The emerging parallel chain protocols represent a breakthrough to address the scalability of blockchain. By composing multiple parallel chain instances, the whole systems' throughput can approach the network capacity. How to coordinate different chains' blocks and to construct them into a global ordering is critical to the performance of parallel chain protocol. However, the existed solutions use either the global synchronization clock with the single-chain bottleneck or pre-defined ordering sequences with distortion of blocks' causality to order blocks. In addition, the prior ordering methods rely on that honest participants faithfully follow the ordering protocol, but remain silent for any denial of ordering (DoR) attack. On the other hand, the conflicting transactions included into the global block sequence will make Simple Payment Verification (SPV) difficult. Clients usually need to store a full record of transactions to distinguish the conflictions and tell whether transactions are confirmed. However, the requirement for a full record will greatly hinder blockchains' application, especially for mobile scenarios. In this technical report, we propose Eunomia, which leverages logical clock and fine-grained UTXO sharding to realize a simple, efficient, secure and permissionless parallel chain protocol. By observing the characteristics of the parallel chain, we find the blocks ordering issue in parallel chain has many similarities with the event ordering in the distributed system. Eunomia thus adopts "virtual" logical clock, which is optimized to have the minimum protocol overhead and runs in a distributed way. In addition, Eunomia combines the mining incentive with block ordering, providing incentive compatibility against DoR attack. What's more, the fine-grained UTXO sharding does well solve the conflicting transactions in parallel chain and is shown to be SPV-friendly.
In @cite_39 , Jiaping Wang and Hao Wang propose a protocol called Monoxide, which composes multiple independent single chain consensus systems, called zones. They also proposed eventual atomicity to ensure transaction atomicity across zones and Chu-ko-nu mining to ensure the effective mining power in each zone. Monoxide is shown to provide @math throughput and @math capacity over Bitcoin and Ethereum. Except for this work, there are some committee-based sharding protocols @cite_29 @cite_52 @cite_41 . Each shard is assigned a subset of the nodes, and nodes run the classical byzantine agreement (BA) to reach an agreement. However, these protocols only can tolerant up to @math adversaries. What's more, all sharding-based protocols have additional overhead and latency for cross-shard transactions.
@cite_41 @cite_29 @cite_52 @cite_39
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A major approach to overcoming the performance and scalability limitations of current blockchain protocols is to use sharding which is to split the overheads of processing transactions among multiple, smaller groups of nodes. These groups work in parallel to maximize performance while requiring significantly smaller communication, computation, and storage per node, allowing the system to scale to large networks. However, existing sharding-based blockchain protocols still require a linear amount of communication (in the number of participants) per transaction, and hence, attain only partially the potential benefits of sharding. We show that this introduces a major bottleneck to the throughput and latency of these protocols. Aside from the limited scalability, these protocols achieve weak security guarantees due to either a small fault resiliency (e.g., 1 8 and 1 4) or high failure probability, or they rely on strong assumptions (e.g., trusted setup) that limit their applicability to mainstream payment systems. We propose RapidChain, the first sharding-based public blockchain protocol that is resilient to Byzantine faults from up to a 1 3 fraction of its participants, and achieves complete sharding of the communication, computation, and storage overhead of processing transactions without assuming any trusted setup. RapidChain employs an optimal intra-committee consensus algorithm that can achieve very high throughputs via block pipelining, a novel gossiping protocol for large blocks, and a provably-secure reconfiguration mechanism to ensure robustness. Using an efficient cross-shard transaction verification technique, our protocol avoids gossiping transactions to the entire network. Our empirical evaluations suggest that RapidChain can process (and confirm) more than 7,300 tx sec with an expected confirmation latency of roughly 8.7 seconds in a network of 4,000 nodes with an overwhelming time-to-failure of more than 4,500 years. This paper introduces a new leaderless Byzantine consensus called the Democratic Byzantine Fault Tolerance (DBFT) for blockchains. While most blockchain consensus protocols rely on a correct leader or coordinator to terminate, our algorithm can terminate even when its coordinator is faulty. The key idea is to allow processes to complete asynchronous rounds as soon as they receive a threshold of messages, instead of having to wait for a message from a coordinator that may be slow. The resulting decentralization is particularly appealing for blockchains for two reasons: (i) each node plays a similar role in the execution of the consensus, hence making the decision inherently “democratic” (ii) decentralization avoids bottlenecks by balancing the load, making the solution scalable. DBFT is deterministic, assumes partial synchrony, is resilience optimal, time optimal and does not need signatures. We first present a simple safe binary Byzantine consensus algorithm, modify it to ensure termination, and finally present an optimized reduction from multivalue consensus to binary consensus whose fast path terminates in 4 message delays. We are interested in the design of automated procedures for analyzing the (in)security of cryptographic protocols in the Dolev-Yao model for a bounded number of sessions when we take into account some algebraic properties satisfied by the operators involved in the protocol. This leads to a more realistic model in comparison to what we get under the perfect cryptography assumption, but it implies that protocol analysis deals with terms modulo some equational theory instead of terms in a free algebra. The main goal of this paper is to setup a general approach that works for a whole class of monoidal theories which contains many of the specific cases that have been considered so far in an ad-hoc way (e.g. exclusive or, Abelian groups, exclusive or in combination with the homomorphism axiom). We follow a classical schema for cryptographic protocol analysis which proves first a locality result and then reduces the insecurity problem to a symbolic constraint solving problem. This approach strongly relies on the correspondence between a monoidal theory E and a semiring S"E which we use to deal with the symbolic constraints. We show that the well-defined symbolic constraints that are generated by reasonable protocols can be solved provided that unification in the monoidal theory satisfies some additional properties. The resolution process boils down to solving particular quadratic Diophantine equations that are reduced to linear Diophantine equations, thanks to linear algebra results and the well-definedness of the problem. Examples of theories that do not satisfy our additional properties appear to be undecidable, which suggests that our characterization is reasonably tight. We consider distributed plurality consensus in a complete graph of size @math with @math initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the initially most frequent opinion. In this model, each node is equipped with a random Poisson clock with parameter @math . Whenever a node's clock ticks, it samples some neighbors, uniformly at random and with replacement, and adjusts its opinion according to the sample. A prominent example is the so-called two-choices algorithm in the synchronous model, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient and well-studied when @math . If @math for some small @math , we show that it converges to the initial plurality opinion within @math rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is @math . On the other side, we show that there are cases in which @math rounds are needed, w.h.p. One can beat this lower bound in the synchronous model by combining the two-choices protocol with randomized broadcasting. Our main contribution is a non-trivial adaptation of this approach to the asynchronous model. If the support of the most frequent opinion is at least @math times that of the second-most frequent one and @math , then our protocol achieves the best possible run time of @math , w.h.p. We relax full synchronicity by allowing @math nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this synchronicity by introducing a novel gadget into the protocol.