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Asymmetric Key Cryptosystem for Image Encryption by Elliptic Curve over Galois Field

Mohammad Mazyad Hazzazi1, Hafeez Ur Rehman2,*, Tariq Shah2, Hajra Younas2

1 Department of Mathematics, College of Science, King Khalid University, Abha, 61421, Saudi Arabia
2 Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

* Corresponding Author: Hafeez Ur Rehman. Email:

Computers, Materials & Continua 2023, 76(2), 2033-2060.


Protecting the integrity and secrecy of digital data transmitted through the internet is a growing problem. In this paper, we introduce an asymmetric key algorithm for specifically processing images with larger bit values. To overcome the separate flaws of elliptic curve cryptography (ECC) and the Hill cipher (HC), we present an approach to picture encryption by combining these two encryption approaches. In addition, to strengthen our scheme, the group laws are defined over the rational points of a given elliptic curve (EC) over a Galois field (GF). The exclusive-or (XOR) function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key matrix. By integrating the inverse function on the pixels of the image, we have improved system security and have a wider key space. Furthermore, through comprehensive analysis of the proposed scheme with different available analyses and standard attacks, it is confirmed that our proposed scheme provides improved speed, security, and efficiency.


Cite This Article

M. M. Hazzazi, H. U. Rehman, T. Shah and H. Younas, "Asymmetric key cryptosystem for image encryption by elliptic curve over galois field," Computers, Materials & Continua, vol. 76, no.2, pp. 2033–2060, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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