A Contract-Theoretic Cyber Insurance for Withdraw Delay in the Blockchain Networks with Shards

As the basis of the most existing blockchain networks, Proof of Work (PoW) consensus protocol highly relies on the computational resources, and thus causing a huge waste of energy. Proof of Stake (PoS) is the alternative to relieve the PoW dilemma. However, it is also under threat, i.e., discouragement attack, which is a way to bring down the blockchain networks without any effective defense against it. To prevent the discouragement attack, the founders of Ethereum argue that the system should set a withdraw delay instead of allowing the validators entry/exit quickly. But how to determine the delay is still an open question. In this paper, we adopt the cyber insurance idea and propose the insurance contract to help determine the withdraw delay, as well as the insurance claim to relieve the loss of victims. Specifically, instead of requiring the insurance premium from the validators, the cyber insurer first signs the contract with the blockchain representative (e.g., beacon chain). Then the blockchain representative would sign a series of contracts with the validators. By such design, the validators can obtain the insurance claim without paying the premium, while the blockchain networks can keep the validators staying online to resist the discouragement attack. Finally, through the simulations, we demonstrate that the proposed model is capable of providing adaptive insurance contracts for the different validators and keeping the profits of the blockchain network and the cyber insurer.