  Extensive research on Nakamoto-style consensus protocols has shown that
network delays degrade the security of these protocols. Established results
indicate that, perhaps surprisingly, maximal security is achieved when the
network is as small as two nodes due to increased delays in larger networks.
This contradicts the very foundation of blockchains, namely that
decentralization improves security. In this paper, we take a closer look at how
the network scale affects security of Nakamoto-style blockchains. We argue that
a crucial aspect has been neglected in existing security models: the larger the
network, the harder it is for an attacker to control a significant amount of
power. To this end, we introduce a probabilistic corruption model to express
the increasing difficulty for an attacker to corrupt resources in larger
networks. Based on our model, we analyze the impact of the number of nodes on
the (maximum) network delay and the fraction of adversarial power. In
particular, we show that (1) increasing the number of nodes eventually violates
security, but (2) relying on a small number of nodes does not provide decent
security provisions either. We then validate our analysis by means of an
empirical evaluation emulating hundreds of thousands of nodes in deployments
such as Bitcoin, Monero, Cardano, and Ethereum Classic. Based on our empirical
analysis, we concretely analyze the impact of various real-world parameters and
configurations on the consistency bounds in existing deployments and on the
adversarial power that can be tolerated while providing security. As far as we
are aware, this is the first work that analytically and empirically explores
the real-world tradeoffs achieved by current popular Nakamoto-style
deployments.
