Consistency of Proof-of-Stake Blockchains with Concurrent Honest Slot Leaders

We improve the fundamental security threshold of eventual consensus Proof-of-Stake (PoS) blockchain protocols under the longest-chain rule by showing, for the first time, the positive effect of rounds with concurrent honest leaders. Current security analyses reduce consistency to the dynamics of an abstract, round-based block creation process that is determined by three events associated with a round: (i) event $A$: at least one adversarial leader, (ii) event $S$: a single honest leader, and (iii) event $M$: multiple, but honest, leaders. We present an asymptotically optimal consistency analysis assuming that an honest round is more likely than an adversarial round (i.e., $\Pr[S] + \Pr[M] > \Pr[A]$); this threshold is optimal. This is a first in the literature and can be applied to both the simple synchronous communication as well as communication with bounded delays. In all existing consistency analyses, event $M$ is either penalized or treated neutrally. Specifically, the consistency analyses in Ouroboros Praos (Eurocrypt 2018) and Genesis (CCS 2018) assume that $\Pr[S] - \Pr[M] > \Pr[A]$; the analyses in Sleepy Consensus (Asiacrypt 2017) and Snow White (Fin. Crypto 2019) assume that $\Pr[S] > \Pr[A]$. Moreover, all existing analyses completely break down when $\Pr[S] < \Pr[A]$. These thresholds determine the critical trade-off between the honest majority, network delays, and consistency error. Our new results can be directly applied to improve the security guarantees of the existing protocols. We also provide an efficient algorithm to explicitly calculate these error probabilities in the synchronous setting. Furthermore, we complement these results by analyzing the setting where $S$ is rare, even allowing $\Pr[S] = 0$, under the added assumption that honest players adopt a consistent chain selection rule.Comment: Includes new sections describing (1) an adaptive online adversary and (2) an efficient algorithm to compute consistency error probabilities. arXiv admin note: text overlap with arXiv:1911.1018

Modeling Resources in Permissionless Longest-chain Total-order Broadcast

Blockchain protocols implement total-order broadcast in a permissionless setting, where processes can freely join and leave. In such a setting, to safeguard against Sybil attacks, correct processes rely on cryptographic proofs tied to a particular type of resource to make them eligible to order transactions. For example, in the case of Proof-of-Work (PoW), this resource is computation, and the proof is a solution to a computationally hard puzzle. Conversely, in Proof-of-Stake (PoS), the resource corresponds to the number of coins that every process in the system owns, and a secure lottery selects a process for participation proportionally to its coin holdings. Although many resource-based blockchain protocols are formally proven secure in the literature, the existing security proofs fail to demonstrate why particular types of resources cause the blockchain protocols to be vulnerable to distinct classes of attacks. For instance, PoS systems are more vulnerable to long-range attacks, where an adversary corrupts past processes to re-write the history, than Proof-of-Work and Proof-of-Storage systems. Proof-of-Storage-based and Proof-of-Stake-based protocols are both more susceptible to private double-spending attacks than Proof-of-Work-based protocols; in this case, an adversary mines its chain in secret without sharing its blocks with the rest of the processes until the end of the attack. In this paper, we formally characterize the properties of resources through an abstraction called resource allocator and give a framework for understanding longest-chain consensus protocols based on different underlying resources. In addition, we use this resource allocator to demonstrate security trade-offs between various resources focusing on well-known attacks (e.g., the long-range attack and nothing-at-stake attacks)

Modeling Resources in Permissionless Longest-Chain Total-Order Broadcast

Blockchain protocols implement total-order broadcast in a permissionless setting, where processes can freely join and leave. In such a setting, to safeguard against Sybil attacks, correct processes rely on cryptographic proofs tied to a particular type of resource to make them eligible to order transactions. For example, in the case of Proof-of-Work (PoW), this resource is computation, and the proof is a solution to a computationally hard puzzle. Conversely, in Proof-of-Stake (PoS), the resource corresponds to the number of coins that every process in the system owns, and a secure lottery selects a process for participation proportionally to its coin holdings. Although many resource-based blockchain protocols are formally proven secure in the literature, the existing security proofs fail to demonstrate why particular types of resources cause the blockchain protocols to be vulnerable to distinct classes of attacks. For instance, PoS systems are more vulnerable to long-range attacks, where an adversary corrupts past processes to re-write the history, than PoW and Proof-of-Storage systems. Proof-of-Storage-based and PoS-based protocols are both more susceptible to private double-spending attacks than PoW-based protocols; in this case, an adversary mines its chain in secret without sharing its blocks with the rest of the processes until the end of the attack. In this paper, we formally characterize the properties of resources through an abstraction called resource allocator and give a framework for understanding longest-chain consensus protocols based on different underlying resources. In addition, we use this resource allocator to demonstrate security trade-offs between various resources focusing on well-known attacks (e.g., the long-range attack and nothing-at-stake attacks)

SoK: Diving into DAG-based Blockchain Systems

Blockchain plays an important role in cryptocurrency markets and technology services. However, limitations on high latency and low scalability retard their adoptions and applications in classic designs. Reconstructed blockchain systems have been proposed to avoid the consumption of competitive transactions caused by linear sequenced blocks. These systems, instead, structure transactions/blocks in the form of Directed Acyclic Graph (DAG) and consequently re-build upper layer components including consensus, incentives, \textit{etc.} The promise of DAG-based blockchain systems is to enable fast confirmation (complete transactions within million seconds) and high scalability (attach transactions in parallel) without significantly compromising security. However, this field still lacks systematic work that summarises the DAG technique. To bridge the gap, this Systematization of Knowledge (SoK) provides a comprehensive analysis of DAG-based blockchain systems. Through deconstructing open-sourced systems and reviewing academic researches, we conclude the main components and featured properties of systems, and provide the approach to establish a DAG. With this in hand, we analyze the security and performance of several leading systems, followed by discussions and comparisons with concurrent (scaling blockchain) techniques. We further identify open challenges to highlight the potentiality of DAG-based solutions and indicate their promising directions for future research.Comment: Full versio