Biblio

Sharding is considered to be the most promising solution to overcome and to improve the scalability limitations of blockchain networks. By doing this, the transaction throughput increases, at the same time compromises the security of blockchain networks. In this paper, a probability distribution model is proposed to analyze this trade-off between scalability and security of sharding-based blockchain networks. For this purpose hypergeometric distribution and Chebyshev's Inequality are mainly used. The upper bounds of hypergeometric distributed transaction processing and failure probabilities for shards are mainly evaluated. The model validation is accomplished with Class A (Omniledger, Elastico, Harmony, and Zilliqa), and Class B (RapidChain) sharding protocols. This validation shows that Class B protocols have a better performance compared to Class A protocols. The proposed model observes the transaction processing and failure probabilities are increased when shard size is reduced or the number of shards increased in sharding-based blockchain networks. This trade-off between the scalability and the security decides on the shard size of the blockchain network based on the real-world application and the blockchain platform. This explains the scalability trilemma in blockchain networks claiming that decentralization, scalability, and security cannot be met at primary grounds. In conclusion, this paper presents a comprehensive analysis providing essential directions to develop sharding protocols in the future to enhance the performance and the best-cost benefit of sharing-based blockchains by improving the scalability and the security at the same time.

This presents a new model to support empirical failure probability estimation for a software-intensive system. The new element of the approach is that it combines the results of testing using a simulated hardware platform with results from testing on the real platform. This approach addresses a serious practical limitation of a technique known as statistical testing. This limitation will be called the test time expansion problem (or simply the 'time problem'), which is that the amount of testing required to demonstrate useful levels of reliability over a time period T is many orders of magnitude greater than T. The time problem arises whether the aim is to demonstrate ultra-high reliability levels for protection system, or to demonstrate any (desirable) reliability levels for continuous operation ('high demand') systems. Specifically, the theoretical feasibility of a platform simulation approach is considered since, if this is not proven, questions of practical implementation are moot. Subject to the assumptions made in the paper, theoretical feasibility is demonstrated.