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Register a new userCob: a Multidimensional Byzantine Agreement Protocol for Asynchronous Incomplete Networks
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Added by
Andrea Flamini
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper we extend the Multidimensional Byzantine Agreement (MBA) Protocol arXiv:2105.13487v2, a leaderless Byzantine agreement for vectors of arbitrary values, into the emph{Cob} protocol, that works in Asynchronous Gossiping (AG) networks. This generalization allows the consensus process to be run by an incomplete network of nodes provided with (non-synchronized) same-speed clocks. Not all nodes are active in every step, so the network size does not hamper the efficiency, as long as the gossiping broadcast delivers the messages to every node in reasonable time. These network assumptions model more closely real-life communication channels, so the Cob protocol may be applicable to a variety of practical problems, such as blockchain platforms implementing sharding. The Cob protocol has the same Bernoulli-like distribution that upper bounds the number of steps required as the MBA protocol, and we prove its correctness and security assuming a supermajority of honest nodes in the network.
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In this paper we will present the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value $bot$ that signals irreconcilable disagreement. The MBA Protocol is probabilistic and its execution halts with probability 1, and the number of steps necessary to halt follows a Bernoulli-like distribution. The design combines a Multidimensional Graded Consensus and a Multidimensional Binary Byzantine Agreement, the generalization to the multidimensional case of two protocols by Micali and Feldman. We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious.
We propose the first deterministic algorithm that tolerates up to $f$ byzantine faults in $3f+1$-sized networks and performs in the asynchronous CORDA model. Our solution matches the previously established lower bound for the semi-synchronous ATOM model on the number of tolerated Byzantine robots. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space.
For asynchronous binary agreement (ABA) with optimal resilience, prior private-setup free protocols (Cachin et al., CCS 2002; Kokoris-Kogias et al., CCS 2020) incur $O({lambda}n^4)$ bits and $O(n^3)$ messages; for asynchronous multi-valued agreement with external validity (VBA), Abraham et al. [2] very recently gave the first elegant construction with $O(n^3)$ messages, relying on public key infrastructure (PKI), but still costs $O({lambda} n^3 log n)$ bits. We for the first time close the remaining efficiency gap, i.e., reducing their communication to $O({lambda} n^3)$ bits on average. At the core of our design, we give a systematic treatment of reasonably fair common randomness: - We construct a reasonably fair common coin (Canetti and Rabin, STOC 1993) in the asynchronous setting with PKI instead of private setup, using only $O({lambda} n^3)$ bit and constant asynchronous rounds. The common coin protocol ensures that with at least 1/3 probability, all honest parties can output a common bit that is as if uniformly sampled, rendering a more efficient private-setup free ABA with expected $O({lambda} n^3)$ bit communication and constant running time. - More interestingly, we lift our reasonably fair common coin protocol to attain perfect agreement without incurring any extra factor in the asymptotic complexities, resulting in an efficient reasonably fair leader election primitive pluggable in all existing VBA protocols, thus reducing the communication of private-setup free VBA to expected $O({lambda} n^3)$ bits while preserving expected constant running time. - Along the way, we improve an important building block, asynchronous verifiable secret sharing by presenting a private-setup free implementation costing only $O({lambda} n^2)$ bits in the PKI setting. By contrast, prior art having the same complexity (Backes et al., CT-RSA 2013) has to rely on a private setup.
Consider a distributed system with $n$ processors out of which $f$ can be Byzantine faulty. In the approximate agreement task, each processor $i$ receives an input value $x_i$ and has to decide on an output value $y_i$ such that - the output values are in the convex hull of the non-faulty processors input values, - the output values are within distance $d$ of each other. Classically, the values are assumed to be from an $m$-dimensional Euclidean space, where $m ge 1$. In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph $G$ and the goal is to output vertices that are within distance $d$ of each other in $G$, but still remain in the graph-induced convex hull of the input values. For $d=0$, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any $d ge 1$, we show that the task is solvable in asynchronous systems when $G$ is chordal and $n > (omega+1)f$, where $omega$ is the clique number of~$G$. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures.
In this paper we address Approximate Agreement problem in the Mobile Byzantine faults model. Our contribution is threefold. First, we propose the the first mapping from the existing variants of Mobile Byzantine models to the Mixed-Mode faults model.This mapping further help us to prove the correctness of class MSR (Mean-Subsequence-Reduce) Approximate Agreement algorithms in the Mobile Byzantine fault model, and is of independent interest. Secondly, we prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine faults models. Interestingly, these lower bounds are different from the static bounds. Finally, we propose matching upper bounds. Our paper is the first to link the Mobile Byzantine Faults models and the Mixed-Mode Faults models, and we advocate that a similar approach can be adopted in order to prove the correctness of other classical distributed building blocks (e.g. agreement, clock synchronization, interactive consistency etc) under Mobile Byzantine Faults model.
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