The Consensus Number of a Cryptocurrency (Extended Version) (1906.05574v1)

Abstract: Many blockchain-based algorithms, such as Bitcoin, implement a decentralized asset transfer system, often referred to as a cryptocurrency. As stated in the original paper by Nakamoto, at the heart of these systems lies the problem of preventing double-spending; this is usually solved by achieving consensus on the order of transfers among the participants. In this paper, we treat the asset transfer problem as a concurrent object and determine its consensus number, showing that consensus is, in fact, not necessary to prevent double-spending. We first consider the problem as defined by Nakamoto, where only a single process---the account owner---can withdraw from each account. Safety and liveness need to be ensured for correct account owners, whereas misbehaving account owners might be unable to perform transfers. We show that the consensus number of an asset transfer object is $1$. We then consider a more general $k$-shared asset transfer object where up to $k$ processes can atomically withdraw from the same account, and show that this object has consensus number $k$. We establish our results in the context of shared memory with benign faults, allowing us to properly understand the level of difficulty of the asset transfer problem. We also translate these results in the message passing setting with Byzantine players, a model that is more relevant in practice. In this model, we describe an asynchronous Byzantine fault-tolerant asset transfer implementation that is both simpler and more efficient than state-of-the-art consensus-based solutions. Our results are applicable to both the permissioned (private) and permissionless (public) setting, as normally their differentiation is hidden by the abstractions on top of which our algorithms are based.

• The paper finds that consensus is not required for basic cryptocurrency asset transfers, establishing the consensus number as 1 for single-owner accounts.
• The research analyzes the problem using Herlihy's hierarchy and shows asset transfers can be implemented efficiently with alternative mechanisms like atomic snapshots.
• These findings imply that cryptocurrency systems can achieve greater scalability and efficiency by using alternative methods instead of global consensus protocols.

Essay: The Consensus Number of a Cryptocurrency

The paper "The Consensus Number of a Cryptocurrency" provides an in-depth theoretical analysis of the asset transfer problem inherent in blockchain-based systems, such as cryptocurrencies. Authored by Guerraoui et al., this research investigates the consensus requirements for preventing double-spending and presents significant findings that alter the common understanding of distributed computing in the context of asset transfers.

Core Contributions

The paper's core contribution is the establishment that consensus, a prevalent operation in distributed computing systems particularly for cryptocurrencies, is not a necessity when addressing the asset transfer problem. By defining the problem as a concurrent object, the authors assess its consensus number, concluding it to be 1 for single-owner asset accounts and extending the analysis to multi-owner scenarios where they ascertain a consensus number equal to $k$ for $k$-shared accounts. This is a profound revelation that challenges the consensus-centric approach traditionally employed by systems like Bitcoin and Ethereum for ensuring transaction validity and order.

Methodology and Results

The authors define the asset transfer problem using a sequential object type and apply Herlihy's consensus hierarchy to investigate the synchronization power required to resolve the double-spending dilemma. The paper's results show that for a single-owner account, the consensus number of the asset transfer object is indeed 1, essentially implying that consensus is unnecessary for basic asset transfers. This finding is embodied through an algorithm employing atomic snapshot objects, demonstrating how asset transfers can be executed efficiently without consensus mechanisms.

Moreover, for scenarios where an account can be accessed by multiple processes (up to $k$), the research illustrates that the consensus number can be generalized to $k$. This implicates that systems using $k$-shared asset transfer objects require consensus only among the involved $k$ nodes, vastly simplifying the implementation compared to global consensus protocols.

Practical Implications and Future Directions

The implications of these findings are substantial. By characterizing asset transfer problems with relatively low consensus numbers, the research opens avenues for deploying cryptocurrency systems that are more scalable and efficient, circumventing the performance bottlenecks associated with global consensus. The paper discusses translating these results into a Byzantine message passing model, offering a practical implementation framework using secure broadcasts rather than consensus, thereby achieving similar reliability and safety without the intensive computational costs.

For future research, the paper suggests investigating dynamic configurations wherein participants may join or leave the network unpredictably—addressing reconfiguration without resorting to consensus—which remains a complex challenge in large-scale distributed systems. Additionally, optimizing the message-passing implementations, particularly under Byzantine assumptions, could further refine the robustness and efficiency of cryptographic protocols experiencing malicious actors.

Conclusion

This rigorous theoretical analysis not only demystifies the necessity of consensus for asset transfers but also proposes efficient methodological frameworks that maintain the integrity and safety of transactions while scaling the blockchain network. As the field moves towards practical deployment in real-world cryptocurrency systems, leveraging the insights from this paper can potentially redefine architectures that have conventionally prioritized consensus as a cornerstone.

In summary, this paper serves as a critical resource for researchers focused on distributed algorithms in the field of decentralized finance, highlighting the nuanced role of consensus and paving the way for novel approaches to asset transfer implementations in cryptocurrency systems.