Polynomial algorithms for multiple processor agreement

Dolev, Danny; Strong, H. Raymond

doi:10.1145/800070.802215

Cited by 117 publications

(64 citation statements)

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“…1 Other solutions [DS82,PW92] 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. The suggested protocols are polynomial in the number of players and are as secure as the underlying signature scheme.…”

Section: Summary Of Known Resultsmentioning

confidence: 99%

“…2 Recently, Lindell, Lysyanskaya, and Rabin [LLR02] proved that, unless unique session identifiers are available, the bound t < n/3 is necessary for feasibility of concurrently composable Broadcast, even when a setup allowing digital signatures is given. To the positive side, they showed that when unique session IDs are available, then the protocols which achieve Broadcast and use signatures for authentication, e.g., [DS82,PW92] can be be transformed to concurrently composable Broadcast protocols.…”

Section: Summary Of Known Resultsmentioning

confidence: 99%

“…In fact, the Universal Composition framework [Can01] which is the most widely accepted framework for arguing about the security of protocols, explicitly excludes such a simultaneous multi-send assumption. Furthermore, for broadcast protocols using signatures and tolerating t ≥ n/3 [DS82,PW92], even this assumption does not help, as still the adversary can learn the message in the first phase of the protocol, and make the broadcast fail afterwards by corrupting the sender and introducing signatures for different messages. 4 The major problem is that in the broadcast literature, protocols are proven secure with respect to properties, but in the cryptographic protocols literature (VSS, MPC, etc), protocols are proven secure in a hybrid world with access to an ideal broadcast functionality (e.g., "secure-channels model with broadcast").…”

Section: Broadcast In the Literaturementioning

confidence: 99%

“…Both bounds are tight. We stress that in the secure channels model, no protocol exists that securely realizes the natural broadcast functionality when t > n/2 (although property-based security is possible for t < n [DS82,PW92]). …”

Section: Contributionsmentioning

confidence: 99%

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Adaptively Secure Broadcast

Hirt

Zikas

2010

Lecture Notes in Computer Science

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Abstract.A broadcast protocol allows a sender to distribute a message through a point-to-point network to a set of parties, such that (i) all parties receive the same message, even if the sender is corrupted, and (ii) this is the sender's message, if he is honest. Broadcast protocols satisfying these properties are known to exist if and only if t < n/3, where n denotes the total number of parties, and t denotes the maximal number of corruptions. When a setup allowing signatures is available to the parties, then such protocols exist even for t < n.Since its invention in [LSP82], broadcast has been used as a primitive in numerous multi-party protocols making it one of the fundamental primitives in the distributed-protocols literature. The security of these protocols is analyzed in a model where a broadcast primitive which behaves in an ideal way is assumed. Clearly, a definition of broadcast should allow for secure composition, namely, it should be secure to replace an assumed broadcast primitive by a protocol satisfying this definition. Following recent cryptographic reasoning, to allow secure composition the ideal behavior of broadcast can be described as an ideal functionality, and a simulation-based definition can be used.In this work, we show that the property-based definition of broadcast does not imply the simulation-based definition for the natural broadcast functionality. In fact, most broadcast protocols in the literature do not securely realize this functionality, which raises a composability issue for these broadcast protocols. In particular, we do not know of any broadcast protocol which could be securely invoked in a multi-party computation protocol in the secure-channels model. The problem is that existing protocols for broadcast do not preserve the secrecy of the message while being broadcasted, and in particular allow the adversary to corrupt the sender (and change the message), depending on the message being broadcasted. For example, when every party should broadcast a random bit, the adversary could corrupt those parties who intend to broadcast 0, and make them broadcast 1.More concretely, we show that simulatable broadcast in a model with secure channels is possible if and only if t < n/3, respectively t ≤ n/2 when a signature setup is available. The positive results are proven by constructing secure broadcast protocols.

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Section: Summary Of Known Resultsmentioning

confidence: 99%

Section: Summary Of Known Resultsmentioning

confidence: 99%

Section: Broadcast In the Literaturementioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

See 2 more Smart Citations

Adaptively Secure Broadcast

Hirt

Zikas

2010

Lecture Notes in Computer Science

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“…In addition to the impossibility of deterministic algorithms in the asynchronous setting mentioned above, there is a sharp lower bound of t rounds for deterministic algorithms in the synchronous setting [13]. This lower bound is proven by assembling a chain of executions where any two adjacent executions are indistinguishable to some non-faulty processor and the two ends of the chain represent different decision values.…”

Section: Related Workmentioning

confidence: 99%

On the complexity of asynchronous agreement against powerful adversaries

Lewko

2014

Distrib. Comput.

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We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a strongly adaptive adversary that is computationally unbounded and has a limited ability to corrupt a dynamic subset of processors by erasing their memories. We demonstrate that the randomized agreement algorithms designed by Ben-Or and Bracha to tolerate crash or Byzantine failures in the asynchronous setting extend to defeat a strongly adaptive adversary. These algorithms have essentially perfect correctness and termination, but at the expense of exponential running time. In the case of the strongly adaptive adversary, we show that this dismally slow running time is inherent : we prove that any algorithm with essentially perfect correctness and termination against the strongly adaptive adversary must have exponential running time. We additionally interpret this result as yielding an enhanced understanding of the tools needed to simultaneously achieving perfect correctness and termination as well as fast running time for randomized algorithms tolerating crash or Byzantine failures.

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Design and Analysis of Distributed Algorithms

Santoro¹

2006

158

147

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Polynomial algorithms for multiple processor agreement

Cited by 117 publications

References 8 publications

Adaptively Secure Broadcast

Adaptively Secure Broadcast

On the complexity of asynchronous agreement against powerful adversaries

Design and Analysis of Distributed Algorithms

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