A Methodology for a Probabilistic Security Analysis of Sharding-Based Blockchain Protocols

  • Abdelatif HafidEmail author
  • Abdelhakim Senhaji Hafid
  • Mustapha Samih
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1010)


In the context of blockchain protocols, each node stores the entire state of the network and processes all transactions. This ensures high security but limits scalability. Sharding is one of the most promising solutions to scale blockchain. In this paper, we analyze the security of three Sharding-based protocols using tail inequalities. The key contribution of our paper is to upper bound the failure probability for one committee and so for each epoch using tail inequalities for sums of bounded hypergeometric and binomial distributions. Two tail inequalities are used: Hoeffding and Chvátal. The first tail (Hoeffding inequality) is much more precise bound. The second (Chvátal inequality) is an exponential bound; it is simple to compute but weaker bound compared to Hoeffding. Our contribution is an alternative solution when the failure probability simulations are impractical. To show the effectiveness of our analysis, we perform simulations of the exponential bound.


Blockchain Sharding Failure probability Tail inequality Hypergeometric distribution Probabilistic security analysis Exponential bound 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Abdelatif Hafid
    • 1
    Email author
  • Abdelhakim Senhaji Hafid
    • 2
  • Mustapha Samih
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesUniversity Moulay IsmailMeknesMorocco
  2. 2.Department of Computer Science and Operations ResearchUniversity of MontrealMontrealCanada

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