Everything is a Race and Nakamoto Always Wins (2005.10484v4)

Abstract: 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.

• The paper demonstrates that Nakamoto’s private attack strategy sets a true security threshold by analyzing PoW, PoS, and PoSpace protocols.
• It employs a unified model with Nakamoto blocks and branching random walks to assess adversarial power limits, revealing that security holds when adversaries control less than roughly 50% of network power in PoW and PoS systems.
• The study highlights that PoSpace protocols require stricter thresholds due to multi-root mining, offering actionable insights for designing resilient blockchain consensus mechanisms.

Analyzing the Security Thresholds of Longest Chain Blockchain Protocols

This paper examines the security thresholds of several longest chain blockchain protocols, revealing that the private attack strategy proposed by Nakamoto is indeed the limiting factor for their security. The analysis is conducted across three major consensus mechanisms: Proof-of-Work (PoW), Proof-of-Stake (PoS), and Proof-of-Space (PoSpace). The paper rigorously characterizes these protocols' tolerance to adversarial power, establishing that the private attack provides a true threshold for security, aptly positioning Nakamoto's original insight across these different blockchain models.

The authors deploy a unified model underpinned by the notion of "Nakamoto blocks" to meticulously evaluate the security conditions of these longest chain protocols. Nakamoto blocks are defined as certain honest blocks in the blockchain that are effectively immune to adversarial takeover. The presence of these blocks guarantees that past transactions in the blockchain remain confirmed across future states of the system. The primary outcome illustrates that if a protocol can regularly produce Nakamoto blocks, it can maintain robust ledger consistency and uphold confirmed transactions against adversarial manipulations.

For the PoW and PoS models, the paper finds the security threshold, where adversarial power equals $\beta$, holds true at $$\beta < \frac{1-\beta}{1 + (1-\beta)\lambda \Delta}$$. This threshold demonstrates that the allowed adversary power should be below 50% (half the network power) to ensure protocol security, assuming small block throughput ($\lambda \Delta$). The analysis also confirms this threshold remains unaffected by whether the network operates under a PoW or PoS framework, showing widespread applicability of Nakamoto's private attack model. The security threshold for the Chia PoSpace model, however, is found to be more restrictive due to its increased adversarial capacity since adversaries can mine on multiple block roots simultaneously. Here, the threshold is set at $$e \beta < \frac{1-\beta}{1 + (1-\beta)\lambda \Delta}$$.

The paper further bridges a conceptual understanding of adversarial actions by leveraging probabilistic tools alongside branching random walks. The authors critically ensure that if the private attack’s growth rate is slower than the genuine growth rate of the honest chain, it is infeasible for an adversarial chain to overtake the main chain persistently.

The unified theoretical analysis offers a comparative perspective across the proof models, confirming the robustness of the unified approach which can highlight differences and similarities in attack vulnerabilities across varied blockchain schemes.

Ultimately, the implications of these findings are profound for both theorists and practitioners within the blockchain domain. Emerging protocols must take note of these security benchmarks to align their consensus mechanisms effectively against adversarial threats. Additionally, this paper sets a foundation for future development of blockchain protocols, highlighting areas where adversary capabilities could be further evaluated or mitigated. The explicit consideration of the network delay, block throughput, and diversification away from reliance on sole computational proof of work constructs could further enrich protocol security and blockchain efficiency.

This methodical research insightfully delineates the operational dynamics and security posture of longest chain blockchain protocols, reaffirming the pivotal role of Nakamoto's private chain analysis while extending it across diverse blockchain frameworks.