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Player-Centric Byzantine Agreement

  • Martin Hirt
  • Vassilis Zikas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

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 \(\ensuremath{\text{PCBA}} =\{\ensuremath{\ensuremath{\text{PCBA}} (\ensuremath{\mathcal{C}} )} \}_{\ensuremath{\mathcal{C}} \subseteq\ensuremath{\mathcal{P}} }\), parametrized by subsets \(\ensuremath{\mathcal{C}} \) of the player set. For each primitive \(\ensuremath{\ensuremath{\text{PCBA}} (\ensuremath{\mathcal{C}} )} \in\ensuremath{\text{PCBA}} \) the validity is defined on the input(s) of the players in \(\ensuremath{\mathcal{C}} \). Broadcast (with sender p) and Consensus are special (extreme) cases of \(\text{PCBA}\) primitives for \(\ensuremath{\mathcal{C}} =\{p\}\) and \(\ensuremath{\mathcal{C}} =\ensuremath{\mathcal{P}} \), respectively.

We study feasibility of \(\ensuremath{\text{PCBA}} \) 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 \(p_i\in\ensuremath{\mathcal{P}} \) but not for some other \(p_j\in\ensuremath{\mathcal{P}} \) being the sender. Finally, we extend the definition of \(\text{PCBA}\) by adding fail corruption to the adversary’s capabilities, and give exact feasibility bounds for computationally secure \(\ensuremath{\text{PCBA}} (\ensuremath{\mathcal{P}} )\) (aka Consensus) in this setting. This answers an open problem from ASIACRYPT 2008 concerning feasibility of computationally secure multi-party computation in this model.

Keywords

Computational Security Byzantine Agreement Acceptable Signature General Adversary Adversary Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Hirt
    • 1
  • Vassilis Zikas
    • 2
  1. 1.Department of Computer ScienceETH ZurichSwitzerland
  2. 2.University of MarylandUSA

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