Larger-scale Nakamoto-style Blockchains Offer Better Security

Abstract: Traditional security models for Nakamoto-style blockchains overestimate adversarial coordination by assuming instantaneous synchronization among malicious nodes, neglecting the critical impact of internal communication delays on security. This paper introduces a dual-delay framework to revisit security analysis, addressing this oversight through two key innovations. First, the static delay model quantifies how adversarial communication delays ((\Delta_a)) constrain the effective growth rate of private chains, derived via an M/D/1 queuing model as (\lambda_{eff} = \lambda_a / (1 + \lambda_a \Delta_a)). This model reveals that the security threshold ((\beta^*)), the maximum adversarial power the system tolerates, increases with (\Delta_a), even exceeding the classic 51\% boundary when (\Delta_a \textgreater \Delta) (honest nodes' delay), breaking the long-standing 50\% assumption. Second, the dynamic delay model integrates probabilistic corruption and scale-dependent delays to characterize the total adversarial delay window ((\Delta_{total} = \Delta(n) e^{-k\beta} + c \log(1 + \beta n))), where (\Delta(n) \in \Theta(\log n)) captures honest nodes' logarithmic delay growth. Asymptotic analysis shows adversarial power decays linearly with network scale, ensuring the probability of (\beta \leq \beta^*) approaches 1 as (n \to \infty). By exposing the interplay between network scale, communication delays, and power dilution, we provide a theoretical foundation for optimizing consensus protocols and assessing robustness in large-scale Nakamoto-style blockchains.