  Blockchain, the technology behind the popular Bitcoin, is considered a
"security by design" system as it is meant to create security among a group of
distrustful parties yet without a central trusted authority. The security of
blockchain relies on the premise of honest-majority, namely, the blockchain
system is assumed to be secure as long as the majority of consensus voting
power is honest. And in the case of proof-of-work (PoW) blockchain, adversaries
cannot control more than 50% of the network's gross computing power. However,
this 50% threshold is based on the analysis of computing power only, with
implicit and idealistic assumptions on the network and node behavior. Recent
researches have alluded that factors such as network connectivity, presence of
blockchain forks, and mining strategy could undermine the consensus security
assured by the honest-majority, but neither concrete analysis nor quantitative
evaluation is provided. In this paper we fill the gap by proposing an
analytical model to assess the impact of network connectivity on the consensus
security of PoW blockchain under different adversary models. We apply our
analytical model to two adversarial scenarios: 1)
honest-but-potentially-colluding, 2) selfish mining. For each scenario, we
quantify the communication capability of nodes involved in a fork race and
estimate the adversary's mining revenue and its impact on security properties
of the consensus protocol. Simulation results validated our analysis. Our
modeling and analysis provide a paradigm for assessing the security impact of
various factors in a distributed consensus system.
