New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols
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 o...
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doaj-a8a2aef8b37a4508929f206da40952492021-03-29T23:12:23ZengIEEEIEEE Access2169-35362019-01-01718544718545710.1109/ACCESS.2019.29610658936849New Mathematical Model to Analyze Security of Sharding-Based Blockchain ProtocolsAbdelatif Hafid0https://orcid.org/0000-0001-8597-7344Abdelhakim Senhaji Hafid1Mustapha Samih2https://orcid.org/0000-0002-9751-9161Department of Mathematics, Faculty of Sciences, Team of EDA–Mathematical Laboratory and Their Applications, University of Moulay Ismail, Meknes, MoroccoDepartment of Computer Science and Operational Research, Montreal Blockchain Lab, University of Montreal, Montreal, QC, CanadaDepartment of Mathematics, Faculty of Sciences, Team of EDA–Mathematical Laboratory and Their Applications, University of Moulay Ismail, Meknes, MoroccoIn 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 Chvátal. To illustrate the effectiveness of our proposed model, we conduct a numerical and comparative analysis of the proposed bounds.https://ieeexplore.ieee.org/document/8936849/Blockchainfailure probabilityhypergeometric distributionprobability boundssharding |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Abdelatif Hafid Abdelhakim Senhaji Hafid Mustapha Samih |
spellingShingle |
Abdelatif Hafid Abdelhakim Senhaji Hafid Mustapha Samih New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols IEEE Access Blockchain failure probability hypergeometric distribution probability bounds sharding |
author_facet |
Abdelatif Hafid Abdelhakim Senhaji Hafid Mustapha Samih |
author_sort |
Abdelatif Hafid |
title |
New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols |
title_short |
New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols |
title_full |
New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols |
title_fullStr |
New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols |
title_full_unstemmed |
New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols |
title_sort |
new mathematical model to analyze security of sharding-based blockchain protocols |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
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 Chvátal. To illustrate the effectiveness of our proposed model, we conduct a numerical and comparative analysis of the proposed bounds. |
topic |
Blockchain failure probability hypergeometric distribution probability bounds sharding |
url |
https://ieeexplore.ieee.org/document/8936849/ |
work_keys_str_mv |
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