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Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

An Image Encryption and Text Encryption Scheme Based on an Elliptic Curve using Montgomery Curve and Haga's function

Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 757--780 | DOI:10.5890/DNC.2025.12.011

Muhammad Aqil$^{1}$, Mukhtar Ahmad$^{2}$, Ather Qayyum$^{3\dagger}$, Ibrahim K. Alsulami$^{4}$, Abdulnaser Fakhrou$^{5}$, Gulnaz Atta$^{6}$

$^{1}$ Department of Mathematics, The Islamia University of Bahawalpur, Pakistan

$^{2}$ Department of Mathematics, Khawja Fareed University of Engineering and Information Technology R.Y.K, Pakistan

$^{3}$ Department of Mathematics, University of Southern Punjab Multan Pakistan

$^{4}$ Department of Science, King Abdulaziz Military Academy (KAMA), Riyadh, Saudi Arabia

$^{5}$ Department of Psychological Sciences-college of Education, Qatar University

$^{6}$ Department of Mathematics, University of Education Lahore DGK Campus, Pakistan

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Abstract

The internet is gradually becoming a riskier medium of communication for all types of highly sensitive information. Individuals, institutions, and organizations greater reliance on the internet to conduct business processes has created a fertile ground for intruders to launch various attacks on the system and network. The security of crucial secret information such as personal identifying information, credit card details, online transactions, and e-commerce is of the utmost importance, and it is dependent on cutting-edge cryptography. The article proposes an alternative cryptography algorithm based on mathematical objects known as elliptic curves. In this paper, firstly a new text encryption technique is described in which a private key can be created using the Haga's theorem. Secondly, a new image encryption technique that makes use of specific functions such as the Haga's function and the Montgomery Curve is introduced. The proposed algorithm's effectiveness is verified by experimental testing and the usage of modern security tools. The simulation results and comparison of the proposed approach to existing image encryption algorithms show that it provides a sufficient level of security.

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