A novel image encryption scheme based on compressive sensing, elliptic curves and a new jerk oscillator with multistability

Abstract

Abstract Compression and encryption are the two main steps generally used to ensure fast and secure transmission of digital images over public communication channels. Among the existing crypto compression approaches, those based on compressive sensing and chaotic systems possess good potential. Unfortunately, the present literature presents some limits including speed issue, security issue and reconstruction problem. These problems are mainly due to the poor performances of the measurement matrix exploited. Note that in some cases these measurement matrices are obtained from chaotic sequences with very poor dynamics. To solve this problem, we proposed in this paper, a novel image encryption scheme based on 2D compressive sensing, elliptic curves and a new septic jerk oscillator with multistability. The proposed scheme adopts the compression before encryption topology to reduce the processing time and is divided into two main parts. The first part concerns image compression using compressive sensing. The input image data is divided into 4 blocks. Then, each block is compressed using 2D compressing sensing based on the measurements matrices generated using chaotic sequences coming from the novel septic jerk system. Next, the compressed blocks are combined to form the compressed image. In the second part, to strengthen the security, elliptic curve theory is used to construct a simple and secure 8 × 8 S-box for digital image substitution. This S-box is combined with the septic chaotic solutions to change the pixel’s positions and values of the compressed image. The analysis of simulation test indicates that the proposed cipher has good compression effect, good reconstruction capability even for low compression ratio, is fast and highly secure compared to some recent schemes. As such the proposed work can be exploited to compress and secure data in Wireless Body Area Network (WBAN) applications.