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A spectre is haunting consensus protocols-the spectre of adversary majority. The literature is inconclusive, with possibilities and impossibilities running abound. Dolev and Strong in 1983 showed an early possibility for up to 99% adversaries. Yet, we have known impossibility results for adversaries above 1/2 in synchrony, and above 1/3 in partial synchrony. What gives? It is high time that we pinpoint the culprit of this confusion: the critical role of the modeling details of clients. Are the clients sleepy or always-on? Are they silent or communicating? Can validators be sleepy too? We systematize models for consensus across four dimensions (sleepy/always-on clients, silent/communicating clients, sleepy/always-on validators, and synchrony/partial-synchrony), some of which are new, and tightly characterize the achievable safety and liveness resiliences with matching possibilities and impossibilities for each of the sixteen models. To this end, we unify folklore and earlier results, and fill gaps left in the literature with new protocols and impossibility theorems.

Proof-of-stake (PoS) blockchains require validators to lock their tokens as collateral, slashing these tokens if they are identified as protocol violators. PoS chains have mostly been secured by their native tokens. However, using only the native token upper-bounds the value eligible for staking by the market capitalization of the native token. In contrast, the remote staking of another crypto asset from a provider chain provides an avenue to improve the consumer chain's economic security. In this paper, we present the first known remote staking protocols with guaranteed optimal economic safety: whenever there is a safety violation on the consumer chain, at least one third of the provider's stake securing the consumer chain is slashed. To achieve this goal for a broad range of provider and consumer chains, two independent contributions are made: 1) a cryptographic protocol to slash stake even without smart contracts on the provider chain; 2) a secure unbonding protocol that ensures slashing before the stake is unbonded on the provider chain if there is safety violation on the consumer chain. A major use case of this work is when the provider chain is Bitcoin, making available an asset worth more than 1.7 trillion USD to secure PoS chains. Such a Bitcoin staking protocol has been launched on the Mainnet in August 2024 and has accumulated 2.1 billion USD worth of stake thus far.

Validators in permissionless, large-scale blockchains (e.g., Ethereum) are typically payoff-maximizing, rational actors. Ethereum relies on in-protocol incentives, like rewards for validators delivering correct and timely votes, to induce honest behavior and secure the blockchain. However, external incentives, such as the block proposer's opportunity to capture maximal extractable value (MEV), may tempt validators to deviate from honest protocol participation. We show a series of commitment attacks on LMD GHOST, a core part of Ethereum's consensus mechanism. We demonstrate how a single adversarial block proposer can orchestrate long-range chain reorganizations by manipulating Ethereum's reward system for timely votes. These attacks disrupt the intended balance of power between proposers and voters: by leveraging credible threats, the adversarial proposer can coerce voters from previous slots into supporting blocks that conflict with the honest chain, enabling a chain reorganization at no cost to the adversary. In response, we introduce a novel reward mechanism that restores the voters' role as a check against proposer power. Our proposed mitigation is fairer and more decentralized -- not only in the context of these attacks -- but also practical for implementation in Ethereum.

Since the creation of Bitcoin 15 years ago, there has been an explosion in the number of permissionless blockchains. Each of these blockchains provides an open ledger that anyone can read from and write to. In this multi-chain world, an important question emerges: how can we build a more secure overlay blockchain by reading from and writing to a given set of blockchains? Drawing an analogy with switching circuits, we approach the problem by defining two basic compositional operations between blockchains, serial and triangular compositions, and use these operations as building blocks to construct general overlay blockchains. Under the partially synchronous setting, we have the following results: 1) the serial composition, between two blockchains, yields an overlay blockchain that is safe if at least one of the two underlay blockchains is safe and that is live if both of them are live; 2) the triangular composition between three blockchains, akin to parallel composition of switching circuits, yields an overlay blockchain that is safe if all underlay blockchains are safe and that is live if over half of them are live; 3) repeated composition of these two basic operations can yield all possible tradeoffs of safety and liveness for an overlay blockchain built on arbitrary number of underlay chains. The results are also extended to the synchronous setting., Comment: In Advances in Financial Technologies (AFT 2024)

Motivated by proof-of-stake (PoS) blockchains such as Ethereum, two key desiderata have recently been studied for Byzantine-fault tolerant (BFT) state-machine replication (SMR) consensus protocols: Finality means that the protocol retains consistency, as long as less than a certain fraction of validators are malicious, even in partially-synchronous environments that allow for temporary violations of assumed network delay bounds. Accountable safety means that in any case of inconsistency, a certain fraction of validators can be identified to have provably violated the protocol. Earlier works have developed impossibility results and protocol constructions for these properties separately. We show that accountable safety implies finality, thereby unifying earlier results., Comment: Financial Cryptography and Data Security 2024

Dynamic vector commitments that enable local updates of opening proofs have applications ranging from verifiable databases with membership changes to stateless clients on blockchains. In these applications, each user maintains a relevant subset of the committed messages and the corresponding opening proofs with the goal of ensuring a succinct global state. When the messages are updated, users are given some global update information and update their opening proofs to match the new vector commitment. We investigate the relation between the size of the update information and the runtime complexity needed to update an individual opening proof. Existing vector commitment schemes require that either the information size or the runtime scale linearly in the number $k$ of updated state elements. We construct a vector commitment scheme that asymptotically achieves both length and runtime that is sublinear in $k$, namely $k^\nu$ and $k^{1-\nu}$ for any $\nu \in (0,1)$. We prove an information-theoretic lower bound on the relation between the update information size and runtime complexity that shows the asymptotic optimality of our scheme. For $\nu = 1/2$, our constructions outperform Verkle commitments by about a factor of $2$ in terms of both the update information size and runtime, but makes use of larger public parameters., Comment: In Advances in Financial Technologies - AFT 2023

Fourteen years after the invention of Bitcoin, there has been a proliferation of many permissionless blockchains. Each such chain provides a public ledger that can be written to and read from by anyone. In this multi-chain world, a natural question arises: what is the optimal security an existing blockchain, a consumer chain, can extract by only reading and writing to k other existing blockchains, the provider chains? We design a protocol, called interchain timestamping, and show that it extracts the maximum economic security from the provider chains, as quantified by the slashable safety resilience. We observe that interchain timestamps are already provided by light-client based bridges, so interchain timestamping can be readily implemented for Cosmos chains connected by the Inter-Blockchain Communication (IBC) protocol. We compare interchain timestamping with cross-staking, the original solution to mesh security, as well as with Trustboost, another recent security sharing protocol., Comment: Forthcoming in ACM Conference on Computer and Communications Security (CCS) 2023

Accountability, the ability to provably identify protocol violators, gained prominence as the main economic argument for the security of proof-of-stake (PoS) protocols. Rollups, the most popular scaling solution for blockchains, typically use PoS protocols as their parent chain. We define accountability for rollups, and present an attack that shows the absence of accountability on existing designs. We provide an accountable rollup design and prove its security, both for the traditional `enshrined' rollups and for sovereign rollups, an emergent alternative built on lazy blockchains, tasked only with ordering and availability of the rollup data., Comment: 28 pages, 4 figures

Popular Ethereum wallets (like MetaMask) entrust centralized infrastructure providers (e.g., Infura) to run the consensus client logic on their behalf. As a result, these wallets are light-weight and high-performant, but come with security risks. A malicious provider can mislead the wallet by faking payments and balances, or censoring transactions. On the other hand, light clients, which are not in popular use today, allow decentralization, but are concretely inefficient, often with asymptotically linear bootstrapping complexity. This poses a dilemma between decentralization and performance. We design, implement, and evaluate a new proof-of-stake (PoS) superlight client with concretely efficient and asymptotically logarithmic bootstrapping complexity. Our proofs of proof-of-stake (PoPoS) take the form of a Merkle tree of PoS epochs. The verifier enrolls the provers in a bisection game, in which honest provers are destined to win once an adversarial Merkle tree is challenged at sufficient depth. We provide an implementation for mainnet Ethereum: compared to the state-of-the-art light client construction of Ethereum, our client improves time-to-completion by 9x, communication by 180x, and energy usage by 30x (when bootstrapping after 10 years of consensus execution). As an important additional application, our construction can be used to realize trustless cross-chain bridges, in which the superlight client runs within a smart contract and takes the role of an on-chain verifier. We prove our construction is secure and show how to employ it for other PoS systems such as Cardano (with fully adaptive adversary), Algorand, and Snow White.

The LMD GHOST consensus protocol is a critical component of proof-of-stake Ethereum. In its current form, this protocol is brittle, as evidenced by recent attacks and patching attempts. We propose Goldfish, a new protocol that satisfies key properties required of a drop-in replacement for LMD GHOST: Goldfish is secure in the sleepy model, assuming a majority of the validators follows the protocol. Goldfish is reorg resilient so that honestly produced blocks are guaranteed inclusion in the ledger, and it supports fast confirmation with expected confirmation latency independent of the desired security level. Subsampling validators can improve the communication efficiency of Goldfish, and Goldfish is composable with finality/accountability gadgets. Crucially, Goldfish is structurally similar to LMD GHOST, providing a credible path to adoption in Ethereum. Attacks on LMD GHOST exploit lack of coordination among honest validators, typically provided by a locking mechanism in classical BFT protocols. However, locking requires votes from a quorum of all participants and is not compatible with fluctuating participation. Goldfish is powered by a novel coordination mechanism to synchronize the honest validators' actions. Experiments with our prototype implementation of Goldfish suggest practicality., Comment: Financial Cryptography and Data Security 2024

Layer 2 systems have received increasing attention due to their potential to scale the throughput of L1 blockchains. To avoid the cost of putting data on chain, these systems increasingly turn to off-chain data availability solutions such as data availability committees (DACs). However, placing trust on DACs conflicts with the goal of obtaining an L2 architecture whose security relies solely on the L1 chain. To eliminate such trust assumptions, we propose a DAC protocol that provides financial incentives to deter the DAC nodes from adversarial behavior such as withholding data upon request. We then analyze the interaction of rational DAC nodes and clients as a dynamic game, with a Byzantine adversary that can corrupt and bribe the participants. We also define a notion of optimality for the DAC protocols, inspired by fairness and economic feasibility. Our main result shows that our protocol is optimal and guarantees security with the highest possible probability under reasonable assumptions on the adversary., Comment: In Financial Cryptography and Data Security 2023

Bitcoin is the most secure blockchain in the world, supported by the immense hash power of its Proof-of-Work miners. Proof-of-Stake chains are energy-efficient, have fast finality but face several security issues: susceptibility to non-slashable long-range safety attacks, low liveness resilience and difficulty to bootstrap from low token valuation. We show that these security issues are inherent in any PoS chain without an external trusted source, and propose a new protocol, Babylon, where an off-the-shelf PoS protocol checkpoints onto Bitcoin to resolve these issues. An impossibility result justifies the optimality of Babylon. A use case of Babylon is to reduce the stake withdrawal delay: our experimental results show that this delay can be reduced from weeks in existing PoS chains to less than 5 hours using Babylon, at a transaction cost of less than 10K USD per annum for posting the checkpoints onto Bitcoin., Comment: Forthcoming in IEEE Symposium on Security and Privacy 2023

Lazy blockchains decouple consensus from transaction verification and execution to increase throughput. Although they can contain invalid transactions (e.g., double spends) as a result, these can easily be filtered out by full nodes that check if there have been previous conflicting transactions. However, creating light (SPV) clients that do not see the whole transaction history becomes a challenge: A record of a transaction on the chain does not necessarily entail transaction confirmation. In this paper, we devise a protocol that enables the creation of efficient light clients for lazy blockchains. The number of interaction rounds and the communication complexity of our protocol are logarithmic in the blockchain execution time. Our construction is based on a bisection game that traverses the Merkle tree containing the ledger of all - valid or invalid - transactions. We prove that our proof system is succinct, complete and sound, and empirically demonstrate the feasibility of our scheme., Comment: Financial Cryptography and Data Security 2024 (FC24)

We present two attacks targeting the Proof-of-Stake (PoS) Ethereum consensus protocol. The first attack suggests a fundamental conceptual incompatibility between PoS and the Greedy Heaviest-Observed Sub-Tree (GHOST) fork choice paradigm employed by PoS Ethereum. In a nutshell, PoS allows an adversary with a vanishing amount of stake to produce an unlimited number of equivocating blocks. While most equivocating blocks will be orphaned, such orphaned `uncle blocks' still influence fork choice under the GHOST paradigm, bestowing upon the adversary devastating control over the canonical chain. While the Latest Message Driven (LMD) aspect of current PoS Ethereum prevents a straightforward application of this attack, our second attack shows how LMD specifically can be exploited to obtain a new variant of the balancing attack that overcomes a recent protocol addition that was intended to mitigate balancing-type attacks. Thus, in its current form, PoS Ethereum without and with LMD is vulnerable to our first and second attack, respectively.

Bitcoin is the most secure blockchain in the world, supported by the immense hash power of its Proof-of-Work miners, but consumes huge amount of energy. Proof-of-Stake chains are energy-efficient, have fast finality and accountability, but face several fundamental security issues: susceptibility to non-slashable long-range safety attacks, non-slashable transaction censorship and stalling attacks and difficulty to bootstrap new PoS chains from low token valuation. We propose Babylon, a blockchain platform which combines the best of both worlds by reusing the immense Bitcoin hash power to enhance the security of PoS chains. Babylon provides a data-available timestamping service, securing PoS chains by allowing them to timestamp data-available block checkpoints, fraud proofs and censored transactions on Babylon. Babylon miners merge mine with Bitcoin and thus the platform has zero additional energy cost. The security of a Babylon-enhanced PoS protocol is formalized by a cryptoeconomic security theorem which shows slashable safety and liveness guarantees., Comment: 26 pages, 10 figures

Recently, two attacks were presented against Proof-of-Stake (PoS) Ethereum: one where short-range reorganizations of the underlying consensus chain are used to increase individual validators' profits and delay consensus decisions, and one where adversarial network delay is leveraged to stall consensus decisions indefinitely. We provide refined variants of these attacks, considerably relaxing the requirements on adversarial stake and network timing, and thus rendering the attacks more severe. Combining techniques from both refined attacks, we obtain a third attack which allows an adversary with vanishingly small fraction of stake and no control over network message propagation (assuming instead probabilistic message propagation) to cause even long-range consensus chain reorganizations. Honest-but-rational or ideologically motivated validators could use this attack to increase their profits or stall the protocol, threatening incentive alignment and security of PoS Ethereum. The attack can also lead to destabilization of consensus from congestion in vote processing.

For applications of Byzantine fault tolerant (BFT) consensus protocols where the participants are economic agents, recent works highlighted the importance of accountability: the ability to identify participants who provably violate the protocol. At the same time, being able to reach consensus under dynamic levels of participation is desirable for censorship resistance. We identify an availability-accountability dilemma: in an environment with dynamic participation, no protocol can simultaneously be accountably-safe and live. We provide a resolution to this dilemma by constructing a provably secure optimally-resilient accountability gadget to checkpoint a longest chain protocol, such that the full ledger is live under dynamic participation and the checkpointed prefix ledger is accountable. Our accountability gadget construction is black-box and can use any BFT protocol which is accountable under static participation. Using HotStuff as the black box, we implemented our construction as a protocol for the Ethereum 2.0 beacon chain, and our Internet-scale experiments with more than 4000 nodes show that the protocol achieves the required scalability and has better latency than the current solution Gasper, which was shown insecure by recent attacks.

The availability-finality dilemma says that blockchain protocols cannot be both available under dynamic participation and safe under network partition. Snap-and-chat protocols have recently been proposed as a resolution to this dilemma. A snap-and-chat protocol produces an always available ledger containing a finalized prefix ledger which is always safe and catches up with the available ledger whenever network conditions permit. In contrast to existing handcrafted finality gadget based designs like Ethereum 2.0's consensus protocol Gasper, snap-and-chat protocols are constructed as a black-box composition of off-the-shelf BFT and longest chain protocols. In this paper, we consider system aspects of snap-and-chat protocols and show how they can provide two important features: 1) accountability, 2) support of light clients. Through this investigation, a deeper understanding of the strengths and challenges of snap-and-chat protocols is gained.

The CAP theorem says that no blockchain can be live under dynamic participation and safe under temporary network partitions. To resolve this availability-finality dilemma, we formulate a new class of flexible consensus protocols, ebb-and-flow protocols, which support a full dynamically available ledger in conjunction with a finalized prefix ledger. The finalized ledger falls behind the full ledger when the network partitions but catches up when the network heals. Gasper, the current candidate protocol for Ethereum 2.0's beacon chain, combines the finality gadget Casper FFG with the LMD GHOST fork choice rule and aims to achieve this property. However, we discovered an attack in the standard synchronous network model, highlighting a general difficulty with existing finality-gadget-based designs. We present a construction of provably secure ebb-and-flow protocols with optimal resilience. Nodes run an off-the-shelf dynamically available protocol, take snapshots of the growing available ledger, and input them into a separate off-the-shelf BFT protocol to finalize a prefix. We explore connections with flexible BFT and improve upon the state-of-the-art for that problem., Comment: Forthcoming in IEEE Symposium on Security and Privacy 2021

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 function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes., Comment: 27 pages, 12 figures. A shorter version of this paper will appear in the 2020 ACM Conference on Computer and Communications Security (CCS)