Asymmetric Image Encryption Based on Singular Cubic Curve with Chaotic Map

Abstract

Due to the potential security problem of the key management and distribution for the symmetric image encryption schemes, this paper proposes a new asymmetric image encryption method based on a singular cubic curve and chaos theory. The Diffie-Hellman algorithm is used to generate the initial values of a chaotic map by exchanging public keys. The image encryption process is carried out using a chaotic map, in which a random sequence of the same length as the image to be encrypted is generated using the standard map, and then bitwise XOR is used to create confusion in the image's pixels. Also, an Arnold cat map is used to change the location of pixels and diffusion in them is obtained. Gray images with size 256×256 are used in this algorithm. The simulation results and security analysis indicate that the scheme can withstand common attacks such as statistical attacks, differential attacks, and other attacks.