MODELING OF A QUANTUM KEY EXCHANGE SCHEME BASED ON ELLIPTIC CURVE CRYPTOGRAPHY

Received: 2026-07-15 13:01:55

Published: 2026-04-18

Abstract

In this article, the key exchange process based on elliptic curve cryptography (ECC) and its quantum simulation are implemented using the Qiskit environment. Alice and Bob generate their secret and public keys by adding and multiplying points on the elliptic curve. After that, they calculate a common key and check whether this key has the same result. In the article, Hadamard and CNOT quantum gates are used as quantum simulation stages, through which the superposition and entanglement processes in quantum states are modeled. The results show that quantum computing can further improve secure key exchange systems based on ECC.

List of references

  1. Swan M. Blockchain: Blueprint for a New Economy. — Sebastopol, CA, USA: O’Reilly Media, 2015. — 352 p.

  2. Bennett C. H., Brassard G. Quantum cryptography: Public key distribution and coin tossing //Proc. IEEE Int. Conf. Comput. Syst. Signal Process. — 1984. — P. 175–179.

  3. Lenstra A. K., Verheul E. R. Selecting cryptographic key sizes // Journal of Cryptology. — 2001. — Vol. 14, № 4. — P. 255–293.

  4. Shor P. W. Polynomial–time algorithms for prime factorization and discrete logarithms on a quantum computer // SIAM Review. — 1997. — Vol. 41, № 2. — P. 303–332.

  5. Diffie W., Hellman M. E. New directions in cryptography // IEEE Transactions on Information Theory. — 1976. — Vol. 22, № 6. — P. 644–654.

  6. Rivest R. L., Shamir A., Adleman L. A method for obtaining digital signatures and public–key cryptosystems // Communications of the ACM. — 1978. — Vol. 21, № 2. — P. 120–126.

  7. Koblitz N. Elliptic curve cryptosystems // Mathematics of Computation. — 1987. — Vol. 48, № 177. — P. 203–209.

  8. Miller V. S. Use of elliptic curves in cryptography // Advances in Cryptology — CRYPTO '85. — 1986. — P. 417–426.

  9. Menezes A. J., van Oorschot P. C., Vanstone S. A. Handbook of Applied Cryptography. — Boca Raton: CRC Press, 1996. — 780 p.

  10. Gentry C. Fully homomorphic encryption using ideal lattices // Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC '09). — 2009. — P. 169–178.

  11. Joye M., Yen S.–M. The Montgomery power ladder in elliptic curve cryptography // Cryptology ePrint Archive, Report 2002/088. — 2002. — URL: https://eprint.iacr.org/2002/088.

  12. Galbraith S. D., Lin X. Implementing cryptographic pairings // Post–Quantum Cryptography.— 2011. — P. 265–289.

  13. Hoffstein J., Pipher J., Silverman J. H. An Introduction to Mathematical Cryptography. — New York: Springer Science & Business Media, 2008. — 512 p.

  14. Menezes A., Vanstone S. Practical Cryptography in the Global Computing Environment // Proceedings of the 1st Workshop on Cryptography and Network Security. — 1994. — P. 1–16.

  15. Wang W. A blockchain–based quality acceptance system for construction projects with human– computer interaction // Proc. Int. Conf. Eng. Constr. Manage. Innov. — 2024. — P. 300–305.

  16. Zhang G. et al. A blockchain–based method and system for the quality acceptance of concealed engineering // Proc. Int. Symp. Cybersecurity Inf. Secur. — 2024. — P. 20–25.

  17. Zubayda Jumayeva, Nurbek Khushvaktov, Rustam Nizomov. BIO Web Conf., 173 (2025) 01030. DOI:https://doi.org/10.1051/bioconf/202517301030

About the Authors

D.T. Muhamediyeva
Tagaev Farkhad Abduvahabovich

License

How to Cite

[1]
D.T. Muhamediyeva and Tagaev Farkhad Abduvahabovich trans. 2026. MODELING OF A QUANTUM KEY EXCHANGE SCHEME BASED ON ELLIPTIC CURVE CRYPTOGRAPHY. Uzbekistan Open Conference. 1 (Apr. 2026), 252–260. DOI:https://doi.org/10.57033/.

Similar Articles

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)