102 research outputs found

    Semitopology: a new topological model of heterogeneous consensus

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    A distributed system is permissionless when participants can join and leave the network without permission from a central authority. Many modern distributed systems are naturally permissionless, in the sense that a central permissioning authority would defeat their design purpose: this includes blockchains, filesharing protocols, some voting systems, and more. By their permissionless nature, such systems are heterogeneous: participants may only have a partial view of the system, and they may also have different goals and beliefs. Thus, the traditional notion of consensus -- i.e. system-wide agreement -- may not be adequate, and we may need to generalise it. This is a challenge: how should we understand what heterogeneous consensus is; what mathematical framework might this require; and how can we use this to build understanding and mathematical models of robust, effective, and secure permissionless systems in practice? We analyse heterogeneous consensus using semitopology as a framework. This is like topology, but without the restriction that intersections of opens be open. Semitopologies have a rich theory which is related to topology, but with its own distinct character and mathematics. We introduce novel well-behavedness conditions, including an anti-Hausdorff property and a new notion of `topen set', and we show how these structures relate to consensus. We give a restriction of semitopologies to witness semitopologies, which are an algorithmically tractable subclass corresponding to Horn clause theories, having particularly good mathematical properties. We introduce and study several other basic notions that are specific and novel to semitopologies, and study how known quantities in topology, such as dense subsets and closures, display interesting and useful new behaviour in this new semitopological context

    The Impossibility of Approximate Agreement on a Larger Class of Graphs

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    Approximate agreement is a variant of consensus in which processes receive input values from a domain and must output values in that domain that are sufficiently close to one another. We study the problem when the input domain is the vertex set of a connected graph. In asynchronous systems where processes communicate using shared registers, there are wait-free approximate agreement algorithms when the graph is a path or a tree, but not when the graph is a cycle of length at least 4. For many graphs, it is unknown whether a wait-free solution for approximate agreement exists. We introduce a set of impossibility conditions and prove that approximate agreement on graphs satisfying these conditions cannot be solved in a wait-free manner. In particular, the graphs of all triangulated d-dimensional spheres that are not cliques, satisfy these conditions. The vertices and edges of an octahedron is an example of such a graph. We also present a family of reductions from approximate agreement on one graph to another graph. This allows us to extend known impossibility results to even more graphs

    Network Agnostic MPC with Statistical Security

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    We initiate the study of the network agnostic MPC protocols with statistical security. Network agnostic protocols give the best possible security guarantees irrespective of the underlying network type. We consider the general-adversary model, where the adversary is characterized by an adversary structure which enumerates all possible candidate subsets of corrupt parties. The Q(k)\mathcal{Q}^{(k)} condition enforces that the union of no kk subsets from the adversary structure covers the party set. Given an unconditionally-secure PKI setup, known statistically-secure synchronous MPC protocols are secure against adversary structures satisfying the Q(2)\mathcal{Q}^{(2)} condition. Known statistically-secure asynchronous MPC protocols can tolerate Q(3)\mathcal{Q}^{(3)} adversary structures. Fix a set of nn parties P={P1,...,Pn}\mathcal{P} = \{P_1, ... ,P_n\} and adversary structures Zs\mathcal{Z}_s and Za\mathcal{Z}_a, satisfying the Q(2)\mathcal{Q}^{(2)} and Q(3)\mathcal{Q}^{(3)} conditions respectively, where Za⊂Zs\mathcal{Z}_a \subset \mathcal{Z}_s. Then, given an unconditionally-secure PKI, we ask whether it is possible to design a statistically-secure MPC protocol resilient against Zs\mathcal{Z}_s and Za\mathcal{Z}_a in a synchronous and an asynchronous network respectively if the parties in P\mathcal{P} are unaware of the network type. We show that it is possible iff Zs\mathcal{Z}_s and Za\mathcal{Z}_a satisfy the Q(2,1)\mathcal{Q}^{(2,1)} condition, meaning that the union of any two subsets from Zs\mathcal{Z}_s and any one subset from Za\mathcal{Z}_a is a proper subset of P\mathcal{P}. We design several important network agnostic building blocks with the Q(2,1)\mathcal{Q}^{(2,1)} condition, such as Byzantine broadcast, Byzantine agreement, information checking protocol, verifiable secret-sharing and secure multiplication protocol, whose complexity is polynomial in nn and ∣Zs∣|\mathcal{Z}_s|

    Fundamentals

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    Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

    General Tasks and Extension-Based Proofs

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    The concept of extension-based proofs models the idea of a valency argument which is widely used in distributed computing. Extension-based proofs are limited in power: it has been shown that there is no extension-based proof of the impossibility of a wait-free protocol for (n,k)(n,k)-set agreement among n>k≥2n > k \geq 2 processes. A discussion of a restricted type of reduction has shown that there are no extension-based proofs of the impossibility of wait-free protocols for some other distributed computing problems. We extend the previous result to general reductions that allow multiple instances of tasks. The techniques used in the previous work are designed for certain tasks, such as the (n,k)(n,k)-set agreement task. We give a necessary and sufficient condition for general colorless tasks to have no extension-based proofs of the impossibility of wait-free protocols, and show that different types of extension-based proof are equivalent in power for colorless tasks. Using this necessary and sufficient condition, the result about reductions can be understood from a topological perspective

    Communication Pattern Logic: Epistemic and Topological Views

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    We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case wherein all agents inform each other. We study this protocol in distributed computing models where communication might fail: an agent is certain about the messages it receives, but it may be uncertain about the messages other agents have received. In a dynamic epistemic logic with distributed knowledge and with modalities for communication patterns, the latter are interpreted by updating Kripke models. We propose an axiomatization of communication pattern logic, and we show that collective bisimilarity (comparing models on their distributed knowledge) is preserved when updating models with communication patterns. We can also interpret communication patterns by updating simplicial complexes, a well-known topological framework for distributed computing. We show that the different semantics correspond, and propose collective bisimulation between simplicial complexes

    Towards Optimal and Practical Asynchronous Byzantine Fault Tolerant Protocols

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    With recent advancements in blockchain technology, people expect Byzantine fault tolerant (BFT) protocols to be deployed more frequently in wide-area networks (WAN) as opposed to conventional in-house settings. Asynchronous BFT protocols, which do not rely on any form of timing assumption, are arguably robust in such a setting. Asynchronous BFT protocols have been studied since the 1980s, but these asynchronous BFT works mainly focus on understanding the theoretical limits and possibilities. Until the recent asynchronous BFT protocol, HoneyBadgerBFT (HBBFT), was proposed, the field received renewed attention. Dumbo family, a series of our works on the asynchronous BFT protocols, significantly pushed those protocols towards practice. First, all complexity metrics are pushed down to asymptotically optimal, simultaneously. Second, we identify the bottleneck in the state of the art and revisit the design methodology, identifying and utilizing the right components, and optimizing the protocol structure in various ways. Last but not least, we also open the box and optimize the critical components themselves. The resulting protocols are indeed significantly more performant, the latest protocol can have 100K tps and a few seconds of latency at a reasonable scale. This thesis focuses on the latest three members of the Dumbo family. To begin, we solved an open problem by proposing an optimal Multi-valued validated asynchronous Byzantine agreement protocol. Next, we present Dumbo-NG to address the challenge of latency-throughput tension by redesigning the methodology of asynchronous BFT protocols. Another benefit of the new methodology is that it can conquer the censorship threat without extra cost. Furthermore, we consider a realistic environment and present Bolt-Dumbo Transformer (BDT), a generic framework for practical optimistic asynchronous BFT to achieve the "best of both worlds" in terms of the advantages of deterministic BFT and randomized (asynchronous) BFT
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