Symmetry all the way down

Christian Cachin; Ignacio Amores-Sesar; Juan Villacis; Simon Holmgaard Kamp

Symmetry all the way down

T0 review · 0 major / 5 minor · reviewed 2026-07-11 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Asymmetric trust does not help solve hard distributed tasks beyond what ordinary symmetric quorums already allow.

desk verdict Tight depth-2 compiler plus matching impossibility: asymmetric trust adds no extra power for reliable broadcast or consensus. read the letter →

arxiv 2607.04887 v1 pith:TWYGVPQS submitted 2026-07-06 cs.DC

Ignacio Amores-Sesar , Christian Cachin , Simon Holmgaard Kamp , Juan Villacis This is my paper

classification cs.DC

keywords asymmetrictrustByzantinequorumsystemsdepthhierarchycompilerreliablebroadcastconsensusconsistentfaulttolerance

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Classical distributed systems force every participant to share the same failure assumptions. Asymmetric trust lets each participant keep its own private list of who it trusts, and this strictly enlarges the set of failure patterns the system can survive. The paper asks whether that extra survival power actually lets you solve harder problems such as reliable broadcast or consensus. Using a depth hierarchy that measures how much a process can still rely on others after faults occur, the authors prove the answer is no: every failure pattern in which a task that needs depth two or higher remains solvable can already be handled by an ordinary symmetric quorum system built from the asymmetric one. The only extra patterns that asymmetric trust alone tolerates leave every correct process with depth at most one, a regime in which only weak primitives such as consistent broadcast are possible. A simple compiler constructs the matching symmetric system, and the authors show that no such compiler can reach depth one. Thus the extra expressive power of asymmetric trust is real but is confined to the simplest tasks.

What carries the argument

The depth-parametrized compiler DC that expands every asymmetric quorum by replacing each of its members with one of that member’s own quorums; the resulting collection of unions is proved to satisfy the classical Q₃ consistency and availability properties precisely on the set of failure patterns that leave a process of depth ≥ 2.

What would settle it

Exhibit a concrete asymmetric quorum system and a failure pattern under which a process of depth two exists, yet the symmetric system produced by the compiler fails either consistency or availability; or exhibit any compiler that yields a valid symmetric system for all patterns that leave only depth-one processes.

Watch

Extended reading notes

Core claim

For any Byzantine asymmetric quorum system, every failure scenario that still leaves at least one process with depth two or higher can also be tolerated by a suitably constructed Byzantine symmetric quorum system; consequently asymmetric trust never enlarges the set of scenarios in which tasks requiring depth two or more (reliable broadcast, consensus, …) are solvable.

Load-bearing premise

The depth hierarchy correctly separates task solvability so that depth at least two is necessary for reliable broadcast and consensus, and that this recursive depth is preserved when quorums are expanded by the compiler.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This paper settles a clean question: the extra failure patterns that only asymmetric quorums can tolerate are exactly the ones where you cannot solve depth-≥2 tasks anyway. For anything that needs depth 2 or higher (reliable broadcast, consensus, …), a suitably compiled symmetric system already covers every solvable scenario.

What is new is the constructive compiler DC (Algorithm 1). It expands every local quorum by the Cartesian product of the members’ own quorums and produces a symmetric system that satisfies Q3 whenever the original satisfies B3 (Lemma 4.1) and that is consistent and available on every F[2] set (Lemma 4.2). The matching impossibility for C[1] is a short three-process counter-example whose F[1] violates Q3 (Lemma 4.4). That improves the earlier infinite-depth compiler and pins the boundary exactly at depth 2. The proofs in the appendix are short, self-contained, and use only the standard intersection properties plus the recursive depth definition; the stress-test found no holes.

Soft spots are minor and already flagged by the authors. The whole argument sits on their own OPODIS ’25 depth hierarchy; if that hierarchy is later refined, the compiler statements would need re-checking, but the hierarchy is used as a black box and the lemmas themselves do not circularly depend on it. They claim the result extends to non-canonical systems without proof, and the unknown-quorums case is left open. The on-the-fly quorum check costs an extra linear factor, which is unavoidable once you expand. None of these touch the central claim.

Citation pattern is heavy on the authors’ recent line, which is natural for a follow-up that closes an open question they themselves posed. The math is solid; there is no free parameter or fitted constant.

This is for people who work on quorum systems, Stellar/XRP-style trust models, or the theory of asymmetric BFT. Practitioners who already run asymmetric protocols for consensus can safely switch to the compiled symmetric system for all depth-≥2 tasks. I would bring it to reading group, I would cite the compiler and the impossibility, and a serious editor should send it to referees.

Referee Report

0 major / 5 minor

Summary. The paper studies the precise power of asymmetric Byzantine quorum systems relative to classical symmetric ones, using the depth hierarchy of Amores-Sesar et al. (OPODIS ’25). It shows that every failure scenario in which at least one process has depth ≥ 2 (the regime needed for reliable broadcast and consensus) can also be tolerated by a symmetric quorum system obtained from a constructive compiler DC (Algorithm 1). The compiler expands each asymmetric quorum by the Cartesian product of the local quorums of its members; Lemmas 4.1–4.2 prove that the resulting system satisfies Q3 and the consistency/availability properties on F[2]. The extra failure patterns that only asymmetric systems tolerate leave all correct processes at depth ≤ 1, where only depth-1 tasks (e.g., consistent broadcast) remain solvable. Tightness is established by an impossibility (Lemma 4.4): no compiler can implement C[1]. The result holds for both known- and unknown-quorums settings, though only the former admits an efficient on-the-fly check.

Significance. If the lemmas hold, the paper cleanly delimits the advantage of asymmetric trust: it strictly enlarges the set of tolerable failure patterns, yet supplies no extra solvability for any task that requires depth two or higher. Practitioners can therefore replace complex asymmetric protocols for reliable broadcast or consensus by ordinary symmetric algorithms run on the compiled system, while still exploiting asymmetry for depth-1 primitives. The constructive compiler, the matching impossibility, and the explicit O(n) on-the-fly quorum check are concrete, reusable contributions that improve on the earlier C[∞] compiler. The work is self-contained once the depth hierarchy is taken as a black box, and the proofs rely only on standard intersection properties.

minor comments (5)

Definition 3.3 states that “Any correct process pi has depth 0” and then adds higher depths; the wording is slightly ambiguous about whether depth 0 is the base case for every correct process or only for those that fail the inductive step. A one-sentence clarification would help.
Table 1 lists “Asynchronous consensus [3]” at depth 10 and reliable broadcast at depth 3; a short remark that these numbers are the best currently known (not proven lower bounds) would prevent readers from treating them as tight.
In the known-quorums cost analysis (Section 5.1) the claim of “at most 2n quorum checks” is correct for the two-step procedure, yet it would be useful to note that each individual check may itself be exponential in the worst case if the original asymmetric system is given explicitly as a power set.
Several author self-citations appear as “Amores-Sesaret al.” (missing space or hyphen); a uniform spelling would improve polish.
The arXiv identifier in the abstract header is 2607.04887; confirm that this matches the final submission identifier once the paper is published.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: compiler C[2] and impossibility of C[1] are proved from B3/Q3 and the stated depth definition; self-citation of the authors' OPODIS '25 depth hierarchy frames interpretation but does not force the lemmas.

full rationale

The load-bearing chain is Definition 4.2 (C[d]), Algorithm 1 / Definition 4.3 (DC), then Lemmas 4.1–4.4 in Appendix A. Lemma 4.1 derives Q3(N) from B3(F) by contradiction on three expanded quorums and their originating asymmetric fail-prone sets. Lemma 4.2 shows consistency and availability of S = DC(Q) for every F in F[2] by taking a depth-≥2 process, expanding a quorum of depth-≥1 members, and invoking Corollary 4.1 / Lemma 4.3 (kernel containment from asymmetric consistency when F is foreseen by both parties). Lemma 4.4 exhibits a concrete 3-process B3 system whose F[1] violates Q3, so no symmetric system can cover all of F[1]. None of these steps is definitional of its conclusion, fitted to data, or reduced to an unverified uniqueness claim. The paper does rely on Amores-Sesar et al. (OPODIS '25) for the depth hierarchy and for the claim that reliable broadcast/consensus need depth ≥2 while consistent broadcast is depth-1; that citation supplies the interpretive link from the compiler theorems to 'task solvability,' but the mathematical statements 'DC implements C[2]' and 'no C[1]' are self-contained against the definitions restated in the manuscript. Score 1 reflects only that minor, non-load-bearing self-citation for framing—not circular derivation of the central results.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

Pure theory paper. No fitted numbers. Load-bearing background is the standard Byzantine asynchronous model plus the B3 condition and the depth hierarchy taken from prior work of the same authors. The compiler itself is an invented algorithmic entity whose correctness is proved, not postulated.

assumptions (4)

domain assumption Asynchronous unauthenticated Byzantine model with authenticated channels (Section 2.1).
Standard setting for the whole paper; all solvability claims are relative to it.
domain assumption B3-condition is necessary and sufficient for existence of an asymmetric Byzantine quorum system (Definition 3.2, citing Damgård et al. and Alpos et al.).
Used to guarantee that the input to the compiler is well-formed.
domain assumption Depth hierarchy of Amores-Sesar et al. OPODIS ’25 correctly characterises which tasks are solvable at each depth (Table 1 and Section 3.2).
The entire separation argument (extra tolerance only helps depth-1 tasks) rests on this characterisation.
ad hoc to paper All quorum systems may be taken to be canonical without loss of generality.
Stated in Section 3; simplifies proofs but is asserted rather than proved for the non-canonical case.

invented entities (1)

Compiler DC (Algorithm 1) and the family of depth-parametrised compilers C[d] independent evidence
purpose: Constructive reduction from asymmetric to symmetric quorum systems that preserves fault tolerance exactly on F[2].
New algorithmic object introduced and proved correct in the paper; independent evidence is the explicit expansion procedure and the four lemmas.

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Cite this review

Pith. "Pith review of Symmetry all the way down." pith.science (2026). https://pith.science/paper/TWYGVPQS

@misc{pith2026260704887,
  author       = {Pith},
  title        = {Pith review of: Symmetry all the way down},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TWYGVPQS}},
  note         = {Machine review of arXiv:2607.04887}
}

read the original abstract

Asymmetric trust generalizes classical symmetric quorum systems by allowing each process to specify its own failure assumptions. While this flexibility enables tolerance of strictly more failure scenarios, it is not known if, in these cases, it is actually possible to solve distributed tasks, and if so, which. We answer this question using the depth hierarchy for asymmetric trust (Amores-Sesar et al., OPODIS~'25), which characterizes how much a process must rely on others to solve a task. We prove that asymmetric trust does not increase the solvability of tasks requiring depth two or more, such as reliable broadcast or consensus. Specifically, for any Byzantine asymmetric quorum system, every failure scenario that permits solving a task requiring depth at least two can also be tolerated by a suitably constructed Byzantine symmetric quorum system. We show this via a compiler that transforms asymmetric quorum systems into symmetric ones. The additional failure patterns tolerated exclusively by asymmetric trust correspond to scenarios in which only simpler tasks requiring depth one or less (such as consistent broadcast) can be solved. We further prove that this result is tight in the depth hierarchy, meaning that there exist no compilers that produce symmetric quorum systems that are valid also in failure scenarios where correct processes have depths one or less. Our results clarify the precise power of asymmetric trust. While it strictly enlarges the set of tolerable failure patterns, it does not provide additional strength for solving tasks requiring depth two or higher.

Figures

Figures reproduced from arXiv: 2607.04887 by the authors.

**Figure 1.** The set of failure scenarios tolerated by any asymmetric quorum system Q (in striped red) is strictly larger than that which can be tolerated by the symmetric quorum system S = C(Q) derived by the compiler from Q (in green). However, in the failure patterns tolerated by Q but not S, only tasks requiring depth one can be solved, this excludes problems like reliable broadcast or consensus. Organization. The remainder … view at source ↗

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Works this paper leans on

32 extracted references · 3 canonical work pages

[2]

pod: An optimal-latency, censorship-free, and accountable generalized consen- sus layer

Orestis Alpos, Bernardo David, Jakov Mitrovski, Odysseas Sofikitis, and Dionysis Zin- dros. pod: An optimal-latency, censorship-free, and accountable generalized consen- sus layer. In Dariusz R. Kowalski, editor,39th International Symposium on Distributed Computing, DISC 2025, Berlin, Germany, October 27-31, 2025, volume 356 ofLIPIcs, 13 pages 4:1–4:24. S...

work page doi:10.4230/lipics.disc.2025.4 2025
[1]

Asymmetric dis- tributed trust.Distributed Comput., 37(3):247–277, 2024

Orestis Alpos, Christian Cachin, Bj¨ orn Tackmann, and Luca Zanolini. Asymmetric dis- tributed trust.Distributed Comput., 37(3):247–277, 2024

2024
[3]

Weaker assumptions for asymmetric trust

Ignacio Amores-Sesar, Christian Cachin, Simon Holmgaard Kamp, and Juan Villacis. Weaker assumptions for asymmetric trust. InOPODIS, volume 361 ofLIPIcs, pages 8:1– 8:18. Schloss Dagstuhl - Leibniz-Zentrum f¨ ur Informatik, 2025

2025
[4]

Security analysis of ripple consensus

Ignacio Amores-Sesar, Christian Cachin, and Jovana Micic. Security analysis of ripple consensus. InOPODIS, volume 184 ofLIPIcs, pages 10:1–10:16. Schloss Dagstuhl - Leibniz- Zentrum f¨ ur Informatik, 2020

2020
[5]

Dag-based con- sensus with asymmetric trust

Ignacio Amores-Sesar, Christian Cachin, Juan Villacis, and Luca Zanolini. Dag-based con- sensus with asymmetric trust. InPODC, pages 151–161. ACM, 2025

2025
[6]

Welch.Distributed computing - fundamentals, simulations, and advanced topics (2

Hagit Attiya and Jennifer L. Welch.Distributed computing - fundamentals, simulations, and advanced topics (2. ed.). Wiley series on parallel and distributed computing. Wiley, 2004

2004
[7]

Fastpay: High-performance byzan- tine fault tolerant settlement

Mathieu Baudet, George Danezis, and Alberto Sonnino. Fastpay: High-performance byzan- tine fault tolerant settlement. In Sarah Meiklejohn and Abhi Shelat, editors,Proceed- ings of the 2nd ACM Conference on Advances in Financial Technologies, AFT 2020, New York, NY, USA, October 21-23, 2020, pages 163–177. ACM, 2020.doi:10.1145/3419614. 3423249

work page doi:10.1145/3419614 2020
[8]

Sui lutris: A blockchain combining broadcast and consensus

Sam Blackshear, Andrey Chursin, George Danezis, Anastasios Kichidis, Lefteris Kokoris- Kogias, Xun Li, Mark Logan, Ashok Menon, Todd Nowacki, Alberto Sonnino, Brandon Williams, and Lu Zhang. Sui lutris: A blockchain combining broadcast and consensus. In Bo Luo, Xiaojing Liao, Jun Xu, Engin Kirda, and David Lie, editors,Proceedings of the 2024 on ACM SIGSA...

doi:10.1145/3658644.3670286 2024

Show all 32 references

[9]

The latest gossip on BFT consensus

Ethan Buchman, Jae Kwon, and Zarko Milosevic. The latest gossip on BFT consensus. CoRR, abs/1807.04938, 2018

2018 arXiv
[10]

Ethereum 2.0: Proof of stake and shard chains.https: //ethereum.org/en/eth2/, 2018

Vitalik Buterin and Danny Ryan. Ethereum 2.0: Proof of stake and shard chains.https: //ethereum.org/en/eth2/, 2018. Accessed: 2025-08-19

2018
[11]

Christian Cachin, Rachid Guerraoui, and Lu´ ıs E. T. Rodrigues.Introduction to Reliable and Secure Distributed Programming (2. ed.). Springer, 2011

2011
[12]

Analysis of the XRP ledger consensus protocol.CoRR, abs/1802.07242, 2018

Brad Chase and Ethan MacBrough. Analysis of the XRP ledger consensus protocol.CoRR, abs/1802.07242, 2018

2018 arXiv
[13]

Secure protocols with asymmetric trust

Ivan Damg˚ ard, Yvo Desmedt, Matthias Fitzi, and Jesper Buus Nielsen. Secure protocols with asymmetric trust. InASIACRYPT, volume 4833 ofLecture Notes in Computer Science, pages 357–375. Springer, 2007

2007
[14]

Closing the efficiency gap between synchronous and network-agnostic consensus

Giovanni Deligios and Mose Mizrahi Erbes. Closing the efficiency gap between synchronous and network-agnostic consensus. In Marc Joye and Gregor Leander, editors,Advances in Cryptology - EUROCRYPT 2024 - 43rd Annual International Conference on the The- ory and Applications of ...

2024 doi
[15]

Algo- rand: Scaling byzantine agreements for cryptocurrencies

Yossi Gilad, Rotem Hemo, Silvio Micali, Georgios Vlachos, and Nickolai Zeldovich. Algo- rand: Scaling byzantine agreements for cryptocurrencies. InSOSP, pages 51–68. ACM, 2017

2017
[16]

The best of both worlds: Guaranteeing termination in fast randomized byzantine agreement protocols.Inf

Oded Goldreich and Erez Petrank. The best of both worlds: Guaranteeing termination in fast randomized byzantine agreement protocols.Inf. Process. Lett., 36(1):45–49, 1990

1990
[17]

Martin Hirt and Ueli M. Maurer. Player simulation and general adversary structures in perfect multiparty computation.J. Cryptol., 13(1):31–60, 2000

2000
[18]

Patrick Hunt, Mahadev Konar, Flavio Paiva Junqueira, and Benjamin C. Reed. Zookeeper: Wait-free coordination for internet-scale systems. InUSENIX ATC. USENIX Association, 2010

2010
[19]

Cassandra: a decentralized structured storage system.ACM SIGOPS Oper

Avinash Lakshman and Prashant Malik. Cassandra: a decentralized structured storage system.ACM SIGOPS Oper. Syst. Rev., 44(2):35–40, 2010

2010
[20]

Permissionless consensus.CoRR, abs/2304.14701, 2023

Andrew Lewis-Pye and Tim Roughgarden. Permissionless consensus.CoRR, abs/2304.14701, 2023. URL:https://doi.org/10.48550/arXiv.2304.14701,arXiv: 2304.14701,doi:10.48550/ARXIV.2304.14701

2023 doi arXiv
[21]

Quorum subsumption for heterogeneous quorum systems

Xiao Li, Eric Chan, and Mohsen Lesani. Quorum subsumption for heterogeneous quorum systems. InDISC, volume 281 ofLIPIcs, pages 28:1–28:19. Schloss Dagstuhl - Leibniz- Zentrum f¨ ur Informatik, 2023

2023
[22]

Fast and secure global payments with stellar

Marta Lokhava, Giuliano Losa, David Mazi` eres, Graydon Hoare, Nicolas Barry, Eli Gafni, Jonathan Jove, Rafal Malinowsky, and Jed McCaleb. Fast and secure global payments with stellar. InSOSP, pages 80–96. ACM, 2019

2019
[23]

Stellar consensus by instantiation

Giuliano Losa, Eli Gafni, and David Mazi` eres. Stellar consensus by instantiation. InDISC, volume 146 ofLIPIcs, pages 27:1–27:15. Schloss Dagstuhl - Leibniz-Zentrum f¨ ur Informatik, 2019

2019
[24]

Combining asynchronous and synchronous byzantine agree- ment: The best of both worlds.IACR Cryptol

Julian Loss and Tal Moran. Combining asynchronous and synchronous byzantine agree- ment: The best of both worlds.IACR Cryptol. ePrint Arch., page 235, 2018. URL: http://eprint.iacr.org/2018/235

2018
[25]

Dahlia Malkhi and Michael K. Reiter. Byzantine quorum systems.Distributed Comput., 11(4):203–213, 1998

1998
[26]

The stellar consensus protocol: A federated model for internet-level con- sensus.Stellar Development Foundation, 32:1–45, 2015

David Mazieres. The stellar consensus protocol: A federated model for internet-level con- sensus.Stellar Development Foundation, 32:1–45, 2015. Available online fromhttps: //stellar.org/learn/stellar-consensus-protocol

2015
[27]

Bitcoin: A peer-to-peer electronic cash system, October 2008

Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system, October 2008. White paper. URL:https://bitcoin.org/bitcoin.pdf

2008
[28]

The load, capacity, and availability of quorum systems

Moni Naor and Avishai Wool. The load, capacity, and availability of quorum systems. SIAM J. Comput., 27(2):423–447, 1998

1998
[29]

Fruitchains: A fair blockchain

Rafael Pass and Elaine Shi. Fruitchains: A fair blockchain. In Elad Michael Schiller and Alexander A. Schwarzmann, editors,Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017, pages 315–324. ACM, 2017.doi:10...

2017 doi
[30]

Pease, Robert E

Marshall C. Pease, Robert E. Shostak, and Leslie Lamport. Reaching agreement in the presence of faults.J. ACM, 27(2):228–234, 1980.doi:10.1145/322186.322188. 15

1980 doi
[31]

Asymmetric failure assumptions for reliable distributed systems

Michael Senn and Christian Cachin. Asymmetric failure assumptions for reliable distributed systems. InPaPoC@EuroSys, pages 8–14. ACM, 2025

2025
[32]

Sheff, Xinwen Wang, Robbert van Renesse, and Andrew C

Isaac C. Sheff, Xinwen Wang, Robbert van Renesse, and Andrew C. Myers. Heterogeneous paxos. InOPODIS, volume 184 ofLIPIcs, pages 5:1–5:17. Schloss Dagstuhl - Leibniz- Zentrum f¨ ur Informatik, 2020. 16 A Proofs Lemma 4.1.LetQbe an asymmetric Byzantine quorum system among proce...

2020

Pith tools

Reviewed July 11, 2026 · model on record in the stance chip above.

[1] [2]

pod: An optimal-latency, censorship-free, and accountable generalized consen- sus layer

Orestis Alpos, Bernardo David, Jakov Mitrovski, Odysseas Sofikitis, and Dionysis Zin- dros. pod: An optimal-latency, censorship-free, and accountable generalized consen- sus layer. In Dariusz R. Kowalski, editor,39th International Symposium on Distributed Computing, DISC 2025, Berlin, Germany, October 27-31, 2025, volume 356 ofLIPIcs, 13 pages 4:1–4:24. S...

work page doi:10.4230/lipics.disc.2025.4 2025

[2] [1]

Asymmetric dis- tributed trust.Distributed Comput., 37(3):247–277, 2024

Orestis Alpos, Christian Cachin, Bj¨ orn Tackmann, and Luca Zanolini. Asymmetric dis- tributed trust.Distributed Comput., 37(3):247–277, 2024

2024

[3] [3]

Weaker assumptions for asymmetric trust

Ignacio Amores-Sesar, Christian Cachin, Simon Holmgaard Kamp, and Juan Villacis. Weaker assumptions for asymmetric trust. InOPODIS, volume 361 ofLIPIcs, pages 8:1– 8:18. Schloss Dagstuhl - Leibniz-Zentrum f¨ ur Informatik, 2025

2025

[4] [4]

Security analysis of ripple consensus

Ignacio Amores-Sesar, Christian Cachin, and Jovana Micic. Security analysis of ripple consensus. InOPODIS, volume 184 ofLIPIcs, pages 10:1–10:16. Schloss Dagstuhl - Leibniz- Zentrum f¨ ur Informatik, 2020

2020

[5] [5]

Dag-based con- sensus with asymmetric trust

Ignacio Amores-Sesar, Christian Cachin, Juan Villacis, and Luca Zanolini. Dag-based con- sensus with asymmetric trust. InPODC, pages 151–161. ACM, 2025

2025

[6] [6]

Welch.Distributed computing - fundamentals, simulations, and advanced topics (2

Hagit Attiya and Jennifer L. Welch.Distributed computing - fundamentals, simulations, and advanced topics (2. ed.). Wiley series on parallel and distributed computing. Wiley, 2004

2004

[7] [7]

Fastpay: High-performance byzan- tine fault tolerant settlement

Mathieu Baudet, George Danezis, and Alberto Sonnino. Fastpay: High-performance byzan- tine fault tolerant settlement. In Sarah Meiklejohn and Abhi Shelat, editors,Proceed- ings of the 2nd ACM Conference on Advances in Financial Technologies, AFT 2020, New York, NY, USA, October 21-23, 2020, pages 163–177. ACM, 2020.doi:10.1145/3419614. 3423249

work page doi:10.1145/3419614 2020

[8] [8]

Sui lutris: A blockchain combining broadcast and consensus

Sam Blackshear, Andrey Chursin, George Danezis, Anastasios Kichidis, Lefteris Kokoris- Kogias, Xun Li, Mark Logan, Ashok Menon, Todd Nowacki, Alberto Sonnino, Brandon Williams, and Lu Zhang. Sui lutris: A blockchain combining broadcast and consensus. In Bo Luo, Xiaojing Liao, Jun Xu, Engin Kirda, and David Lie, editors,Proceedings of the 2024 on ACM SIGSA...

doi:10.1145/3658644.3670286 2024