Blockchain technology has been gaining great interest from a variety of sectors including healthcare, supply chain, and cryptocurrencies. However, Blockchain suffers from a limited ability to scale (i.e., low throughput and high latency). Several solutions have been proposed to tackle this. In particular, sharding has proved to be one of the most promising solutions to Blockchain's scalability issue. Sharding can be divided into two major categories: (1) Sharding-based Proof-of-Work (PoW) Blockchain protocols, and (2) Sharding-based Proof-of-Stake (PoS) Blockchain protocols. The two categories achieve good performances (i.e., good throughput with a reasonable latency), but raise security issues. This article focuses on the second category. In this paper, we start by introducing the key components of sharding-based PoS Blockchain protocols. We then briefly introduce two consensus mechanisms, namely PoS and practical Byzantine Fault Tolerance (pBFT), and discuss their use and limitations in the context of sharding-based Blockchain protocols. Next, we provide a probabilistic model to analyze the security of these protocols. More specifically, we compute the probability of committing a faulty block and measure the security by computing the number of years to fail. We achieve a number of years to fail of approximately 4000 in a network of 4000 nodes, 10 shards, and a shard resiliency of 33%.
Keywords: blockchain; malicious nodes; practical Byzantine fault tolerance; probabilistic analysis; proof of stake; security analysis; sharding-based blockchain protocols.