Brief Announcement: Revisiting Signature-Free Asynchronous Byzantine Consensus

Among asynchronous, randomized, and signature-free implementations of consensus, the protocols of Mostéfaoui et al. (PODC 2014 and JACM 2015) represent a landmark result, which has been extended later and taken up in practical systems. The protocols achieve optimal resilience and take, in expectation, only a constant expected number of rounds and have quadratic message complexity. Randomization is provided through a common-coin primitive. However, the first version of this simple and appealing protocol suffers from a little-known liveness issue due to asynchrony. The JACM 2015 version avoids the problem, but is considerably more complex. This work revisits the original protocol of PODC 2014 and points out in detail why it may not progress. A fix for the protocol is presented, which does not affect any of its properties, but lets it regain the original simplicity in asynchronous networks enhanced with a common-coin protocol

Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement

Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply to deterministic algorithms only. Probabilistic protocols have been around for at least four decades and are receiving a lot of attention with the emergence of blockchain systems. Nonetheless, we are aware of only a handful of randomized lower bounds. In this work we provide a formal framework for reasoning about randomized distributed algorithms. We generalize the notion of indistinguishability, the most useful tool in deterministic lower bounds, to apply to a probabilistic setting. We apply this framework to prove a result of independent interest. Namely, we completely characterize the quality of decisions that protocols for a randomized multi-valued Consensus problem can guarantee in an asynchronous environment with Byzantine faults. We use the new notion to prove a lower bound on the guaranteed probability that honest parties will not decide on a possibly bogus value proposed by a malicious party. Finally, we show that the bound is tight by providing a protocol that matches it. This brief announcement consists of an introduction to the full paper [Guy Goren et al., 2020] by the same title. The interested reader is advised to consult the full paper for a detailed exposition

Fast self-stabilizing byzantine tolerant digital clock synchronization

Consider a distributed network in which up to a third of the nodes may be Byzantine, and in which the non-faulty nodes may be subject to transient faults that alter their memory in an arbitrary fashion. Within the context of this model, we are interested in the digital clock synchronization problem; which consists of agreeing on bounded integer counters, and increasing these counters regularly. It has been postulated in the past that synchronization cannot be solved in a Byzantine tolerant and self-stabilizing manner. The first solution to this problem had an expected exponential convergence time. Later, a deterministic solution was published with linear convergence time, which is optimal for deterministic solutions. In the current paper we achieve an expected constant convergence time. We thus obtain the optimal probabilistic solution, both in terms of convergence time and in terms of resilience to Byzantine adversaries

Optimal and Player-Replaceable Consensus with an Honest Majority

We construct a Byzantine Agreement protocol that tolerates t < n/2 corruptions, is very efficient in terms of the number of rounds and the number of bits of communication, and satisfies a strong notion of robustness called player replaceability (defined in [Mic16]). We provide an analysis of our protocol when executed on real-world networks such as the ones employed in the bitcoin protocol

Scheduling real-time, periodic jobs using imprecise results

A process is called a monotone process if the accuracy of its intermediate results is non-decreasing as more time is spent to obtain the result. The result produced by a monotone process upon its normal termination is the desired result; the error in this result is zero. External events such as timeouts or crashes may cause the process to terminate prematurely. If the intermediate result produced by the process upon its premature termination is saved and made available, the application may still find the result unusable and, hence, acceptable; such a result is said to be an imprecise one. The error in an imprecise result is nonzero. The problem of scheduling periodic jobs to meet deadlines on a system that provides the necessary programming language primitives and run-time support for processes to return imprecise results is discussed. This problem differs from the traditional scheduling problems since the scheduler may choose to terminate a task before it is completed, causing it to produce an acceptable but imprecise result. Consequently, the amounts of processor time assigned to tasks in a valid schedule can be less than the amounts of time required to complete the tasks. A meaningful formulation of this problem taking into account the quality of the overall result is discussed. Three algorithms for scheduling jobs for which the effects of errors in results produced in different periods are not cumulative are described, and their relative merits are evaluated