Close Latency--Security Trade-off for the Nakamoto Consensus
Jing Li, Ling Ren, Dongning Guo
备注：
This work will be presented at the ACM Conference on Advances in Financial Technologies. This is the authors' version of the work with additional details in the appendix
Bitcoin is a peer-to-peer electronic cash system invented by Nakamoto in 2008. While it has attracted much research interest, its exact latency and security properties remain open. Existing analyses provide security and latency (or confirmation time) guarantees that are too loose for practical use. In fact the best known upper bounds are several orders of magnitude larger than a lower bound due to a well-known private-mining attack. This paper describes a continuous-time model for blockchains and develops a rigorous analysis that yields close upper and lower bounds for the latency--security trade-off. For example, when the adversary controls 10\% of the total mining power and the block propagation delays are within 10 seconds, a Bitcoin block is secured with less than $10^{-3}$ error probability if it is confirmed after four hours, or with less than $10^{-9}$ error probability if confirmed after ten hours. These confirmation times are about two hours away from their corresponding lower bounds. To establish such close bounds, the blockchain security question is reduced to a race between the Poisson adversarial mining process and a renewal process formed by a certain species of honest blocks. The moment generation functions of relevant renewal times are derived in closed form. The general formulas from the analysis are then applied to study the latency--security trade-off of several well-known proof-of-work longest-chain cryptocurrencies. Guidance is also provided on how to set parameters for different purposes.
In the Bitcoin white paper, Nakamoto proposed a very simple Byzantine fault tolerant consensus algorithm that is also known as Nakamoto consensus. Despite its simplicity, some existing analysis of Nakamoto consensus appears to be long and involved. In this technical report, we aim to make such analysis simple and transparent so that we can teach senior undergraduate students and graduate students in our institutions. This report is largely based on a 3-hour tutorial given by one of the authors in June 2019.
Initiated from Nakamoto's Bitcoin system, blockchain technology has demonstrated great capability of building secure consensus among decentralized parties at Internet-scale, i.e., without relying on any centralized trusted party. Nowadays, blockchain systems find applications in various fields. But the performance is increasingly becoming a bottleneck, especially when permissionless participation is retained for full decentralization. In this work, we present a new consensus protocol named GHAST (Greedy Heaviest Adaptive Sub-Tree) which organizes blocks in a Tree-Graph structure (i.e., a direc…
Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a fu…
Blockchains based on the celebrated Nakamoto consensus protocol have shown promise in several applications, including cryptocurrencies. However, these blockchains have inherent scalability limits caused by the protocol's consensus properties. In particular, the \emph{consistency} property demonstrates a tight trade-off between block production speed and the system's security in terms of resisting adversarial attacks. This paper proposes a novel method, Ironclad, that improves blockchain consistency bound by assigning a different weight to randomly selected blocks. We apply our method to the or…
A fundamental conflict of many proof-of-work systems is that they want to achieve inclusiveness and security at the same time. We analyze and resolve this conflict with a theory of proof-of-work quorums, which enables a new bridge between Byzantine and Nakamoto consensus. The theory yields stochastic uniqueness of quorums as a function of a security parameter. We employ the theory in HotPoW, a scalable permissionless distributed log protocol that supports finality based on the pipelined three-phase commit previously presented for HotStuff. We evaluate HotPoW and variants with adversarial modif…
Nakamoto consensus, the protocol underlying Bitcoin, has the potential to secure a new class of systems which agree on non-mathematical truths. As an example of this capability, we propose a design for a trustless, data availability oracle. This exposition reduces the problem of determining whether or not a registered datum is publicly available to the problem of constructing a network in which either almost all nodes can download a given datum, or almost none of them can.
Byzantine fault tolerant (BFT) state machine replication (SMR) is an important building block for constructing permissioned blockchain systems. In contrast to Nakamoto Consensus where any block obtains higher assurance as buried deeper in the blockchain, in BFT SMR, any committed block is secure has a fixed resilience threshold. In this paper, we investigate strengthened fault tolerance (SFT) in BFT SMR under partial synchrony, which provides gradually increased resilience guarantees (like Nakamoto Consensus) during an optimistic period when the network is synchronous and the number of Byzanti…
The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and with the explanation for the stability of in terms of the existence of consensus equilibria related to mining gap game's behaviors by using one new concept called consensus games in Blockchain Ecosystems, here, the Blockchain ecosystem mainly means the economic activities by taking into the account of three types of different factors which are expenses, reward mechanism and mining power for the work on blockschain by applying the key consensus called Proof of…
Simple closed-form upper and lower bounds are developed for the security of the Nakamoto consensus as a function of the confirmation depth, the honest and adversarial block mining rates, and an upper bound on the block propagation delay. The bounds are exponential in the confirmation depth and apply regardless of the adversary's attack strategy. The gap between the upper and lower bounds is small for Bitcoin's parameters. For example, assuming an average block interval of 10 minutes, a network delay bound of ten seconds, and 10% adversarial mining power, the widely used 6-block confirmation ru…
Bitcoin is a peer-to-peer payment system proposed by Nakamoto in 2008. Based on the Nakamoto consensus, Bagaria, Kannan, Tse, Fanti, and Viswanath proposed the Prism protocol in 2018 and showed that it achieves near-optimal blockchain throughput while maintaining a similar level of security as bitcoin. Previous probabilistic security guarantees for the bitcoin and Prism backbone protocols were either established under a simplified discrete-time model or expressed in terms of exponential order results. This paper presents a streamlined and strengthened analysis under a more realistic continuous…
Since the inception of Bitcoin, cryptocurrencies and the underlying blockchain technology have attracted an increasing interest from both academia and industry. Among various core components, consensus protocol is the defining technology behind the security and performance of blockchain. From incremental modifications of Nakamoto consensus protocol to innovative alternative consensus mechanisms, many consensus protocols have been proposed to improve the performance of the blockchain network itself or to accommodate other specific application needs. In this survey, we present a comprehensive re…
Designing distributed, fast and reliable wireless consensus protocols is instrumental in enabling mission-critical decentralized systems, such as robotic networks in the industrial Internet of Things (IIoT), drone swarms in rescue missions, and so forth. However, chasing both low-latency and reliability of consensus protocols is a challenging task. The problem is aggravated under wireless connectivity that may be slower and less reliable, compared to wired connections. To tackle this issue, we investigate fundamental relationships between consensus latency and reliability through the lens of w…
We propose separating the task of reliable transaction dissemination from transaction ordering, to enable high-performance Byzantine fault-tolerant quorum-based consensus. We design and evaluate a mempool protocol, Narwhal, specializing in high-throughput reliable dissemination and storage of causal histories of transactions. Narwhal tolerates an asynchronous network and maintains high performance despite failures. Narwhal is designed to easily scale-out using multiple workers at each validator, and we demonstrate that there is no foreseeable limit to the throughput we can achieve. Composing N…
Blockmania is a byzantine consensus protocol. Nodes emit blocks forming a directed acyclic graph (block DAG) that is subsequently interpreted by each node separately to ensure consensus with safety, liveness and finality. The resulting system has communication complexity $O(N^2)$ even in the worse case, and very low constant factors --- as compared to $O(N^4)$ for PBFT; it is leaderless; and network operations do not depend on the composition of the quorum or node stake. This makes Blockmania very efficient (leading to over 400K transactions per second on a wide area network), and ideal for dy…
This paper proposes Consensus-Before-Talk (CBT), a spectrum etiquette architecture leveraged by distributed ledger technology (DLT). In CBT, secondary users' spectrum access requests reach a consensus in a distributed way, thereby enabling collision-free distributed dynamic spectrum access. To achieve this consensus, the secondary users need to pay for the extra request exchanging delays. Incorporating the consensus delay, the end-to-end latency under CBT is investigated. Both the latency analysis and numerical evaluation validate that the proposed CBT achieves the lower end-to-end latency par…
Byzantine fault-tolerant (BFT) state machine replication (SMR) has been studied for over 30 years. Recently it has received more attention due to its application in permissioned blockchain systems. A sequence of research efforts focuses on improving the commit latency of the SMR protocol in the common good case, including PBFT with $3$-round latency and $n\geq 3f+1$ and FaB with $2$-round latency and $n\geq 5f+1$. In this paper, we propose an authenticated protocol that solves $2$-round BFT SMR with only $n\geq 5f-1$ replicas, which refutes the optimal resiliency claim made in FaB for needing …
While showing great promise, Bitcoin requires users to wait tens of minutes for transactions to commit, and even then, offering only probabilistic guarantees. This paper introduces ByzCoin, a novel Byzantine consensus protocol that leverages scalable collective signing to commit Bitcoin transactions irreversibly within seconds. ByzCoin achieves Byzantine consensus while preserving Bitcoin's open membership by dynamically forming hash power-proportionate consensus groups that represent recently-successful block miners. ByzCoin employs communication trees to optimize transaction commitment and v…
This thesis proposes techniques aiming to make blockchain technologies and smart contract platforms practical by improving their scalability, latency, and privacy. This thesis starts by presenting the design and implementation of Chainspace, a distributed ledger that supports user defined smart contracts and execute user-supplied transactions on their objects. The correct execution of smart contract transactions is publicly verifiable. Chainspace is scalable by sharding state; it is secure against subsets of nodes trying to compromise its integrity or availability properties through Byzantine …
Bitcoin is the first fully-decentralized permissionless blockchain protocol to achieve a high level of security, but at the expense of poor throughput and latency. Scaling the performance of Bitcoin has a been a major recent direction of research. One successful direction of work has involved replacing proof of work (PoW) by proof of stake (PoS). Proposals to scale the performance in the PoW setting itself have focused mostly on parallelizing the mining process, scaling throughput; the few proposals to improve latency have either sacrificed throughput or the latency guarantees involve large co…
Sei Labs（Sei实验室）；University of California, Berkeley（加州大学伯克利分校）；University of California, Davis（加州大学戴维斯分校）；UC Santa Barbara（加州大学圣塔芭芭拉分校）；University of Portsmouth（朴茨茅斯大学）
In the paper, we present designs for multiple blockchain consensus primitives and a novel blockchain system, all based on the use of trusted execution environments (TEEs), such as Intel SGX-enabled CPUs. First, we show how using TEEs for existing proof of work schemes can make mining equitably distributed by preventing the use of ASICs. Next, we extend the design with proof of time and proof of ownership consensus primitives to make mining energy- and time-efficient. Further improving on these designs, we present a blockchain using a proof of luck consensus protocol. Our proof of luck blockcha…
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