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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

A comparative study of isogeny-based and elliptic curve cryptographic protocols for post-quantum secure applications

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pp. 4753–4763Vol. 29Issue 10-COctober 2026DOI: 10.47974/JDMSC-3089 Crossmark XML
Received:
01 Apr 2026
Published Online:
31 Oct 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-3089
Pages:
4753–4763

Abstract

The fast development of quantum computing presents a major challenge to classical public-key cryptographic systems and especially the Elliptic Curve Cryptography (ECC) which is based on the hardness of the elliptic curve discrete logarithm problem. This paper provides a comparative study of isogeny-based cryptographic protocols with ECC-based schemes of post-quantum secure applications. A SIKE-like protocol is adopted and used to test isogeny-based mechanisms under real-world conditions, in addition to typical ECC protocols. The comparison is based on the size of key, complexity of computation, use of memory and communication latency. Experimental results show that, whereas ECC is more efficient and has lower latency in a classical setting, isogeny-based schemes have a higher resistance to quantum attacks, but with a higher computational cost. The findings show a performance-quantum security trade-off, thus requiring to design optimized hybrid cryptographic frameworks in the future to support a secure communication system.

Keywords

Subject Classifications

81P9494A60

References

[1] B. Drzazga and Ł. Krzywiecki, “Review of chosen isogeny-based cryptographic schemes,” Cryptography, vol. 6, no. 2, Art. no. 27 (2022), doi: 10.3390/cryptography6020027.

[2] B. Jankowski, K. Szydłowski, M. Niemiec, and P. Chołda, “An Internet messenger using post-quantum cryptography algorithms based on isogenies of elliptic curves,” Electronics, vol. 14, no. 14, Art. no. 2905 (2025), doi: 10.3390/electronics14142905.

[3] S.Y. Chang and Q. Khan, “Post-quantum cryptography in networking protocols: Challenges, solutions, and future directions,” Cryptography, vol. 10, no. 1, Art. no. 12 (2026), doi: 10.3390/cryptography10010012.

[4] J.-A. Septien-Hernandez, M. Arellano-Vazquez, M. A. Contreras-Cruz, and J.-P. Ramirez-Paredes, “A comparative study of post-quantum cryptosystems for Internet-of-Things applications,” Sensors, vol. 22, no. 2, Art. no. 489 (2022), doi: 10.3390/s22020489.

[5] A. Havasi and M. H. Dehkordi, “Enhancing secret sharing security: A verifiable hierarchical threshold model and cheating detection based on integer factorization,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 77–86 (2026), doi: 10.47974/JDMSC-2217.

[6] I. Martinez-Diaz, R. Ali, and M. K. Jamil, “On the search for supersingular elliptic curves and their applications,” Mathematics, vol. 13, no. 2, Art. no. 188 (2025), doi: 10.3390/math13020188.

[7] S. Li, Y. Chen, L. Chen, J. Liao, C. Kuang, K. Li, W. Liang, and N. Xiong, “Post-quantum security: Opportunities and challenges,” Sensors, vol. 23, no. 21, Art. no. 8744 (2023), doi: 10.3390/s23218744.

[8] A. U. Abubakar and E. Chandrasekaran, “A new variable step-size hybrid block method for the numerical solution of ordinary differential equations,” J. Interdiscip. Math., vol. 29, no. 4, pp. 987–1000 (2026), doi: 10.47974/JIM-2412.

[9] Y. Wen, T. Jin, and W. Li, “Reusable fuzzy extractor from isogeny-based assumptions,” Symmetry, vol. 17, no. 7, Art. no. 1065 (2025), doi: 10.3390/sym17071065.

[10] R. C. Poonia, T. Singh, C. K. Rajashri, D. Mondal, and S. M. Patil, “Optimizing communication system security through comprehensive testing and intelligent network configurations,” J. Inf. Optim. Sci., vol. 47, no. 5-A, pp. 1709–1717 (2026), doi: 10.47974/JIOS-2261.

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