{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T03:33:17Z","timestamp":1769052797098,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>Scalability and security restrictions are posing new challenges for blockchain networks, especially in the face of Distributed Denial-of-Service (DDoS) attacks and upcoming quantum threats. Previous research also found that post-quantum blockchains, despite their improved cryptographic algorithms, are still vulnerable to DDoS attacks, emphasizing the need for more resilient architectural solutions. This research studies the use of dynamic sharding, an innovative approach for post-quantum blockchains that allows for adaptive division of the network into shards based on workload and network conditions. Unlike static sharding, dynamic sharding optimizes resource allocation in real time, increasing transaction throughput and minimizing DDoS-induced disruptions. We provide a detailed study using Monte Carlo simulations to examine transaction success rates, resource consumption, and fault tolerance for both dynamic sharding-based and non-sharded post-quantum blockchains under simulated DDoS attack scenarios. The findings show that dynamic sharding leads to higher transaction success rates and more efficient resource use than non-sharded infrastructures, even in high-intensity attack scenarios. Furthermore, the combination of dynamic sharding and the Falcon post-quantum signature technique creates a layered strategy that combines cryptographic robustness, scalability, and resilience. This paper provides light on the potential of adaptive blockchain designs to address major scalability and security issues, opening the path for quantum-resilient systems.<\/jats:p>","DOI":"10.3390\/cryptography9020022","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T06:45:31Z","timestamp":1744353931000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Sharding and Monte Carlo for Post-Quantum Blockchain Resilience"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-5730-085X","authenticated-orcid":false,"given":"Dahhak","family":"Hajar","sequence":"first","affiliation":[{"name":"C3S Laboratory, Department of Computer Science, ENSEM, Hassan II University, Casablanca 20000, Morocco"}]},{"given":"Nadia","family":"Afifi","sequence":"additional","affiliation":[{"name":"C3S Laboratory, Department of Computer Science, ENSEM, Hassan II University, Casablanca 20000, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0082-5438","authenticated-orcid":false,"given":"Imane","family":"Hilal","sequence":"additional","affiliation":[{"name":"Itqan Team, School of Computer Science (ESI), Mohammed V University, Rabat 10100, Morocco"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"ref_1","unstructured":"Shor, P.W. (1994, January 20\u201322). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_2","unstructured":"Boneh, D., and Shoup, V. (2024, October 01). A Graduate Course in Applied Cryptography. Version 0.5. Stanford University. Available online: https:\/\/toc.cryptobook.us."},{"key":"ref_3","unstructured":"Ducas, L., and Prest, T. (2018, January 9\u201311). Falcon: Fast-Fourier lattice-based compact signatures over NTRU. Proceedings of the Post-Quantum Cryptography Conference, Fort Lauderdale, FL, USA."},{"key":"ref_4","unstructured":"NIST (2025, January 01). Post-Quantum Cryptography Standardization, Available online: https:\/\/csrc.nist.gov\/."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wani, S., Imthiyas, M., Almohamedh, H., Alhamed, K.M., Almotairi, S., and Gulzar, Y. (2021). Distributed Denial of Service (DDoS) Mitigation Using Blockchain\u2014A Comprehensive Insight. Symmetry, 13.","DOI":"10.3390\/sym13020227"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Manikumar, D.V.V.S., and Maheswari, B.U. (2020, January 15\u201317). Blockchain Based DDoS Mitigation Using Machine Learning Techniques. Proceedings of the 2020 Second International Conference on Inventive Research in Computing Applications (ICIRCA), Coimbatore, India.","DOI":"10.1109\/ICIRCA48905.2020.9183092"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/MITP.2017.3051335","article-title":"Can blockchain strengthen the internet of things?","volume":"19","author":"Kshetri","year":"2017","journal-title":"IT Prof."},{"key":"ref_8","unstructured":"Buterin, V. (2025, February 07). Sharding FAQs. Available online: https:\/\/vitalik.eth.limo\/general\/2017\/12\/31\/sharding_faq.html."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.isatra.2023.06.029","article-title":"A Survey on Blockchain Sharding","volume":"141","author":"Liu","year":"2023","journal-title":"ISA Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1080\/01621459.1949.10483310","article-title":"The Monte Carlo Method","volume":"44","author":"Metropolis","year":"1949","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_11","first-page":"1","article-title":"Security Analysis of Classical and Post-Quantum Blockchains","volume":"64","author":"Dahhak","year":"2024","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_12","first-page":"45","article-title":"Resilience against DDoS attacks in blockchain networks","volume":"35","author":"Shi","year":"2021","journal-title":"J. Distrib. Comput. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kokoris-Kogias, E., Jovanovic, P., Gasser, L., Gailly, N., Syta, E., and Ford, B. (2018, January 20\u201324). OmniLedger: A secure, scale-out, decentralized ledger via sharding. Proceedings of the IEEE Symposium on Security and Privacy, San Francisco, CA, USA.","DOI":"10.1109\/SP.2018.000-5"},{"key":"ref_14","first-page":"57","article-title":"Post-quantum cryptography: Quantum-resistant algorithms","volume":"60","author":"Bernstein","year":"2017","journal-title":"Commun. ACM"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wan, L., Eyers, D., and Zhang, H. (2019, January 14\u201317). Evaluating the Impact of Network Latency on the Safety of Blockchain Transactions. Proceedings of the 2019 IEEE International Conference on Blockchain (Blockchain), Atlanta, GA, USA.","DOI":"10.1109\/Blockchain.2019.00033"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Alajlan, R., Alhumam, N., and Frikha, M. (2023). Cybersecurity for Blockchain-Based IoT Systems: A Review. Appl. Sci., 13.","DOI":"10.3390\/app13137432"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Chaganti, R., Bhushan, B., and Ravi, V. (2022). The role of Blockchain in DDoS attacks mitigation: Techniques, open challenges and future directions. arXiv.","DOI":"10.1016\/j.comcom.2022.10.026"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Raikwar, M., and Gligoroski, D. (2022). DoS Attacks on Blockchain Ecosystem. arXiv.","DOI":"10.1007\/978-3-031-06156-1_19"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, Y., Liu, J., Vaz Salles, M.A., Zhang, Z., Li, T., Hu, B., Henglein, F., and Lu, R. (2021). Building Blocks of Sharding Blockchain Systems: Concepts, Approaches, and Open Problems. arXiv.","DOI":"10.1016\/j.cosrev.2022.100513"},{"key":"ref_20","unstructured":"Doger, M., and Ulukus, S. (2024). Transaction Capacity, Security and Latency in Blockchains. arXiv."},{"key":"ref_21","unstructured":"Zhang, L., and Zhang, F. (2023). Understanding Waiting Time in Transaction Fee Mechanism: An Interdisciplinary Perspective. arXiv."},{"key":"ref_22","first-page":"45","article-title":"Hierarchical sharding to mitigate DDoS attacks in large-scale blockchain systems","volume":"10","author":"Sousa","year":"2022","journal-title":"IEEE Trans. Netw. Secur."},{"key":"ref_23","unstructured":"Roughgarden, T. (2020). Transaction Fee Mechanism Design for the Ethereum Blockchain: An Economic Analysis of EIP-1559. arXiv."},{"key":"ref_24","first-page":"123","article-title":"Sharding in distributed databases: Challenges and opportunities for blockchains","volume":"12","author":"Kumar","year":"2020","journal-title":"Database Syst. J."},{"key":"ref_25","unstructured":"Han, R., Yu, J., Lin, H., Chen, S., and Ver\u00edssimo, P.E. (2021). On the Security and Performance of Blockchain Sharding. Cryptol. Eprint Arch., Available online: https:\/\/eprint.iacr.org\/2021\/1276."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bulgakov, A.L., Aleshina, A.V., Smirnov, S.D., Demidov, A.D., Milyutin, M.A., and Xin, Y. (2024). Scalability and Security in Blockchain Networks: Evaluation of Sharding Algorithms and Prospects for Decentralized Data Storage. Mathematics, 12.","DOI":"10.20944\/preprints202410.1078.v1"},{"key":"ref_27","first-page":"1","article-title":"Scalability improvements in blockchain through sharding","volume":"3","author":"Jovanovic","year":"2019","journal-title":"ACM Trans. Blockchain"},{"key":"ref_28","first-page":"33","article-title":"Adaptive sharding strategies for dynamic blockchain networks","volume":"6","author":"Zhang","year":"2021","journal-title":"Blockchain Res. J."},{"key":"ref_29","first-page":"203","article-title":"DDoS mitigation in sharded blockchain systems: A review and evaluation","volume":"23","author":"Shi","year":"2021","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_30","first-page":"99","article-title":"Sharding-based blockchain systems: Enhancing resilience against DDoS attacks","volume":"4","author":"Li","year":"2021","journal-title":"Blockchain Secur. J."},{"key":"ref_31","first-page":"78","article-title":"Hybrid sharding for secure and scalable blockchain applications","volume":"8","author":"Han","year":"2020","journal-title":"Int. J. Blockchain Stud."},{"key":"ref_32","first-page":"88","article-title":"Multi-layer sharding for enhanced blockchain resilience","volume":"5","author":"Wang","year":"2021","journal-title":"Distrib. Ledger Res."},{"key":"ref_33","unstructured":"Grover, L.K. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA."},{"key":"ref_34","first-page":"377","article-title":"Post-quantum signatures","volume":"21","author":"Buchmann","year":"2008","journal-title":"J. Cryptol."},{"key":"ref_35","unstructured":"NIST (2025, January 01). Post-Quantum Cryptography Standardization Project, Available online: https:\/\/csrc.nist.gov\/projects\/post-quantum-cryptography."},{"key":"ref_36","unstructured":"Falcon Development Team (2018, January 9\u201311). Fast-Fourier lattice-based compact signatures. Proceedings of the Post-Quantum Cryptography Conference, Fort Lauderdale, FL, USA."},{"key":"ref_37","first-page":"45","article-title":"Falcon integration into blockchain systems: A feasibility study","volume":"7","author":"Chen","year":"2020","journal-title":"J. Blockchain Res."},{"key":"ref_38","first-page":"12","article-title":"Lattice-based cryptography for blockchain quantum resistance","volume":"3","author":"Han","year":"2021","journal-title":"IEEE Blockchain Lett."},{"key":"ref_39","first-page":"87","article-title":"Quantum-resistant cryptography and its applications","volume":"25","author":"Bernstein","year":"2019","journal-title":"Adv. Cryptol."},{"key":"ref_40","unstructured":"Falcon Development Team (2024, November 01). Falcon: Fast-Fourier Lattice-Based Compact Signatures over NTRU. Available online: https:\/\/falcon-sign.info\/."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Bappy, F.H., Zaman, T.S., Sajid, M.S.I., Pritom, M.M.A., and Islam, T. (2024). Maximizing Blockchain Performance: Mitigating Conflicting Transactions through Parallelism and Dependency Management. arXiv.","DOI":"10.1109\/Blockchain62396.2024.00027"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Esmaili, M., and Christensen, K. (2024). Performance modeling of public permissionless blockchains: A survey. arXiv.","DOI":"10.1145\/3715094"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Yu, G., Sun, C., Wang, X., Wang, Y., Zhang, M., Ni, W., Liu, R.P., Reeves, A., and Georgalas, N. (2024). TBDD: A New Trust-based, DRL-driven Framework for Blockchain Sharding in IoT. arXiv.","DOI":"10.2139\/ssrn.4665614"},{"key":"ref_44","unstructured":"(2024, November 01). Monte The Application of Monte Carlo Simulation to Assess the Value at Risk in Cryptocurrency. Available online: https:\/\/www.researchgate.net\/publication\/383997972_The_Application_of_Monte_Carlo_Simulation_to_Assess_the_Value_at_Risk_in_Cryptocurrency."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:12:47Z","timestamp":1760029967000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,11]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["cryptography9020022"],"URL":"https:\/\/doi.org\/10.3390\/cryptography9020022","relation":{},"ISSN":["2410-387X"],"issn-type":[{"value":"2410-387X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,11]]}}}