The optimized Diffie-Hellman key exchange using the graphical method

Aljader, Huda Kadhim M.; Ajeena, Ruma Kareem K.

doi:10.47974/JDMSC-1615

Open Access Research Article

The optimized Diffie-Hellman key exchange using the graphical method

^*Huda Kadhim M. AljaderCorresponding authorhuda.kadom.pure347@student.uobabylon.edu.iqDepartment of MathematicsEducation College for Pure SciencesUniversity of BabylonBabil, IraqView full profile → , Ruma Kareem K. Ajeenapure.rume.k@uobabylon.edu.iqDepartment of MathematicsEducation College for Pure SciencesUniversity of BabylonBabil, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1691–1697Vol. 26Issue 6September 2023DOI: 10.47974/JDMSC-1615 Crossmark XML

Received:: 05 Mar 2022
Accepted:: 05 Apr 2022
Published Online:: 01 Jun 2023
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1615
Pages:: 1691–1697

Abstract

In this paper, we describe a new contribution that uses the optimization problem to create a new version of the Diffie-Hellman key exchange (DHKE). The proposed version depended on the optimized discrete logarithm functions (ODLFs) that are given as a new definition in this work. A graphical method considers a fundamental tool to compute a shared secret key (SSK) in the proposed optimized Diffie-Hellman key exchange (ODHKE). The ODHKE is a more secure protocol for computing the SSK in comparison with the original DHKE.

Keywords

Cryptography Optimization problem Graphical method ODHKE ODLFs Security

Subject Classifications

11T7114G5049-xx

References

[1] Ajeena, Ruma Kareem K. “The Graph and its Role for Speeding up the Elliptic Scalar Multiplication Algorithms.” 2019 2nd International Conference on Engineering Technology and its Applications (IICETA). IEEE (2019).
[2] Ajeena, Ruma Kareem K. “The soft graphic integer sub-decomposition method for elliptic scalar multiplication.” Journal of Discrete Mathematical Sciences and Cryptography 24.6, 1751-1765 (2021).
[3] Aljamaly, Karrar Taher R., and Ruma Kareem K. Ajeena. “The elliptic scalar multiplication graph and its application in elliptic curve cryptography.” Journal of Discrete Mathematical Sciences and Cryptography 24.6, 1793-1807 (2021).
[4] Aljamaly, Karrar Taher R., and Ruma Kareem K. Ajeena. “Undirected Complete Graph to Design New Public Key Cryptosystem.” Journal of Physics: Conference Series, IOP Publishing, Vol. 1897. No. 1. (2021).
[5] Hashim, Hashim Madlool, and Ruma Kareem K. Ajeena. “The Computational Complexity of the Elliptic Curve Factorization Algorithm over Real Field.” Journal of Physics: Conference Series, IOP Publishing, Vol. 1897. No. 1. (2021).
[6] Diffie, Whitfield, and Martin E. Hellman. “New directions in cryptography.” Secure communications and asymmetric cryptosystems. Routledge, 143-180 (2019).
[7] Kumar, Chaithanya, and PM Durai Raj Vincent. “Enhanced diffie-hellman algorithm for reliable key exchange.” IOP conference series: materials science and engineering, IOP Publishing, Vol. 263. No. 4. (2017).
[8] Jirakitpuwapat, Wachirapong, and Poom Kumam. “The generalized Diffie-Hellman key exchange protocol on groups.” International Econometric Conference of Vietnam. Springer, Cham (2018).
[9] Hoffstein, Jeffrey, et. al. An introduction to mathematical cryptography, New York: springer, Vol. 1. (2008).
[10] Mäurer, Nils, et. al. “Comparing different Diffie-Hellman key exchange flavors for LDACS.” 2020 AIAA/IEEE 39th Digital Avionics Systems Conference (DASC). IEEE (2020).
[11] Gupta, Chiradeep, and NV Subba Reddy. “Enhancement of Security of Diffie-Hellman Key Exchange Protocol using RSA Cryptography.” Journal of Physics: Conference Series, IOP Publishing, Vol. 2161. No. 1. (2022).

Views: 343Downloads: 122Citations: 0