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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 novel public key cryptosystem considering elliptic curve principles

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pp. 343–348Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-2600 Crossmark XML
Received:
08 Apr 2025
Published Online:
27 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2600
Pages:
343–348

Abstract

The unique public key cryptosystem presented in this work is built on the fundamental concepts of elliptic curves. The proposed method aims to offer a versatile and efficient Public Key Cryptography (PKC) solution by utilizing the inherent properties of elliptic curves. The mathematical foundations of elliptic curves are reviewed, with particular emphasis on their suitability for cryptography applications. This work improves the study of elliptic curve principles in the design of public key cryptosystems by providing a fresh perspective on generating efficient cryptographic solutions without compromising security.

Keywords

Subject Classifications

11G0794A6015A09

References

[1] W. Diffie and M. E. Hellman, “New directions in cryptography,” in Democratizing Cryptography: The Work of Whitfield Diffie and Martin Hellman, pp. 365–390 (2022).
[2] L. R. Celemín, “McEliece Cryptosystem,” Citeseer (2011). 
[3] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, vol. 21, no. 2, pp. 120-126 (1978).
[4] T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Transactions on Information Theory, vol. 31, no. 4, pp. 469–472 (1985).
[5] M. I. Saju, R. Varghese, and E. F. A. John, “A design of public key cryptosystem in an algebraic extension field over a finite field using the difficulty of solving DLP,” Malaya Journal of Matematik, vol. 8, pp. 459–463 (2020).
[6] J. Pauly, M. I. Saju, R. Varghese, and E. F. A. John, “Design of public key cryptosystem based on the underlying mathematical complexity,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 3, pp. 973–984 (2025).
[7] N. Koblitz, “Elliptic curve cryptosystems,” Mathematics of Computation, vol. 48, no. 177, pp. 203–209 (1987). 
[8] V. S. Miller, “Use of elliptic curves in cryptography,” in Proceedings of the Conference on the Theory and Application of Cryptographic Techniques, Springer, pp. 417–426 (1985).
[9] R. Haakegaard and J. Lang, “The elliptic curve Diffie-Hellman (ECDH),” [Online]. Available: https://koclab.cs.ucsb.edu/teaching/ecc/project/2015Projects/Haakegaard+Lang.pdf, December (2015). 
[10] G. Filippone, “On the discrete logarithm problem for elliptic curves over local fields,” arXiv preprint arXiv:2304.14150 (2023).
[11] S. Aikins-Bekoe and J. B. Hayfron-Acquah, “Elliptic curve Diffie-Hellman (ECDH) analogy for secured wireless sensor networks,” International Journal of Computer Applications, vol. 176, no. 10, pp. 1–8 (2020). 
[12] M. S. Hijazi, N. Tahat, A. A. Tahat, R. Raft, and E. S. Ismail, “Authenticated encryption scheme based on ECDLP and DLP,” Applied Mathematics and Information Sciences, vol. 14, no. 3, pp. 425–430 (2020).
[13] J. H. Silverman, “The Arithmetic of Elliptic Curves,” 2nd ed., vol. 106, Springer, June (2009). 
[14] D. S. Kumar, C. Suneetha, and Chandrasekhar, “Encryption of data using elliptic curve over finite fields,” arXiv preprint arXiv:1202.1895, February (2012).
[15] G. Mittal, S. Kumar, and S. Kumar, “Novel public-key cryptosystems based on NTRU and algebraic structure of group rings,” Journal of Information and Optimization Sciences, vol. 42, no. 7, pp. 1507–1521 (2021).
[16] Ö. Küsmüş and T. Hanoymak, “A novel public-key encryption scheme based on Bass cyclic units in integral group rings,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 2, pp. 579–589 (2022).
[17] Q. M. Luhaib and R. K. K. Ajeena, “Elliptic curve matrices over group rings to improve elliptic curve–discrete logarithm cryptosystems,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 6, pp. 1699–1704 (2023).

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