Revisiting Asynchronous Fault Tolerant Computation with Optimal Resilience

Abraham, Ittai; Dolev, Danny; Stern, Gilad

doi:10.1145/3382734.3405722

Cited by 13 publications

(3 citation statements)

References 9 publications

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“…In this section we prove the n > 4t lower bound for t-secure computation (also proved or claimed in [Abraham, Dolev, and Stern 2020;Ben-Or, Kelmer, and Rabin 1994;Canetti 1996]), which we strengthen slightly by showing that it applies to t-weak secure computation.…”

Section: Proof Of Theorems 12 and 11supporting

confidence: 65%

“…To do so, we would like to reduce implementing (k + t)-secure computation to implementing (k, t)robust mediators. If such a reduction were possible, the n > 4(k + t) lower bound for implementing (k, t)-robust mediators would follow immediately from the same lower bound for secure computation [Abraham, Dolev, and Stern 2020;Ben-Or, Kelmer, and Rabin 1994;Canetti 1996]. Unfortunately, there does not seem to be such a reduction.…”

Section: Introductionmentioning

confidence: 99%

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Lower Bounds Implementing Mediators in Asynchronous Systems

Geffner¹,

Halpern²

2021

Preprint

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Abraham, Dolev, Geffner, and Halpern [2019] proved that, in asynchronous systems, a (k, t)robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4(k + t), where an equilibrium is (k, t)-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4(k+t) there exist (k, t)-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing (k, t)-robust mediators seems closely related to implementing asynchronous multiparty (k + t)-secure computation [Ben-Or, Canetti, and Goldreich 1993], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of (k + t)-secure computation, which we call (k + t)-strict secure computation, to implementing (k, t)-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be (k + t)-strictly securely computed if n ≤ 4(k + t). This also provides a simple alternative proof for the well-known lower bound of 4t + 1 on asynchronous secure computation in the presence of up to t malicious agents [

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Section: Proof Of Theorems 12 and 11supporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Lower Bounds Implementing Mediators in Asynchronous Systems

Geffner¹,

Halpern²

2021

Preprint

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“…For example, the required agreement can be approximate [29], randomized [30], or differential [31]. The communication network can be asynchronous [32,33,34], partially connected [35], or even sparse [16,36]. And the BFT algorithms can be self-stabilizing [37,38], self-optimizing [39], just to name a few.…”

Section: B From Theory To Realitymentioning

confidence: 99%

Reaching Efficient Byzantine Agreements in Bipartite Networks

Yu¹,

Zhu²,

Yang³

et al. 2022

Preprint

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For reaching efficient deterministic synchronous Byzantine agreement upon partially connected networks, the traditional broadcast primitive is extended and integrated with a general framework. With this, the Byzantine agreement is extended to fully connected bipartite networks and some bipartite bounded-degree networks. The complexity of the Byzantine agreement is lowered and optimized with the so-called Byzantinelevers under a general system structure. Some bipartite simulation of the butterfly networks and some finer properties of bipartite bounded-degree networks are also provided for building efficient incomplete Byzantine agreement under the same system structure. It shows that efficient real-world Byzantine agreement systems can be built with the provided algorithms with sufficiently high system assumption coverage. Meanwhile, the proposed bipartite solutions can improve the dependability of the systems in some open, heterogeneous, and even antagonistic environments.

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Network Agnostic MPC with Statistical Security

Appan,

Choudhury

2023

Lecture Notes in Computer Science

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Revisiting Asynchronous Fault Tolerant Computation with Optimal Resilience

Cited by 13 publications

References 9 publications

Lower Bounds Implementing Mediators in Asynchronous Systems

Lower Bounds Implementing Mediators in Asynchronous Systems

Reaching Efficient Byzantine Agreements in Bipartite Networks

Network Agnostic MPC with Statistical Security

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