Efficient Byzantine Agreement with Faulty Minority

Beerliová-Trubíniová, Zuzana; Hirt, Martin; Riser, Micha

doi:10.1007/978-3-540-76900-2_24

Cited by 11 publications

(11 citation statements)

References 16 publications

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“…All known schemes [PW96,BHR07,GGO12] use temporary broadcast in strictly more than one round in the setup phase. We give a broadcast scheme for t < n/2 which requires only 1 round of the temporary broadcast.…”

Section: Discussionmentioning

confidence: 99%

“…The number of bits broadcast by their protocol in the setup phase is Ω(n 6 κ). Another construction by Hirt et al [BHR07] yields a broadcast scheme for t < n/2 which needs Ω(n) rounds of temporary broadcast with Ω(nκ) bits broadcast in the setup phase. 2 This paper gives the first information-theoretically secure broadcast scheme that requires only 1 round of the temporary broadcast in the setup phase for t < n/2, which is trivially optimal.…”

Section: Contributionsmentioning

confidence: 99%

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On the Complexity of Broadcast Setup

Hirt

Raykov

2013

Automata, Languages, and Programming

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Byzantine broadcast is a distributed primitive that allows a specific party (called "sender") to consistently distribute a value v among n parties in the presence of potential misbehavior of up to t of the parties. Broadcast requires that correct parties always agree on the same value and if the sender is correct, then the agreed value is v. Broadcast without a setup (i.e., from scratch) is achievable from point-to-point channels if and only if t < n/3. In case t ≥ n/3 a trusted setup is required. The setup may be assumed to be given initially or generated by the parties in a setup phase. It is known that generating setup for protocols with cryptographic security is relatively simple and only consists of setting up a public-key infrastructure. However, generating setup for information-theoretically secure protocols is much more involved. In this paper we study the complexity of setup generation for informationtheoretic protocols using point-to-point channels and temporarily available broadcast channels. We optimize the number of rounds in which the temporary broadcast channels are used while minimizing the number of bits broadcast with them. We give the first information-theoretically secure broadcast protocol tolerating t < n/2 that uses the temporary broadcast channels during only 1 round in the setup phase. Furthermore, only O(n 3 ) bits need to be broadcast with the temporary broadcast channels during that round, independently of the security parameter employed. The broadcast protocol presented in this paper allows to construct the first informationtheoretically secure MPC protocol which uses a broadcast channel during only one round. Additionally, the presented broadcast protocol supports refreshing, which allows to broadcast an a priori unknown number of times given a fixed-size setup.

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Section: Discussionmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

On the Complexity of Broadcast Setup

Hirt

Raykov

2013

Automata, Languages, and Programming

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“…In particular, often in our sub-protocols a player p i is instructed to send a message m to some p j along with his signature sig i (m) on it, so that p j has a proof that he indeed got this message from this sender in the corresponding round 6 . However, if p i is passively corrupted, the adversary might introduce into the protocol arbitrary signatures with signer p i .…”

Section: Remark 2 (The Use Of Signatures)mentioning

confidence: 99%

“…This model has been extensively studied [10,29,12,8,9,2,17] and protocols with optimal resiliency and complexity (communication and computation) polynomial in the number of players were suggested. Later solutions [11,4,28,6] considered a setting where a setup allowing digital signatures is available, and showed that Broadcast tolerating an arbitrary number of cheaters (t < n) is possible, whereas Consensus is possible if and only if t < n/2; for both primitives corresponding protocols with optimal resiliency and complexity polynomial in the number of players were suggested 2 . Lamport and Fischer [25] considered an adversary who can fail corrupt up to t players, and showed that any n − 1 players being fail corrupted can be tolerated for Broadcast.…”

Section: Introductionmentioning

confidence: 99%

Player-Centric Byzantine Agreement

Hirt

Zikas

2011

Automata, Languages and Programming

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Abstract. Most of the existing feasibility results on Byzantine Agreement (BA) are of an all-or-nothing fashion: in Broadcast they address the question whether or not there exists a protocol which allows any player to broadcast his input. Similarly, in Consensus the question is whether or not consensus can be reached which respects pre-agreement on the inputs of all correct players. In this work, we introduce the natural notion of player-centric BA which is a class of BA primitives, denoted as PCBA = {PCBA(C)} C⊆P , parametrized by subsets C of the player set. For each primitive PCBA(C) ∈ PCBA the validity is defined on the input(s) of the players in C. Broadcast (with sender p) and Consensus are special (extreme) cases of PCBA primitives for C = {p} and C = P, respectively.We study feasibility of PCBA in the presence of a general (aka non-threshold) mixed (active/passive) adversary, and give a complete characterization for perfect, statistical, and computational security. Our results expose an asymmetry of Broadcast which has, so far, been neglected in the literature: there exist non-trivial adversaries which can be tolerated for Broadcast with sender some pi ∈ P but not for some other pj ∈ P being the sender. Finally, we extend the definition of PCBA by adding fail corruption to the adversary's capabilities, and give exact feasibility bounds for computationally secure PCBA(P) (aka Consensus) in this setting. This answers an open problem from ASIACRYPT 2008 concerning feasibility of computationally secure multi-party computation in this model.

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“…The number of broadcast rounds in the [PW96] setup construction is O(n 2 ), and it works for an arbitrary number of corruptions (t < n). This was later improved to O(n) broadcast rounds by Beerliová-Trubíniová et al in [BTHR07], at the price of tolerating t < n/2 corruptions, and recently by Hirt and Raykov to just 1, as mentioned above. However, the overall round complexity of this construction (as well as that in [BTHR07]…”

Section: Introductionmentioning

confidence: 99%

Broadcast (and Round) Efficient Verifiable Secret Sharing

Garay

Givens

Ostrovsky

et al. 2014

Lecture Notes in Computer Science

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Verifiable secret sharing (VSS) is a fundamental cryptographic primitive, lying at the core of secure multi-party computation (MPC) and, as the distributed analogue of a commitment functionality, used in numerous applications. In this paper we focus on unconditionally secure VSS protocols with honest majority.In this setting it is typically assumed that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a "broadcast" channel. Because broadcast cannot be simulated on a point-to-point network when a third or more of the parties are corrupt, it is impossible to construct VSS (and more generally, MPC) protocols in this setting without using a broadcast channel (or some equivalent addition to the model).A great deal of research has focused on increasing the efficiency of VSS, primarily in terms of round complexity. In this work we consider a refinement of the round complexity of VSS, by adding a measure we term broadcast complexity. We view the broadcast channel as an expensive resource and seek to minimize the number of rounds in which it is invoked as well.We construct a (linear) VSS protocol which uses the broadcast channel only twice in the sharing phase, while running in an overall constant number of rounds.

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Efficient Byzantine Agreement with Faulty Minority

Cited by 11 publications

References 16 publications

On the Complexity of Broadcast Setup

On the Complexity of Broadcast Setup

Player-Centric Byzantine Agreement

Broadcast (and Round) Efficient Verifiable Secret Sharing

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