Double image encryption algorithm based on compressive sensing and elliptic curve

A new improved three-dimensional continuous chaotic system (ImproBsys) is designed in this paper. It can achieve from an ordinary chaotic state to a hyperchaotic state, that is, chaotic behavior tends to become more complex. Furthermore, by using ImproBsys, this paper proposes a double image encryption algorithm based on compressive sensing and public key elliptic curve. First, the two plain images of the same size are excuted by discrete wavelet transformation (DWT), and then the DWT coefficients are thresholded. Second, the quantization matrix is compressed by compressive sensing, and the size is reduced to half of the original one, and then the two compressed matrices are spliced together to form a new matrix. Finally, the new matrix is encrypted by elliptic curve cipher to get the cipher image. Our contributions are: (1) A new ImproBsys is designed with better chaotic behavior, which has two positive Lyapunov exponents to show hyperchaos phenomenon. (2) Compressive sensing technique is employed to reduce the amount of data transmission for two single images, and then we use ImproBsys to control the measurement matrix. (3) The initial values of the ImproBsys depend on the information entropy of the plain image by a new constructed mathematical model.(c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

This paper designs a new improved three-dimensional continuous chaotic system that can achieve a transition from an ordinary chaotic state to a hyperchaotic state. Based on this system, a double image encryption algorithm is proposed using compressive sensing and public key elliptic curve. The algorithm employs discrete wavelet transformation, compressive sensing, and elliptic curve cipher to encrypt and compress the images.