1 CASes per k-CAS. This leads to the natural desire to minimize the number of CASes required to implement MCAS.
We first prove in this paper that it is impossible to "pack" the information required to perform a k-word CAS (k-CAS) in less than k locations to be CASed. Then we present the first algorithm that requires k+1 CASes per call to k-CAS in the common uncontended case. We implement our algorithm and show that it outperforms a state-of-the-art baseline in a variety of benchmarks in most considered workloads. We also present a durably linearizable (persistent memory friendly) version of our MCAS algorithm using only 2 persistence fences per call, while still only requiring k+1 CASes per k-CAS.

Rachid Guerraoui, Alex Kogan, Virendra J. Marathe, and Igor Zablotchi. Efficient Multi-Word Compare and Swap. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guerraoui_et_al:LIPIcs.DISC.2020.4, author = {Guerraoui, Rachid and Kogan, Alex and Marathe, Virendra J. and Zablotchi, Igor}, title = {{Efficient Multi-Word Compare and Swap}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {4:1--4:19}, 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.2020.4}, URN = {urn:nbn:de:0030-drops-130827}, doi = {10.4230/LIPIcs.DISC.2020.4}, annote = {Keywords: lock-free, multi-word compare-and-swap, persistent memory} }

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

Gossip protocols (also called rumor spreading or epidemic protocols) are widely used to disseminate information in massive peer-to-peer networks. These protocols are often claimed to guarantee privacy because of the uncertainty they introduce on the node that started the dissemination. But is that claim really true? Can the source of a gossip safely hide in the crowd? This paper examines, for the first time, gossip protocols through a rigorous mathematical framework based on differential privacy to determine the extent to which the source of a gossip can be traceable. Considering the case of a complete graph in which a subset of the nodes are curious, we study a family of gossip protocols parameterized by a "muting" parameter s: nodes stop emitting after each communication with a fixed probability 1-s. We first prove that the standard push protocol, corresponding to the case s = 1, does not satisfy differential privacy for large graphs. In contrast, the protocol with s = 0 (nodes forward only once) achieves optimal privacy guarantees but at the cost of a drastic increase in the spreading time compared to standard push, revealing an interesting tension between privacy and spreading time. Yet, surprisingly, we show that some choices of the muting parameter s lead to protocols that achieve an optimal order of magnitude in both privacy and speed. Privacy guarantees are obtained by showing that only a small fraction of the possible observations by curious nodes have different probabilities when two different nodes start the gossip, since the source node rapidly stops emitting when s is small. The speed is established by analyzing the mean dynamics of the protocol, and leveraging concentration inequalities to bound the deviations from this mean behavior. We also confirm empirically that, with appropriate choices of s, we indeed obtain protocols that are very robust against concrete source location attacks (such as maximum a posteriori estimates) while spreading the information almost as fast as the standard (and non-private) push protocol.

Aurélien Bellet, Rachid Guerraoui, and Hadrien Hendrikx. Who Started This Rumor? Quantifying the Natural Differential Privacy of Gossip Protocols. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bellet_et_al:LIPIcs.DISC.2020.8, author = {Bellet, Aur\'{e}lien and Guerraoui, Rachid and Hendrikx, Hadrien}, title = {{Who Started This Rumor? Quantifying the Natural Differential Privacy of Gossip Protocols}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {8:1--8:18}, 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.2020.8}, URN = {urn:nbn:de:0030-drops-130868}, doi = {10.4230/LIPIcs.DISC.2020.8}, annote = {Keywords: Gossip Protocol, Rumor Spreading, Differential Privacy} }

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Keynote Abstract

**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

This talk will explain the bitcoin algorithm from the distributed computing perspective, precisely define the underlying double-payment problem, and present a much simpler alternative to solve the problem without relying on consensus and consuming so much energy.
Rachid Guerraoui is professor in Computer Science at EPFL where he leads the Distributed Computing Laboratory. He worked in the past with École des Mines de Paris, CEA Saclay, HP Labs in Palo Alto and MIT. He has been elected ACM Fellow and Professor of the College de France. He was awarded a Senior ERC Grant and a Google Focused Award.

Rachid Guerraoui. Demystifying Bitcoin (Keynote Abstract). In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guerraoui:LIPIcs.OPODIS.2019.1, author = {Guerraoui, Rachid}, title = {{Demystifying Bitcoin}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {1:1--1:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.1}, URN = {urn:nbn:de:0030-drops-117870}, doi = {10.4230/LIPIcs.OPODIS.2019.1}, annote = {Keywords: Bitcoin, Payment systems} }

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**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Byzantine reliable broadcast is a powerful primitive that allows a set of processes to agree on a message from a designated sender, even if some processes (including the sender) are Byzantine. Existing broadcast protocols for this setting scale poorly, as they typically build on quorum systems with strong intersection guarantees, which results in linear per-process communication and computation complexity.
We generalize the Byzantine reliable broadcast abstraction to the probabilistic setting, allowing each of its properties to be violated with a fixed, arbitrarily small probability. We leverage these relaxed guarantees in a protocol where we replace quorums with stochastic samples. Compared to quorums, samples are significantly smaller in size, leading to a more scalable design. We obtain the first Byzantine reliable broadcast protocol with logarithmic per-process communication and computation complexity.
We conduct a complete and thorough analysis of our protocol, deriving bounds on the probability of each of its properties being compromised. During our analysis, we introduce a novel general technique that we call adversary decorators. Adversary decorators allow us to make claims about the optimal strategy of the Byzantine adversary without imposing any additional assumptions. We also introduce Threshold Contagion, a model of message propagation through a system with Byzantine processes. To the best of our knowledge, this is the first formal analysis of a probabilistic broadcast protocol in the Byzantine fault model. We show numerically that practically negligible failure probabilities can be achieved with realistic security parameters.

Rachid Guerraoui, Petr Kuznetsov, Matteo Monti, Matej Pavlovic, and Dragos-Adrian Seredinschi. Scalable Byzantine Reliable Broadcast. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{guerraoui_et_al:LIPIcs.DISC.2019.22, author = {Guerraoui, Rachid and Kuznetsov, Petr and Monti, Matteo and Pavlovic, Matej and Seredinschi, Dragos-Adrian}, title = {{Scalable Byzantine Reliable Broadcast}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {22:1--22:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.22}, URN = {urn:nbn:de:0030-drops-113293}, doi = {10.4230/LIPIcs.DISC.2019.22}, annote = {Keywords: Byzantine reliable broadcast, probabilistic distributed algorithms, scalable distributed systems, stochastic processes} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Consensus and State Machine Replication (SMR) are generally considered to be equivalent problems. In certain system models, indeed, the two problems are computationally equivalent: any solution to the former problem leads to a solution to the latter, and vice versa.
In this paper, we study the relation between consensus and SMR from a complexity perspective. We find that, surprisingly, completing an SMR command can be more expensive than solving a consensus instance. Specifically, given a synchronous system model where every instance of consensus always terminates in constant time, completing an SMR command does not necessarily terminate in constant time. This result naturally extends to partially synchronous models. Besides theoretical interest, our result also corresponds to practical phenomena we identify empirically. We experiment with two well-known SMR implementations (Multi-Paxos and Raft) and show that, indeed, SMR is more expensive than consensus in practice. One important implication of our result is that - even under synchrony conditions - no SMR algorithm can ensure bounded response times.

Karolos Antoniadis, Rachid Guerraoui, Dahlia Malkhi, and Dragos-Adrian Seredinschi. State Machine Replication Is More Expensive Than Consensus. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{antoniadis_et_al:LIPIcs.DISC.2018.7, author = {Antoniadis, Karolos and Guerraoui, Rachid and Malkhi, Dahlia and Seredinschi, Dragos-Adrian}, title = {{State Machine Replication Is More Expensive Than Consensus}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {7:1--7:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.7}, URN = {urn:nbn:de:0030-drops-97961}, doi = {10.4230/LIPIcs.DISC.2018.7}, annote = {Keywords: Consensus, State machine replication, Synchronous model} }

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**Published in:** LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Shoals of small fishes can change their collective shape and form a specific pattern. They do so efficiently (in parallel) and without collision.
In this paper, we study the analog problem of distributed pattern formation. A set of processes needs to move from a set of initial positions to a set of final positions. The processes are oblivious (no internal memory) and must preserve, at any time, a minimal distance between them.
A naive solution would be to move the processes one by one, but this would take too long. The difficulty here is to move the processes simultaneously in clearly delimited phases, no matter how unfavorable the initial configuration may be. We solve this by treating the problem "dimension by dimension": the processes first form 1D trails, then gather into a 2D shape (this technique can be generalized to higher dimensions).
We present an optimal algorithm which time complexity depends linearly on the radius of the smallest circle containing both initial and final positions. The algorithm is self-stabilizing, as the processes are oblivious and the initial positions are arbitrary.

Rachid Guerraoui and Alexandre Maurer. Collision-Free Pattern Formation. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guerraoui_et_al:LIPIcs.OPODIS.2016.16, author = {Guerraoui, Rachid and Maurer, Alexandre}, title = {{Collision-Free Pattern Formation}}, booktitle = {20th International Conference on Principles of Distributed Systems (OPODIS 2016)}, pages = {16:1--16:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-031-6}, ISSN = {1868-8969}, year = {2017}, volume = {70}, editor = {Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.16}, URN = {urn:nbn:de:0030-drops-70856}, doi = {10.4230/LIPIcs.OPODIS.2016.16}, annote = {Keywords: Pattern formation, Collision, Landmarks} }

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**Published in:** LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

A distributed computing system can be viewed as the result of the interplay between a distributed algorithm specifying the effects of a local event (e.g. reception of a message), and an adversary choosing the interleaving (schedule) of these events in the execution. In the context of large networks of mobile pairwise interacting agents (population protocols), the adversary models the mobility of the agents by choosing the successive pairs of interacting agents. For some problems, assuming that the adversary selects the schedule according to some probability distribution greatly helps to devise (almost) correct solutions. But how much randomness is really necessary? To what extent does a problem admit implementations that are robust against a "not so random" schedule? This paper takes a first step in addressing this question by borrowing the concept of T-randomness, 0 <= T <= 1, from algorithmic information theory. Roughly speaking, the value T fixes the entropy rate of the considered schedules. For instance, the case T = 1 corresponds, in a specific sense, to schedules in which the pairs of interacting agents are chosen independently and uniformly (perfect randomness). The holy grail question can then be precisely stated as determining the optimal entropy rate to solve a given problem. We first show that perfect randomness is never required. Precisely, if a finite-state algorithm solves a problem with 1-randomness, then this algorithm still solves the same problem with T-randomness for some T < 1. Second, we illustrate how to compute bounds on the optimal entropy rate of a specific problem, namely the leader election problem.

Joffroy Beauquier, Peva Blanchard, Janna Burman, and Rachid Guerraoui. The Benefits of Entropy in Population Protocols. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{beauquier_et_al:LIPIcs.OPODIS.2015.21, author = {Beauquier, Joffroy and Blanchard, Peva and Burman, Janna and Guerraoui, Rachid}, title = {{The Benefits of Entropy in Population Protocols}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {21:1--21:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-98-9}, ISSN = {1868-8969}, year = {2016}, volume = {46}, editor = {Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.21}, URN = {urn:nbn:de:0030-drops-66128}, doi = {10.4230/LIPIcs.OPODIS.2015.21}, annote = {Keywords: algorithmic randomness, entropy, leader election, distributed computing, scheduler, population protocols} }

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