On the Complexity of Broadcast Setup

Hirt, Martin; Raykov, Pavel

doi:10.1007/978-3-642-39206-1_47

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…In [HR13], Hirt and Raykov recently showed how to prepare a setup allowing to simulate 2-cast channels (protocols Setup 3 and Broadcast 3 in [HR13]). The setup protocol Setup 3 takes 3 rounds, where in the first two rounds point-to-point channels are used and in the third round a physical broadcast is used.…”

Section: Further Reducing the Number Of Broadcast Roundsmentioning

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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Section: Further Reducing the Number Of Broadcast Roundsmentioning

confidence: 99%

Broadcast (and Round) Efficient Verifiable Secret Sharing

Garay

Givens

Ostrovsky

et al. 2014

Lecture Notes in Computer Science

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“…In [HR13] the authors give a protocol for 3 players allowing to broadcast message of any length by broadcasting 10 bits only is given. In our notation this shows that log φ 3 (d) ≤ 10 for all d.…”

Section: Related Workmentioning

confidence: 99%

“…An identifying predicate allows to identify a specific element v from some small subset S ⊆ D, where D is a potentially large domain. To our knowledge, this concept has been firstly introduced in [HR13].…”

Section: Identifyingmentioning

confidence: 99%

Broadcast Amplification

Hirt¹,

Maurer²,

Raykov³

2014

Theory of Cryptography

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Abstract. A d-broadcast primitive is a communication primitive that allows a sender to send a value from a domain of size d to a set of parties. A broadcast protocol emulates the d-broadcast primitive using only point-to-point channels, even if some of the parties cheat, in the sense that all correct recipients agree on the same value v (consistency), and if the sender is correct, then v is the value sent by the sender (validity). A celebrated result by Pease, Shostak and Lamport states that such a broadcast protocol exists if and only if t < n/3, where n denotes the total number of parties and t denotes the upper bound on the number of cheaters. This paper is concerned with broadcast protocols for any number of cheaters (t < n), which can be possible only if, in addition to point-topoint channels, another primitive is available. Broadcast amplification is the problem of achieving d-broadcast when d -broadcast can be used once, for d < d. Let φn(d) denote the minimal such d for domain size d. We show that for n = 3 parties, broadcast for any domain size is possible if only a single 3-broadcast is available, and broadcast of a single bit (d = 2) is not sufficient, i.e., φ3(d) = 3 for any d ≥ 3. In contrast, for n > 3 no broadcast amplification is possible, i.e., φn(d) = d for any d. However, if other parties than the sender can also broadcast some short messages, then broadcast amplification is possible for any n. Let φ * n (d) denote the minimal d such that d-broadcast can be constructed from primitivesWe show that broadcasting 8n log n bits in total suffices, independently of d, and that at least n−2 parties, including the sender, must broadcast at least one bit. Hence min(log d, n − 2) ≤ log φ * n (d) ≤ 8n log n.

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“…Kumaresan et al in [12] introduced a (2,2)-broadcast and (3,2)-round algorithm but their algorithm is not linear and also is in exponential time complexity. Hirt and Raykov in [13] proposed a (1,0)broadcast protocol in which the overall number of their protocol rounds is linear in n.…”

Section: Introductionmentioning

confidence: 99%

Broadcast Complexity and Adaptive Adversaries in Verifiable Secret Sharing

Beghaeiraveri

Izadi

Rezvani

2020

Security and Communication Networks

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Verifiable secret sharing (VSS) is one of the basic problems in the theory of distributed cryptography and has an important role in secure multiparty computation. In this case, it is tried to share a confidential data as secret, between multiple nodes in a distributed system, in the presence of an active adversary that can destroy some nodes, such that the secret can be reconstructed with the participation of certain size of honest nodes. A dynamic adversary can change its corrupted nodes among the protocol. So far, there is not a formal definition and there are no protocols of dynamic adversaries in VSS context. Also, another important question is, would there exist a protocol to share a secret with a static adversary with at most 1 broadcast round? In this paper, we provide a formal definition of the dynamic adversary. The simulation results prove the efficiency of the proposed protocol in terms of the runtime, the memory usage, and the number of message exchanges. We show that the change period of the dynamic adversary could not happen in less than 4 rounds in order to have a perfectly secure VSS, and then we establish a protocol to deal with this type of adversary. Also, we prove that the lower bound of broadcast complexity for the static adversary is (2,0)-broadcast rounds.

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On the Complexity of Broadcast Setup

Cited by 6 publications

References 9 publications

Broadcast (and Round) Efficient Verifiable Secret Sharing

Broadcast (and Round) Efficient Verifiable Secret Sharing

Broadcast Amplification

Broadcast Complexity and Adaptive Adversaries in Verifiable Secret Sharing

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