2,351 research outputs found
On the Round Complexity of Randomized Byzantine Agreement
We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that:
1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)].
2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1).
3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)].
The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI).
The third bound essentially matches the recent protocol of Micali (ITCS\u2717) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability
The Contest Between Simplicity and Efficiency in Asynchronous Byzantine Agreement
In the wake of the decisive impossibility result of Fischer, Lynch, and
Paterson for deterministic consensus protocols in the aynchronous model with
just one failure, Ben-Or and Bracha demonstrated that the problem could be
solved with randomness, even for Byzantine failures. Both protocols are natural
and intuitive to verify, and Bracha's achieves optimal resilience. However, the
expected running time of these protocols is exponential in general. Recently,
Kapron, Kempe, King, Saia, and Sanwalani presented the first efficient
Byzantine agreement algorithm in the asynchronous, full information model,
running in polylogarithmic time. Their algorithm is Monte Carlo and drastically
departs from the simple structure of Ben-Or and Bracha's Las Vegas algorithms.
In this paper, we begin an investigation of the question: to what extent is
this departure necessary? Might there be a much simpler and intuitive Las Vegas
protocol that runs in expected polynomial time? We will show that the
exponential running time of Ben-Or and Bracha's algorithms is no mere accident
of their specific details, but rather an unavoidable consequence of their
general symmetry and round structure. We define a natural class of "fully
symmetric round protocols" for solving Byzantine agreement in an asynchronous
setting and show that any such protocol can be forced to run in expected
exponential time by an adversary in the full information model. We assume the
adversary controls Byzantine processors for , where is an
arbitrary positive constant . We view our result as a step toward
identifying the level of complexity required for a polynomial-time algorithm in
this setting, and also as a guide in the search for new efficient algorithms.Comment: 21 page
Randomization Adaptive Self-Stabilization
We present a scheme to convert self-stabilizing algorithms that use
randomization during and following convergence to self-stabilizing algorithms
that use randomization only during convergence. We thus reduce the number of
random bits from an infinite number to a bounded number. The scheme is
applicable to the cases in which there exits a local predicate for each node,
such that global consistency is implied by the union of the local predicates.
We demonstrate our scheme over the token circulation algorithm of Herman and
the recent constant time Byzantine self-stabilizing clock synchronization
algorithm by Ben-Or, Dolev and Hoch. The application of our scheme results in
the first constant time Byzantine self-stabilizing clock synchronization
algorithm that uses a bounded number of random bits
Randomized protocols for asynchronous consensus
The famous Fischer, Lynch, and Paterson impossibility proof shows that it is
impossible to solve the consensus problem in a natural model of an asynchronous
distributed system if even a single process can fail. Since its publication,
two decades of work on fault-tolerant asynchronous consensus algorithms have
evaded this impossibility result by using extended models that provide (a)
randomization, (b) additional timing assumptions, (c) failure detectors, or (d)
stronger synchronization mechanisms than are available in the basic model.
Concentrating on the first of these approaches, we illustrate the history and
structure of randomized asynchronous consensus protocols by giving detailed
descriptions of several such protocols.Comment: 29 pages; survey paper written for PODC 20th anniversary issue of
Distributed Computin
Lower Bounds on Implementing Robust and Resilient Mediators
We consider games that have (k,t)-robust equilibria when played with a
mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by
coalitions of size up to k and deviations by up to players with unknown
utilities. We prove lower bounds that match upper bounds on the ability to
implement such mediators using cheap talk (that is, just allowing communication
among the players). The bounds depend on (a) the relationship between k, t, and
n, the total number of players in the system; (b) whether players know the
exact utilities of other players; (c) whether there are broadcast channels or
just point-to-point channels; (d) whether cryptography is available; and (e)
whether the game has a k+t$ players, guarantees that every player gets a
worse outcome than they do with the equilibrium strategy
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