A Novel Methodology-Based Joint Hypergeometric Distribution to Analyze the Security of Sharded Blockchains

Cryptocurrencies (e.g., Bitcoin and Ethereum), which promise to become the future of money transactions, are mainly implemented with blockchain technology. However, blockchain suffers from scalability issues. Sharding is the leading solution for blockchain scalability. Sharding splits the blockchain network into sub-chains called shards/committees. Each shard processes a sub-set of transactions, rather than the entire network processing all transactions. This raises security issues for sharding-based blockchain protocols. In this paper, we propose a novel methodology to analyze the security of these protocols (e.g., OmniLedger and RapidChain). In particular, this methodology estimates the failure probability of one sharding round taking into consideration the failure probabilities of all shards. To illustrate the effectiveness of the estimated failure probability, we conduct a numerical analysis of our methodology based on a huge number of trials. Finally, we compute confidence intervals to accurately estimate the failure probability and compare our methodology with existing approaches.