Resilience of Hybrid Casper Under Varying Values of Parameters

Hybrid Casper is the new Ethereum blockchain protocol that uses both Proof of Work and Proof of Stake to reach a consensus between nodes. Here, we analyse the protocol using PRISM+ , an extension of the probabilistic model checker PRISM with primitives for expressing blockchain data types. First, we extend PRISM+ to include data types and operations for modelling and analysing Proof of Stake-based consensus protocols. Then, we model Hybrid Casper in PRISM+ as a parallel composition of stochastic processes, thus precisely describing the behaviour of the protocol and highlighting its corner cases. PRISM+ is therefore used to rapidly and automatically analyse the resilience of Hybrid Casper when tuning, up or down, several basic parameters of the protocol, such as the rates of creating blocks, and the strategies for determining penalties. Finally, we study the robustness of Hybrid Casper to two well known attacks: the Eclipse attack and the majority attack.