Security analyses for consensus protocols in blockchain research have primarily focused on the synchronous model, where point-to-point communication delays are upper bounded by a known finite constant. These models are unrealistic in noisy settings, where messages may be lost (i.e. incur infinite delay). In this work, we study the impact of message losses on the security of the proof-of-work longest-chain protocol. We introduce a new communication model to capture the impact of message loss called the 0-∞ model, and derive a region of tolerable adversarial power under which the consensus protocol is secure. The guarantees are derived as a simple bound for the probability that a transaction violates desired security properties. Specifically, we show that this violation probability decays almost exponentially in the security parameter. Our approach involves constructing combinatorial objects from blocktrees, and identifying random variables associated with them that are amenable to analysis. This approach improves existing bounds and extends the known regime for tolerable adversarial threshold in settings where messages may be lost.
more »
« less
Practical Settlement Bounds for Longest-Chain Consensus
Nakamoto’s longest-chain consensus paradigm now powers the bulk of the world’s cryptocurrencies and distributed finance infrastructure. An emblematic property of longest-chain consensus is that it provides probabilistic settlement guarantees that strengthen over time. This makes the exact relationship between settlement error and settlement latency a critical aspect of the protocol that both users and system designers must understand to make informed decisions. A recent line of work has finally provided a satisfactory rigorous accounting of this relationship for proof-of-work longest-chain protocols, but those techniques do not appear to carry over to the proof-of-stake setting.
This article develops a new analytic approach for establishing such settlement guarantees that yields explicit, rigorous settlement bounds for proof-of-stake longest-chain protocols, placing them on equal footing with their proof-of-work counterparts. Our techniques apply with some adaptations to the proof-of-work setting where they provide improvements to the state-of-the-art settlement bounds for proof-of-work protocols.
more »
« less
- Award ID(s):
- 2143058
- PAR ID:
- 10494782
- Publisher / Repository:
- Springer
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Nakamoto proof-of-work ledger consensus currently underlies the majority of deployed cryptocurrencies and smart-contract blockchains. While a long and fruitful line of work has succeeded to identify its exact security region---that is, the set of parametrizations under which it possesses asymptotic security---the existing theory does not provide concrete settlement time guarantees that are tight enough to inform practice. In this work we provide a new approach for obtaining concrete and practical settlement time guarantees suitable for reasoning about deployed systems. We give an efficient method for computing explicit upper bounds on settlement time as a function of primary system parameters: honest and adversarial computational power and a bound on network delays. We implement this computational method and provide a comprehensive sample of concrete bounds for several settings of interest. We also analyze a well-known attack strategy to provide lower bounds on the settlement times. For Bitcoin, for example, our upper and lower bounds are within 90 seconds of each other for 1-hour settlement assuming 10 second network delays and a 10% adversary. In comparison, the best prior result has a gap of 2 hours in the upper and lower bounds with the same parameters.more » « less
-
Blockchain technology that came with the introduction of Bitcoin offers many powerful use-cases while promising the establishment of distributed autonomous organizations (DAOs) that may transform our current understanding of client-server interactions on the cyberspace. They employ distributed consensus mechanisms that were subject to a lot of research in recent years. While most of such research focused on security and performance of consensus protocols, less attention was given to their incentive mechanisms which relate to a critical feature of blockchains. Unfortunately, while blockchains are advocating decentralized operations, they are not egalitarian due to existing incentive mechanisms. Many current consensus protocols inadvertently incentivize centralization of mining power and inequitable participation. This paper explores and evaluates alternative incentive mechanisms for a more decentralized and equitable participation. We first evaluate inequality in existing Proof of Stake (PoS) based incentive mechanisms, then we examine three alternatives in which rewards scheme is more partial to low-stakeholders. Through simulation, we show that two of our alternative mechanisms can reduce inequality and offer an attractive solution for sustainability of blockchain-based applications and DAOs.more » « less
-
A proof of work (PoW) is an important cryptographic construct enabling a party to convince others that they invested some effort in solving a computational task. Arguably, its main impact has been in the setting of cryptocurrencies such as Bitcoin and its underlying blockchain protocol, which received significant attention in recent years due to its potential for various applications as well as for solving fundamental distributed computing questions in novel threat models. PoWs enable the linking of blocks in the blockchain data structure and thus the problem of interest is the feasibility of obtaining a sequence (chain) of such proofs. In this work, we examine the hardness of finding such chain of PoWs against quantum strategies. We prove that the chain of PoWs problem reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. Effectively, this is an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the recording technique of Zhandry (Crypto'19). As an application, we revisit the formal treatment of security of the core of the Bitcoin consensus protocol, the Bitcoin backbone (Eurocrypt'15), against quantum adversaries, while honest parties are classical and show that protocol's security holds under a quantum analogue of the classical “honest majority'' assumption. Our analysis indicates that the security of Bitcoin backbone is guaranteed provided the number of adversarial quantum queries is bounded so that each quantum query is worth O ( p − 1 / 2 ) classical ones, where p is the success probability of a single classical query to the protocol's underlying hash function. Somewhat surprisingly, the wait time for safe settlement in the case of quantum adversaries matches the safe settlement time in the classical case.more » « less
-
Safety, liveness, and privacy are three critical properties for any private proof-of-stake (PoS) blockchain. However, prior work (SP'21) has shown that to obtain safety and liveness, a PoS blockchain must, in theory, forgo privacy. In particular, to obtain safety and liveness, PoS blockchains elect parties proportional to their stake, which, in turn, can potentially reveal the stake of a party even if the transaction processing mechanism is private. In this work, we make two key contributions. First, we present the first stake inference attack that can be actually run in practice. Specifically, our attack applies to both deterministic and randomized PoS protocols and has exponentially lesser running time in comparison with the SOTA approach. Second, we use differentially private stake distortion to achieve privacy in PoS blockchains. We formulate certain privacy requirements to achieve transaction and stake privacy, and design two stake distortion mechanisms that any PoS protocol can use. Moreover, we analyze our proposed mechanisms with Ethereum 2.0, a well-known PoS blockchain that is already operating in practice. The results indicate that our mechanisms mitigate stake inference risks and, at the same time, provide reasonable privacy while preserving required safety and liveness properties.more » « less