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Documents authored by Hirt, Martin

Document
DOI: 10.4230/LIPIcs.OPODIS.2020.6
Multi-Threshold Asynchronous Reliable Broadcast and Consensus

Authors: Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f > t, these protocols are completely deemed insecure. We consider the relaxed notion of multi-threshold reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f ≤ t_v, f ≤ t_c and f ≤ t_t respectively. For consensus, we consider both variants of (1-ε)-consensus and almost-surely terminating consensus, where termination is guaranteed with probability (1-ε) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: - Multi-threshold reliable broadcast is possible if and only if max{t_c,t_v} + 2t_t < n. - Multi-threshold almost-surely consensus is possible if max{t_c, t_v} + 2t_t < n, 2t_v + t_t < n and t_t < n/3. Assuming a global coin, it is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n. - Multi-threshold (1-ε)-consensus is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n.
Cite as

Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hirt_et_al:LIPIcs.OPODIS.2020.6,
  author =	{Hirt, Martin and Kastrati, Ard and Liu-Zhang, Chen-Da},
  title =	{{Multi-Threshold Asynchronous Reliable Broadcast and Consensus}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.6},
  URN =		{urn:nbn:de:0030-drops-134917},
  doi =		{10.4230/LIPIcs.OPODIS.2020.6},
  annote =	{Keywords: broadcast, byzantine agreement, multi-threshold}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.29
From Partial to Global Asynchronous Reliable Broadcast

Authors: Diana Ghinea, Martin Hirt, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
Broadcast is a fundamental primitive in distributed computing. It allows a sender to consistently distribute a message among n recipients. The seminal result of Pease et al. [JACM'80] shows that in a complete network of synchronous bilateral channels, broadcast is achievable if and only if the number of corruptions is bounded by t < n/3. To overcome this bound, a fascinating line of works, Fitzi and Maurer [STOC'00], Considine et al. [JC'05], and Raykov [ICALP'15], proposed strengthening the communication network by assuming partial synchronous broadcast channels, which guarantee consistency among a subset of recipients. We extend this line of research to the asynchronous setting. We consider reliable broadcast protocols assuming a communication network which provides each subset of b parties with reliable broadcast channels. A natural question is to investigate the trade-off between the size b and the corruption threshold t. We answer this question by showing feasibility and impossibility results: - A reliable broadcast protocol Π_{RBC} that: - For 3 ≤ b ≤ 4, is secure up to t < n/2 corruptions. - For b > 4 even, is secure up to t < ((b-4)/(b-2) n + 8/(b-2)) corruptions. - For b > 4 odd, is secure up to t < ((b-3)/(b-1) n + 6/(b-1)) corruptions. - A nonstop reliable broadcast Π_{nRBC}, where parties are guaranteed to obtain output as in reliable broadcast but may need to run forever, secure up to t < (b-1)/(b+1) n corruptions. - There is no protocol for (nonstop) reliable broadcast secure up to t ≥ (b-1)/(b+1) n corruptions, implying that Π_{RBC} is an asymptotically optimal reliable broadcast protocol, and Π_{nRBC} is an optimal nonstop reliable broadcast protocol.
Cite as

Diana Ghinea, Martin Hirt, and Chen-Da Liu-Zhang. From Partial to Global Asynchronous Reliable Broadcast. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ghinea_et_al:LIPIcs.DISC.2020.29,
  author =	{Ghinea, Diana and Hirt, Martin and Liu-Zhang, Chen-Da},
  title =	{{From Partial to Global Asynchronous Reliable Broadcast}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.29},
  URN =		{urn:nbn:de:0030-drops-131074},
  doi =		{10.4230/LIPIcs.DISC.2020.29},
  annote =	{Keywords: asynchronous broadcast, partial broadcast}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2020.48
Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus

Authors: Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f > t, these protocols are completely deemed insecure. We consider the relaxed notion of multi-threshold reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f ≤ t_v, f ≤ t_c and f ≤ t_t respectively. For consensus, we consider both variants of (1-ε)-consensus and almost-surely terminating consensus, where termination is guaranteed with probability (1-ε) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: - Multi-threshold reliable broadcast is possible if and only if max{t_c,t_v} + 2t_t < n. - Multi-threshold almost-surely consensus is possible if max{t_c, t_v} + 2t_t < n, 2t_v + t_t < n and t_t < n/3. Assuming a global coin, it is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n. - Multi-threshold (1-ε)-consensus is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n.
Cite as

Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hirt_et_al:LIPIcs.DISC.2020.48,
  author =	{Hirt, Martin and Kastrati, Ard and Liu-Zhang, Chen-Da},
  title =	{{Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{48:1--48:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.48},
  URN =		{urn:nbn:de:0030-drops-131267},
  doi =		{10.4230/LIPIcs.DISC.2020.48},
  annote =	{Keywords: broadcast, byzantine agreement, multi-threshold}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.3
Efficient MPC with a Mixed Adversary

Authors: Martin Hirt and Marta Mularczyk

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Over the past 20 years, the efficiency of secure multi-party protocols has been greatly improved. While the seminal protocols from the late 80’s require a communication of Ω(n⁶) field elements per multiplication among n parties, recent protocols offer linear communication complexity. This means that each party needs to communicate a constant number of field elements per multiplication, independent of n. However, these efficient protocols only offer active security, which implies that at most t<n/3 (perfect security), respectively t<n/2 (statistical or computational security) parties may be corrupted. Higher corruption thresholds (i.e., t≥ n/2) can only be achieved with degraded security (unfair abort), where one single corrupted party can prevent honest parties from learning their outputs. The aforementioned upper bounds (t<n/3 and t<n/2) have been circumvented by considering mixed adversaries (Fitzi et al., Crypto' 98), i.e., adversaries that corrupt, at the same time, some parties actively, some parties passively, and some parties in the fail-stop manner. It is possible, for example, to achieve perfect security even if 2/3 of the parties are faulty (three quarters of which may abort in the middle of the protocol, and a quarter may even arbitrarily misbehave). This setting is much better suited to many applications, where the crash of a party is more likely than a coordinated active attack. Surprisingly, since the presentation of the feasibility result for the mixed setting, no progress has been made in terms of efficiency: the state-of-the-art protocol still requires a communication of Ω(n⁶) field elements per multiplication. In this paper, we present a perfectly-secure MPC protocol for the mixed setting with essentially the same efficiency as the best MPC protocols for the active-only setting. For the first time, this allows to tolerate faulty majorities, while still providing optimal efficiency. As a special case, this also results in the first fully-secure MPC protocol secure against any number of crashing parties, with optimal (i.e., linear in n) communication. We provide simulation-based proofs of our construction.
Cite as

Martin Hirt and Marta Mularczyk. Efficient MPC with a Mixed Adversary. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hirt_et_al:LIPIcs.ITC.2020.3,
  author =	{Hirt, Martin and Mularczyk, Marta},
  title =	{{Efficient MPC with a Mixed Adversary}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.3},
  URN =		{urn:nbn:de:0030-drops-121083},
  doi =		{10.4230/LIPIcs.ITC.2020.3},
  annote =	{Keywords: Multi-party Computation, Communication Cost}
}
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