  Blockchain like Bitcoin and Ethereum suffer from scalability issues. Sharding
is one of the most promising and leading solutions to scale blockchain. The
basic idea behind sharding is to divide the blockchain network into multiple
committees, where each processing a separate set of transactions, rather than
the entire network processes all transactions. In this paper, we propose a
probabilistic approach to analyze the security of sharding-based blockchain
protocols. Based on this approach, we investigate the threat of Sybil attacks
in these protocols. The key contribution of our paper is a tractable
probabilistic approach to accurately compute the failure probability that at
least one committee fails and ultimately compute the probability of a
successful attack. To show the effectiveness of our approach, we conduct a
numerical and comparative analysis of the proposed approach with existing
approaches.
