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

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.