Abstract
In recent years, the scalability issue of blockchain protocols has received huge attention. Sharding is one of the most promising solutions to scale blockchain. The basic idea behind sharding is to divide the blockchain network into multiple committees where each committee processes a separate set of transactions. In this paper, we propose a mathematical model to analyze the security of sharding-based blockchain protocols. Moreover, we analyze well-known sharding protocols including RapidChain, OmniLedger, and Zilliga to validate our model. The key contribution of our paper is to bound the failure probability for one committee and so for each epoch using probability bounds for sums of upper-bounded hypergeometric and binomial distributions. In addition, this paper contribution answers the following fundamental question: “how to keep the failure probability, for a given sharding protocol, smaller than a predefined threshold?”. Three probability bounds are used: Chebyshev, Hoeffding, and Chvatal. To illustrate the effectiveness of our proposed model, we conduct a numerical and comparative analysis of the proposed bounds.
Highlights
Blockchain is a technology that, when used, can have a great impact in almost all industry segments including banking, healthcare, supply chain, and government sector [9], [13]
We develop a general model to analyze the security for any sharding-based blockchain protocol
ANALYTICAL MODEL In sharding-based blockchain protocols, we propose to use the hypergeometric distribution instead of the binomial distribution; this is because the process of assigning nodes to shards can be defined as a sampling without replacement; in this case, hypergeometric distribution yields better approximation compared to binomial’s [22]
Summary
Blockchain is a technology that, when used, can have a great impact in almost all industry segments including banking, healthcare, supply chain, and government sector [9], [13]. The paper contribution consists of a solution to analyze security of sharding-based blockchain protocols, i.e., bound the failure probability and how to keep this failure probability smaller than a given threshold. We select three probability bounds to analyze the security of sharding-based blockchain protocols; Chebyshev [47], Chvátal [21], and Hoeffding [19]. To the best of our knowledge, there is no existing work that analyzes security of Blockchain protocols using Hoeffding and Chvátal inequalities except our contribution [1] In this contribution [1], we presented a probabilistic security analysis that is specific to Elastico, OmniLedger, and RapidChain.
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