Isogeny-based cryptosystems for post-quantum security
R. A. Kapgaterakapgate@sanjivani.org.inDepartment of Mechatronics EngineeringSanjivani College of EngineeringSavitribai Phule Pune UniversityKopargaon, Ahilyanagar, Maharashtra, 423603, IndiaView full profile → , *Dheeravath RajuCorresponding authordheeravathraju.dr@rediffmail.comCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, IndiaView full profile → , Chetansinh R. Vaghelacrvaghela.maths.gsc@gokuluniversity.ac.inFaculty of ScienceGokul Global UniversitySidhpur, Gujarat, 384151, IndiaView full profile → , Neema Sajju Balanneema@rungta.orgDepartment of Computer Science & EngineeringRungta College of Engineering & TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Amol Bardeamol.barde1@vit.eduDepartment of Mechanical EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Krishna Chaitanya Pidugukrishnacp@outlook.comDepartment of CSE (Artificial Intelligence)Pragati Engineering CollegeSurampalem, Kakinada District, Andhra Pradesh, 533437, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3058
- Pages:
- 4369–4381
Abstract
The fast progress of quantum computing is a serious threat to classical cryptographic schemes like RSA and elliptic curve cryptography, and it is time to come up with safe post-quantum schemes. One of the new solutions is isogeny-based cryptography which has attracted attention because of its good-security basis and comparatively small key sizes. Nevertheless, currently used post-quantum cryptographic (PQC) designs, such as lattice-based and code-based ones, are typically characterized by the high key sizes, high computational costs, or scaling issues, with the necessity to have a well-balanced and efficient cryptographic design. This paper presents a powerful isogeny-based cryptosystem, which can allow safe communication in the post-quantum context. The mathematical complexity of isogenies over supersingular elliptic curves forms the foundation of the proposed framework and it has a structured architecture comprising of parameterization, key generation, encryption/decryption and communication layers. The design of the optimization of algorithms to generate keys, exchange keys securely and encrypt messages using shared secret derivation mechanisms is part of the methodology. Security analysis is also carried out to assess the resistance to quantum attacks and against known cryptanalytic vulnerabilities. The metrics used to conduct performance evaluation are computed cost, key size, and latency, and the results are compared to typical PQC schemes, like lattice-based (Kyber) and code-based (McEliece) systems. The results show that the model proposed has much smaller key sizes (330 bytes public key) with moderate computational efficiency although a little bit more latency than lattice-based methods.
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References
[1] G. Alagic, D. Cooper, Q. Dang, T. Dang, J. M. Kelsey, J. Lichtinger, Y.-K. Liu, C. A. Miller, D. Moody, R. Peralta, R. Perlner, A. Robinson, D. Smith-Tone, and D. Apon, “Status report on the third round of the NIST post-quantum cryptography standardization process,” National Institute of Standards and Technology, Gaithersburg, MD, USA, NISTIR 8413 (2022), doi: 10.6028/NIST.IR.8413.
[2] C. Balamurugan, K. Singh, G. Ganesan, and M. Rajarajan, “Post-quantum and code-based cryptography—Some prospective research directions,” Cryptography, vol. 5, no. 4, Art. no. 38 (2021), doi: 10.3390/cryptography5040038.
[3] W. Beullens, L. De Feo, S. D. Galbraith, and C. Petit, “Proving knowledge of isogenies: A survey,” Des. Codes Cryptogr., vol. 91, no. 11, pp. 3425–3456 (2023), doi: 10.1007/s10623-023-01243-3.
[4] R. C. Poonia, R. Almakki, A. K. J. Saudagar, A. Altameem, and M. Albathan, “An optimization approach for real-time object detection in IoT devices through edge computing and deep learning,” J. Inf. Optim. Sci., vol. 45, no. 5, pp. 1465–1475 (2024), doi: 10.47974/JIOS-1768.
[5] D. Boneh, D. Kogan, and K. Woo, “Oblivious pseudorandom functions from isogenies,” in Advances in Cryptology—ASIACRYPT 2020, S. Moriai and H. Wang, Eds., Lecture Notes in Computer Science, vol. 12492. Cham, Switzerland: Springer (2020).
[6] J. Dey and R. Dutta, “Progress in multivariate cryptography: Systematic review, challenges, and research directions,” ACM Comput. Surv., vol. 55, no. 12, pp. 1–34 (2023), doi: 10.1145/3571071.
[7] 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.
[8] M. Fukumitsu and S. Hasegawa, “A lattice-based provably secure multisignature scheme in quantum random oracle model,” in Proc. Int. Conf. Provable Security (ProvSec), pp. 45–64 (2020).
[9] J. J. Mershia Rabuni, R. Mehala Devi, S. Subhalakshmi, and J. Sudha, “Analysis of operation on spherical fuzzy soft topology and its application,” J. Interdiscip. Math., vol. 28, no. 7, pp. 2707–2732 (2025), doi: 10.47974/JIM-2329.
[10] S. Uygun and E. Akıncı, “A new method for coding theory by third order Jacobsthal sequence,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 3, pp. 1267–1278 (2026), doi: 10.47974/JDMSC-2233.
[11] S. Limkar, S. Singh, W. V. Ashok, V. Wadne, R. Phursule, and S. N. Ajani, “Modified elliptic curve cryptography for efficient data protection in wireless sensor network,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 2-A, pp. 305–316 (2024).
