DROPS

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DOI: 10.4230/LIPIcs.ITCS.2026.93

Analyzing the Economic Impact of Decentralization on Users

Authors: Amit Levy, S. Matthew Weinberg, and Chenghan Zhou

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

We model the ultimate price paid by users of a decentralized ledger as resulting from a two-stage game where Miners (/Proposers/etc.) first purchase blockspace via a Tullock contest, and then price that space to users. When analyzing our distributed ledger model, we find: - A characterization of all possible pure equilibria (although pure equilibria are not guaranteed to exist). - A natural sufficient condition, implied by Regularity (à la [Myerson, 1981]), for existence of a "market-clearing" pure equilibrium where Miners choose to sell all space allocated by the Distributed Ledger Protocol, and that this equilibrium is unique. - The market share of the largest miner is the relevant "measure of decentralization" to determine whether a market-clearing pure equilibrium exists. - Block rewards do not impact users' prices at equilibrium, when pure equilibria exist. But, higher block rewards can cause pure equilibria to exist. We also discuss aspects of our model and how they relate to blockchains deployed in practice. For example, only "patient" users (who are happy for their transactions to enter the blockchain under any miner) would enjoy the conclusions highlighted by our model, whereas "impatient" users (who are interested only for their transaction to be included in the very next block) still face monopoly pricing.

Cite as

Amit Levy, S. Matthew Weinberg, and Chenghan Zhou. Analyzing the Economic Impact of Decentralization on Users. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 93:1-93:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levy_et_al:LIPIcs.ITCS.2026.93,
  author =	{Levy, Amit and Weinberg, S. Matthew and Zhou, Chenghan},
  title =	{{Analyzing the Economic Impact of Decentralization on Users}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{93:1--93:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.93},
  URN =		{urn:nbn:de:0030-drops-253805},
  doi =		{10.4230/LIPIcs.ITCS.2026.93},
  annote =	{Keywords: Blockchain, Cryptocurrency, Blockspace Markets, Decentralization, Distributed Ledgers, Equilibrium Analysis, Tullock Contests}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.65

Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms

Authors: Aadityan Ganesh, Clayton Thomas, and S. Matthew Weinberg

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Roughgarden [Roughgarden, 2020] initiates the study of Transaction Fee Mechanisms (TFMs), and posits that the on-chain game of a "good" TFM should be on-chain simple (OnC-S), i.e., incentive compatible for both the users and the miner. Recent work of Ganesh, Thomas an Weinberg [Ganesh et al., 2024] posit that they should additionally be Off-Chain Influence-Proof (OffC-IP), which means that the miner cannot achieve any additional revenue by separately conducting an off-chain auction to determine on-chain inclusion. They observe that a cryptographic second-price auction satisfies both properties, but leave open the question of whether other mechanisms (such as those not dependent on cryptography) satisfy these properties. In this paper, we characterize OffC-IP TFMs: They are those satisfying a burn identity relating the burn rule to the allocation rule. In particular, we show that auction is OffC-IP if and only if its (induced direct-revelation) allocation rule X̄(⋅) and burn rule B̅(⋅) (both of which take as input users' values v₁, … , v_n) are truthful when viewing (X̄(⋅), B̅(⋅)) as the allocation and pricing rule of a multi-item auction for a single additive buyer with values (φ(v₁),…, φ(v_n)) equal to the users' virtual values. Building on this burn identity, we characterize OffC-IP and OnC-S TFMs that are deterministic and do not use cryptography: They are posted-price mechanisms with specially-tuned burns. As a corollary, we show that such TFMs can only exist with infinite supply and prior-dependence. However, we show that for randomized TFMs, there are additional OnC-S and OffC-IP auctions that do not use cryptography (even when there is {finite} supply, under prior-dependence with a bounded prior distribution). Holistically, our results show that while OffC-IP is a fairly stringent requirement, families of OffC-IP mechanisms can be found for a variety of settings.

Cite as

Aadityan Ganesh, Clayton Thomas, and S. Matthew Weinberg. Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 65:1-65:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganesh_et_al:LIPIcs.ITCS.2026.65,
  author =	{Ganesh, Aadityan and Thomas, Clayton and Weinberg, S. Matthew},
  title =	{{Characterizing Off-Chain Influence Proof Transaction Fee Mechanisms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{65:1--65:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.65},
  URN =		{urn:nbn:de:0030-drops-253527},
  doi =		{10.4230/LIPIcs.ITCS.2026.65},
  annote =	{Keywords: Transaction Fee Mechanism Design, Off-Chain Influence Proofness, Blockchain, Decentralized Finance, Simple Auctions}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.12

Efficient Byzantine Reliable Broadcast in the Failure Case

Authors: Thomas Locher

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract

Reliable broadcast is a fundamental primitive in distributed computing that is widely used in various applications. Several new reliable broadcast algorithms have been presented in recent years, primarily focusing on reducing the communication complexity, which is the total number of exchanged bits in the worst case. While significant progress has been achieved, all proposed algorithms share a common weakness. Executions may fail, i.e., no message is ever delivered, while incurring a communication complexity equal or nearly equal to the communication complexity of executions where a message is delivered. In fact, a single Byzantine node, acting as the dedicated sender, is sufficient to trigger such executions, causing all nodes to consume bandwidth in vain. This paper introduces the novel concept of a reliable broadcast detector, a distributed algorithm that can be coupled with a reliable broadcast algorithm to minimize the communication complexity of failed executions. Two concrete detectors are presented with different requirements and properties. Additionally, reliable broadcast algorithms that utilize detectors are introduced, the main algorithm guaranteeing an overhead factor, compared to an ideal failure-free execution, that tends to 2 as the network size increases. Furthermore, a lower bound is proven that an overhead factor of 5/3 is inevitable when the sender initially broadcasts the message, as is the case for the proposed algorithm. Therefore, it achieves a bound that is close to optimal for any algorithm with this property.

Cite as

Thomas Locher. Efficient Byzantine Reliable Broadcast in the Failure Case. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{locher:LIPIcs.OPODIS.2025.12,
  author =	{Locher, Thomas},
  title =	{{Efficient Byzantine Reliable Broadcast in the Failure Case}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.12},
  URN =		{urn:nbn:de:0030-drops-251854},
  doi =		{10.4230/LIPIcs.OPODIS.2025.12},
  annote =	{Keywords: asynchronous networks, reliable broadcast, communication complexity}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.16

Asynchronous Approximate Agreement with Quadratic Communication

Authors: Mose Mizrahi Erbes and Roger Wattenhofer

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract

We study approximate agreement in an asynchronous network of n parties, up to t of which are byzantine. This an agreement task where the parties obtain approximately equal inputs in the convex hull of their inputs. In an asynchronous network, it can be solved with the optimal resilience t < n/3 by forcing the parties to reliably broadcast their messages and thus preventing inconsistent byzantine behavior. This costs Θ(n²) messages per reliable broadcast, or Θ(n³) messages per protocol iteration. In this work, we forgo reliable broadcast to achieve asynchronous approximate agreement against t < n/3 faults with quadratic communication. In a tree with the maximum degree Δ and the centroid decomposition height h, we achieve edge agreement (agreement on two adjacent vertices) in at most 6h + 1 rounds with 𝒪(n²) messages of size 𝒪(log Δ + log h) per round. We do this by designing a 6-round multivalued 2-graded consensus protocol and using it to construct a recursive edge agreement protocol. Then, we achieve edge agreement in the infinite path ℤ, again by using 2-graded consensus. Finally, we show that our edge agreement protocol enables approximate agreement in ℝ (with outputs that are at most some small parameter ε > 0 apart) in 6log₂M/(ε) + 𝒪(log log M/(ε)) rounds with 𝒪(n²) messages of size 𝒪(log log M/(ε)) per round, where M is the maximum non-byzantine input magnitude.

Cite as

Mose Mizrahi Erbes and Roger Wattenhofer. Asynchronous Approximate Agreement with Quadratic Communication. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mizrahierbes_et_al:LIPIcs.OPODIS.2025.16,
  author =	{Mizrahi Erbes, Mose and Wattenhofer, Roger},
  title =	{{Asynchronous Approximate Agreement with Quadratic Communication}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.16},
  URN =		{urn:nbn:de:0030-drops-251890},
  doi =		{10.4230/LIPIcs.OPODIS.2025.16},
  annote =	{Keywords: Approximate agreement, byzantine fault tolerance, communication complexity}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2025.24

On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two

Authors: Alan Ernesto Arteaga Vázquez

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract

A common question in the asynchronous model is whether some given notion of agreement between processes is achievable. Usually, we formalise such agreement notions in the form of agreement problems. Some of these problems also receive the name of coordination primitives. Several fault-tolerant algorithms in asynchronous systems rely upon the use of different primitives as building blocks, such as adopt-commit, crusader agreement, or graded broadcast. Recently, the connected consensus problem - a form of agreement over a specific family of graphs parametrised by a positive integer R- was introduced. This problem unifies the three mentioned primitives while extending them for multi-valued inputs. Moreover, the problem is equipped with a security condition called binding, which limits the effect of malicious processes over the decision of correct parties. While fault-tolerant connected consensus algorithms for R = 1 and R = 2 are known, the existence of algorithmic solutions for any positive integer parameter remained an open question. In this work, we introduce a pair of fault-tolerant algorithms for connected consensus when the R parameter is any positive integer. We introduce a crash-resilient algorithm, which is optimal with respect to the maximum number of possible faulty processes. Our second algorithm is resilient to Byzantine failures; whose failure-resilience is optimal for a specific class of algorithms. Both algorithms satisfy the binding property and match the best known time complexities achieved for the R = 1 and R = 2 cases, further achieving time optimality for the general case in the crash-failure setting, and asymptotic time optimality in the Byzantine scenario.

Cite as

Alan Ernesto Arteaga Vázquez. On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 24:1-24:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arteagavazquez:LIPIcs.OPODIS.2025.24,
  author =	{Arteaga V\'{a}zquez, Alan Ernesto},
  title =	{{On Time-Optimal, Fault-Tolerant Algorithms for Connected Consensus Beyond Grade Two}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{24:1--24:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.24},
  URN =		{urn:nbn:de:0030-drops-251973},
  doi =		{10.4230/LIPIcs.OPODIS.2025.24},
  annote =	{Keywords: Approximate Agreement, Binding, Connected Consensus}
}

Document

DOI: 10.4230/LIPIcs.DISC.2025.15

Asynchronous Latency and Fast Atomic Snapshot

Authors: João Paulo Bezerra, Luciano Freitas, Petr Kuznetsov, and Matthieu Rambaud

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

This paper introduces a novel, fast atomic-snapshot protocol for asynchronous message-passing systems. In the process of defining what "fast" means exactly, we spot a few interesting issues that arise when conventional time metrics are applied to long-lived asynchronous algorithms. We reveal some gaps in latency claims made in earlier work on snapshot algorithms, which hamper their comparative time-complexity analysis. We then come up with a new unifying time-complexity metric that captures the latency of an operation in an asynchronous, long-lived implementation. This allows us to formally grasp latency improvements of our atomic-snapshot algorithm with respect to the state-of-the-art protocols: optimal latency in fault-free runs without contention, short constant latency in fault-free runs with contention, the worst-case latency proportional to the number of active concurrent failures, and constant amortized latency.

Cite as

João Paulo Bezerra, Luciano Freitas, Petr Kuznetsov, and Matthieu Rambaud. Asynchronous Latency and Fast Atomic Snapshot. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bezerra_et_al:LIPIcs.DISC.2025.15,
  author =	{Bezerra, Jo\~{a}o Paulo and Freitas, Luciano and Kuznetsov, Petr and Rambaud, Matthieu},
  title =	{{Asynchronous Latency and Fast Atomic Snapshot}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.15},
  URN =		{urn:nbn:de:0030-drops-248326},
  doi =		{10.4230/LIPIcs.DISC.2025.15},
  annote =	{Keywords: Asynchronous systems, time complexity, atomic snapshot, crash faults}
}

Document

Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2025.45

Brief Announcement: DAGs for the Masses

Authors: Michael Anoprenko, Andrei Tonkikh, Alexander Spiegelman, and Petr Kuznetsov

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

A recent approach to building consensus protocols on top of Directed Acyclic Graphs (DAGs) shows much promise due to its simplicity and stable throughput. However, as each node in the DAG typically includes a linear number of references to the nodes in the previous round, prior DAG protocols only scale up to a certain point when the overhead of maintaining the graph becomes the bottleneck. To enable large-scale deployments of DAG-based protocols, we propose a sparse DAG architecture, where each node includes only a constant number of references to random nodes in the previous round. We present a sparse version of Bullshark - one of the most prominent DAG-based consensus protocols - and demonstrate its improved scalability. Remarkably, unlike other protocols that use random sampling to reduce communication complexity, we manage to avoid sacrificing resilience: the protocol can tolerate up to f < n/3 Byzantine faults (where n is the number of participants), same as its less scalable deterministic counterpart. The proposed "sparse" methodology can be applied to any protocol that maintains disseminated system updates and causal relations between them in a graph-like structure. Our simulations show that the considerable reduction of transmitted metadata in sparse DAGs results in more efficient network utilization and better scalability.

Cite as

Michael Anoprenko, Andrei Tonkikh, Alexander Spiegelman, and Petr Kuznetsov. Brief Announcement: DAGs for the Masses. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 45:1-45:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anoprenko_et_al:LIPIcs.DISC.2025.45,
  author =	{Anoprenko, Michael and Tonkikh, Andrei and Spiegelman, Alexander and Kuznetsov, Petr},
  title =	{{Brief Announcement: DAGs for the Masses}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{45:1--45:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.45},
  URN =		{urn:nbn:de:0030-drops-248617},
  doi =		{10.4230/LIPIcs.DISC.2025.45},
  annote =	{Keywords: Consensus, Atomic Broadcast, Byzantine Fault Tolerance, DAGs, Scalability, Sampling}
}

Document

Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2025.46

Brief Announcement: Communication Patterns for Optimal Resilience

Authors: Hagit Attiya, Itay Flam, and Jennifer L. Welch

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract

In response to the impossibility of solving the consensus problem in asynchronous systems subject to failures, various relaxations of the consensus problem have been proposed, including approximate agreement, crusader agreement, gather, and reliable broadcast. Some are interesting in their own right while others are useful building blocks for solving other problems. We focus on message-passing systems of n processes, up to f of which can experience malicious (Byzantine) failures. These problems all require that n > 3f and they frequently have fairly simple and efficient algorithms when n > 5f. Challenges arise when considering resilience between 3f+1 and 5f. For instance, nearly twenty years elapsed between the discovery of an approximate agreement algorithm for n > 5f [Danny Dolev et al., 1986] and one for n > 3f [Abraham et al., 2004]. A stumbling block could be too much focus on looking for algorithms in a certain natural and intuitive form, which we call canonical (asynchronous) rounds. In such an algorithm, each process repeatedly sends a message containing its entire state tagged with a round number, then waits to receive n-f messages with that same round number, does some local computation and proceeds to the next round number. The n > 5f approximate agreement algorithm is in canonical round form but the n > 3f one is not. For algorithms in canonical round form, an obvious way of measuring time is the number of canonical rounds until the algorithm completes. However, this approach does not apply to other algorithms, such as those in which processes wait to receive a certain number of messages that have other properties besides simply having a certain round number. Attempts to rewrite these latter algorithms in canonical round form can result in drastically increased round complexity. This blow-up in the round complexity is inherent, as we show in this paper that for a wide set of problems, there is no algorithm in canonical round form that has a finite upper bound on the number of rounds if n ≤ 5f. In contrast, the standard way of measuring time results in constant time complexity. We first show the impossibility of a bounded number of canonical rounds for a generic problem that captures the key properties needed in the proof. The result then follows immediately for, most notably, crusader agreement and flavors of approximate agreement. We then show via reductions that the same result holds for reliable broadcast and gather, since there are crusader agreement algorithms that use reliable broadcast and gather with no round overhead.

Cite as

Hagit Attiya, Itay Flam, and Jennifer L. Welch. Brief Announcement: Communication Patterns for Optimal Resilience. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 46:1-46:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{attiya_et_al:LIPIcs.DISC.2025.46,
  author =	{Attiya, Hagit and Flam, Itay and Welch, Jennifer L.},
  title =	{{Brief Announcement: Communication Patterns for Optimal Resilience}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{46:1--46:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.46},
  URN =		{urn:nbn:de:0030-drops-248620},
  doi =		{10.4230/LIPIcs.DISC.2025.46},
  annote =	{Keywords: canonical rounds, reliable broadcast, gather, crusader agreement, approximate agreement, time complexity}
}

Document

DOI: 10.4230/LIPIcs.AFT.2025.12

How Much Public Randomness Do Modern Consensus Protocols Need?

Authors: Joseph Bonneau, Benedikt Bünz, Miranda Christ, and Yuval Efron

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

Modern blockchain-based consensus protocols aim for efficiency (i.e., low communication and round complexity) while maintaining security against adaptive adversaries. These goals are usually achieved using a public randomness beacon to select roles for each participant. We examine to what extent this randomness is necessary. Specifically, we provide tight bounds on the amount of entropy a Byzantine Agreement protocol must consume from a beacon in order to enjoy efficiency and adaptive security. We first establish that no consensus protocol can simultaneously be efficient, be adaptively secure, and use O(log n) bits of beacon entropy. We then show this bound is tight and, in fact, a trilemma by presenting three consensus protocols that achieve any two of these three properties.

Cite as

Joseph Bonneau, Benedikt Bünz, Miranda Christ, and Yuval Efron. How Much Public Randomness Do Modern Consensus Protocols Need?. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonneau_et_al:LIPIcs.AFT.2025.12,
  author =	{Bonneau, Joseph and B\"{u}nz, Benedikt and Christ, Miranda and Efron, Yuval},
  title =	{{How Much Public Randomness Do Modern Consensus Protocols Need?}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.12},
  URN =		{urn:nbn:de:0030-drops-247310},
  doi =		{10.4230/LIPIcs.AFT.2025.12},
  annote =	{Keywords: Consensus, Randomness Beacon}
}

Document

DOI: 10.4230/LIPIcs.AFT.2025.31

Trustless Bridges via Random Sampling Light Clients

Authors: Bhargav Nagaraja Bhatt, Fatemeh Shirazi, and Alistair Stewart

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

The increasing number of blockchain projects introduced annually has led to a pressing need for secure and efficient interoperability solutions. Currently, the lack of such solutions forces end-users to rely on centralized intermediaries, contradicting the core principle of decentralization and trust minimization in blockchain technology. We propose a decentralized and efficient interoperability solution (aka Bridge Protocol) that operates without additional trust assumptions, relying solely on the Byzantine Fault Tolerance (BFT) properties of the two chains being connected. In particular, relayers (actors that exchange messages between networks) are permissionless and decentralized, hence eliminating any single point of failure. We introduce Random Sampling, a novel technique for on-chain light clients to efficiently follow the history of PoS blockchains by reducing the signature verifications required. Here, the randomness is drawn on-chain, for example, using Ethereum’s RANDAO. We analyze the security of the bridge from a crypto- economic perspective and provide a framework to derive the security parameters. This includes handling subtle concurrency issues and randomness bias in strawman designs. While the protocol is applicable to various PoS chains, we demonstrate the protocol’s practical feasibility by showcasing an instantiated bridge between Polkadot and Ethereum (currently deployed), and discuss some practical security challenges. Furthermore, we evaluate the efficiency of our on-chain light client verifier (implemented as an Ethereum smart contract) against SNARK-based approaches, demonstrating significantly lower gas costs for signature verification - even for validator sets up to 10⁶.

Cite as

Bhargav Nagaraja Bhatt, Fatemeh Shirazi, and Alistair Stewart. Trustless Bridges via Random Sampling Light Clients. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 31:1-31:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhatt_et_al:LIPIcs.AFT.2025.31,
  author =	{Bhatt, Bhargav Nagaraja and Shirazi, Fatemeh and Stewart, Alistair},
  title =	{{Trustless Bridges via Random Sampling Light Clients}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{31:1--31:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.31},
  URN =		{urn:nbn:de:0030-drops-247503},
  doi =		{10.4230/LIPIcs.AFT.2025.31},
  annote =	{Keywords: PoS Blockchains, Trustless Bridges, Light Clients, Decentralised Relayers, RANDAO Bias}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.1

Simple Is COOL: Graded Dispersal and Its Applications for Byzantine Fault Tolerance

Authors: Ittai Abraham, Gilad Asharov, and Anirudh Chandramouli

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

The COOL protocol of Chen (DISC'21) is a major advance that enables perfect security for various tasks (in particular, Byzantine Agreement in Synchrony and Reliable Broadcast in Asynchrony). For an input of size L bits, its communication complexity is O(nL+n² log n), which is optimal up to a log n factor. Unfortunately, Chen’s analysis is rather intricate and complex. Our main contribution is a simple analysis of a new variant of COOL based on elementary counting arguments. Our main consistency proof takes less than two pages (instead of over 20 pages), making the COOL protocol much more accessible. In addition, the simple analysis allows us to improve the protocol by reducing one round of communication and reducing the communication complexity by 40%. In addition, we suggest a new way of extracting the core properties of COOL as a new primitive, which we call Graded Dispersal. We show how Graded Dispersal can then be used to obtain efficient solutions for Byzantine Agreement, Verifiable Information Dispersal, Gradecast, and Reliable Broadcast (in both Synchrony and Asynchrony, where appropriate). Our improvement of COOL directly applies here, and we improve the state-of-the-art in all those primitives by reducing at least one round and 40% communication.

Cite as

Ittai Abraham, Gilad Asharov, and Anirudh Chandramouli. Simple Is COOL: Graded Dispersal and Its Applications for Byzantine Fault Tolerance. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abraham_et_al:LIPIcs.ITCS.2025.1,
  author =	{Abraham, Ittai and Asharov, Gilad and Chandramouli, Anirudh},
  title =	{{Simple Is COOL: Graded Dispersal and Its Applications for Byzantine Fault Tolerance}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.1},
  URN =		{urn:nbn:de:0030-drops-226295},
  doi =		{10.4230/LIPIcs.ITCS.2025.1},
  annote =	{Keywords: Byzantine Agreement, Broadcast}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2024.15

Quit-Resistant Reliable Broadcast and Efficient Terminating Gather

Authors: Mose Mizrahi Erbes and Roger Wattenhofer

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract

Termination is a central property in distributed computing. A party terminates a protocol once it stops accepting and sending messages. We discover that byzantine reliable broadcast is sometimes used in a manner which leads to non-terminating protocols. We consider an asynchronous network of n parties up to t of which are byzantine, and show that if each party is to broadcast its value and terminate upon obtaining n - t values, then composing n parallel reliable broadcast instances leads to non-termination. The issue is that a party must quit t broadcast instances early in order to terminate, a behaviour not supported by ordinary reliable broadcast. So, we modify Bracha’s protocol into a quit-resistant reliable broadcast (QBRB) protocol which lets the parties quit early. This protocol retains its termination guarantees as long as no party quits before some party terminates. Then, we turn our attention to Gather, an all-to-all broadcast primitive which guarantees that the parties obtain n - t common values. Existing error-free deterministic Gather protocols either run forever, or fail to terminate since the parties quit reliable broadcast instances. We design an error-free, deterministic, terminating (and binding) Gather protocol for 𝓁-bit inputs with the communication complexity 𝒪(𝓁 n² + n³log n). This matches the state-of-the-art for non-terminating Gather. Finally, inspired by our QBRB protocol, we design a reliable broadcast protocol which retains its termination guarantees no matter when any party quits. To achieve this, we give each party the option to output ⊥ if more than q parties quit before some party terminates. The protocol requires 4t + q < n, which is optimal, and it lets parties quit after they have suffered transient crash failures so that they can help the remaining parties terminate.

Cite as

Mose Mizrahi Erbes and Roger Wattenhofer. Quit-Resistant Reliable Broadcast and Efficient Terminating Gather. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mizrahierbes_et_al:LIPIcs.OPODIS.2024.15,
  author =	{Mizrahi Erbes, Mose and Wattenhofer, Roger},
  title =	{{Quit-Resistant Reliable Broadcast and Efficient Terminating Gather}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.15},
  URN =		{urn:nbn:de:0030-drops-225519},
  doi =		{10.4230/LIPIcs.OPODIS.2024.15},
  annote =	{Keywords: Asynchronous networks, byzantine fault tolerance, protocol termination, reliable broadcast, all-to-all broadcast, gather}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2024.16

Byzantine Reliable Broadcast with Low Communication and Time Complexity

Authors: Thomas Locher

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract

Byzantine reliable broadcast is a fundamental problem in distributed computing, which has been studied extensively over the past decades. State-of-the-art algorithms are predominantly based on the approach to share encoded fragments of the broadcast message, yielding an asymptotically optimal communication complexity when the message size exceeds the network size, a condition frequently encountered in practice. However, algorithms following the standard coding approach incur an overhead factor of at least 3, which can already be a burden for bandwidth-constrained applications. Minimizing this overhead is an important objective with immediate benefits to protocols that use a reliable broadcast routine as a building block. This paper introduces a novel mechanism to lower the communication and computational complexity. Two algorithms are presented that employ this mechanism to reliably broadcast messages in an asynchronous network where less than a third of all nodes are Byzantine. The first algorithm reduces the overhead factor to 2 and has a time complexity of 3 if the sender is honest, whereas the second algorithm attains an optimal time complexity of 2 with the same overhead factor in the absence of equivocation. Moreover, an optimization is proposed that reduces the overhead factor to 3/2 under normal operation in practice. Lastly, a lower bound is proved that an overhead factor lower than 3/2 cannot be achieved for a relevant class of reliable broadcast algorithms.

Cite as

Thomas Locher. Byzantine Reliable Broadcast with Low Communication and Time Complexity. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{locher:LIPIcs.OPODIS.2024.16,
  author =	{Locher, Thomas},
  title =	{{Byzantine Reliable Broadcast with Low Communication and Time Complexity}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.16},
  URN =		{urn:nbn:de:0030-drops-225524},
  doi =		{10.4230/LIPIcs.OPODIS.2024.16},
  annote =	{Keywords: Asynchronous Networks, Reliable Broadcast, Communication Complexity}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2024.25

Reliable Communication in Hybrid Authentication and Trust Models

Authors: Rowdy Chotkan, Bart Cox, Vincent Rahli, and Jérémie Decouchant

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract

Reliable communication is a fundamental distributed communication abstraction that allows any two nodes within a network to communicate with each other. It is necessary for more powerful communication primitives, such as broadcast and consensus. Using different authentication models, two classical protocols implement reliable communication in unknown and sufficiently connected networks. In the former, network links are authenticated, and processes rely on dissemination paths to authenticate messages. In the latter, processes generate digital signatures that are flooded throughout the network. This work considers the hybrid system model that combines authenticated links and authenticated processes. Additionally, we aim to leverage the possible presence of trusted nodes (e.g., network gateways) and trusted components (e.g., Intel SGX enclaves). We first extend the two classical reliable communication protocols to leverage trusted nodes. Then we propose DualRC, our most generic algorithm that considers the hybrid authentication model by manipulating dissemination paths and digital signatures, and leverages the possible presence of trusted nodes and trusted components. We describe and prove methods that establish whether our algorithms implement reliable communication on a given network.

Cite as

Rowdy Chotkan, Bart Cox, Vincent Rahli, and Jérémie Decouchant. Reliable Communication in Hybrid Authentication and Trust Models. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 25:1-25:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chotkan_et_al:LIPIcs.OPODIS.2024.25,
  author =	{Chotkan, Rowdy and Cox, Bart and Rahli, Vincent and Decouchant, J\'{e}r\'{e}mie},
  title =	{{Reliable Communication in Hybrid Authentication and Trust Models}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{25:1--25:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.25},
  URN =		{urn:nbn:de:0030-drops-225611},
  doi =		{10.4230/LIPIcs.OPODIS.2024.25},
  annote =	{Keywords: Reliable communication, Byzantine, Authentication models, Trust}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2023.29

On the Round Complexity of Asynchronous Crusader Agreement

Authors: Ittai Abraham, Naama Ben-David, Gilad Stern, and Sravya Yandamuri

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract

We present new lower and upper bounds on the number of communication rounds required for asynchronous Crusader Agreement (CA) and Binding Crusader Agreement (BCA), two primitives that are used for solving binary consensus. We show results for the information theoretic and authenticated settings. In doing so, we present a generic model for proving round complexity lower bounds in the asynchronous setting. In some settings, our attempts to prove lower bounds on round complexity fail. Instead, we show new, tight, rather surprising round complexity upper bounds for Byzantine fault tolerant BCA with and without a PKI setup.

Cite as

Ittai Abraham, Naama Ben-David, Gilad Stern, and Sravya Yandamuri. On the Round Complexity of Asynchronous Crusader Agreement. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abraham_et_al:LIPIcs.OPODIS.2023.29,
  author =	{Abraham, Ittai and Ben-David, Naama and Stern, Gilad and Yandamuri, Sravya},
  title =	{{On the Round Complexity of Asynchronous Crusader Agreement}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{29:1--29:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.29},
  URN =		{urn:nbn:de:0030-drops-195195},
  doi =		{10.4230/LIPIcs.OPODIS.2023.29},
  annote =	{Keywords: lower bounds, asynchronous protocols, round complexity}
}

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