Design and analysis of a discrete mathematical model for secure and encrypted dynamic sharding in blockchain systems
Satpal Singh Kushwahasatpal.singh@jaipur.manipal.eduDepartment of Computer Science and EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Sushanth Chandra Addimulamsushanth93@gmail.comKforce Inc.2681 Sidney St.Pittsburgh, PA 15203, USAView full profile → , Manoj Kumar Rawatmanojkumar.rawat@medicaps.ac.inDepartment of Computer Science and EngineeringMedicaps UniversityIndore, Madhya Pradesh, 453331, IndiaView full profile → , S. Sridevisrisat1617@gmail.comDepartment of Internet of Things (IoT)Koneru Lakshmaiah Education FoundationGuntur, Andhra Pradesh, 522302, IndiaView full profile → , *Ajit NooniaCorresponding authorajit.noonia@jaipur.manipal.eduDepartment of Computer Science and EngineeringManipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Dec 2025
- Published Online:
- 14 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2696
- Pages:
- 3117–3125
Abstract
Blockchain sharding enhances scalability by dividing the network and ledger into parallel-processing shards, but dynamic sharding introduces security risks, especially under adaptive adversarial attacks. This paper presents a rigorous discrete mathematical framework for secure and encrypted dynamic sharding. It models shard formation, node assignment, and reconfiguration as discrete-time stochastic processes over dynamic graphs, with cryptographic hash functions ensuring secure shard allocation. Security is analyzed using combinatorics and probability theory, while a Markov-chain-based model captures system evolution under adversarial influence. The paper derives bounds on shard compromise probability using binomial distributions and Chernoff bounds. Additionally, a key-evolving encryption mechanism is introduced to ensure correct and forward-secure state transitions. Theoretical results show that shard takeover probability decreases exponentially with shard size, while encrypted state migration preserves consistency. Overall, this work provides a mathematically rigorous foundation with provable security and correctness guarantees for scalable blockchain systems.
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References
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