Quaternion keyed Least Square Approximation for image encryption

Abstract

Securing image data from prying hackers is crucial in safeguarding the secrecy of data. Over the years, this was done by encrypting the image using an algorithm and a key, where the visible image was converted into a meaningless object. It is a difficult problem to design an image encryption technique based on chaotic systems with predictable cryptographic features. In this paper, the Quaternion, along with the Rossler attractor, was used to generate the key combination. The ciphering was done using the Least Square Approximation Algorithm (LSA). The algorithm was tested on a grayscale image database. The algorithm was initially tested in software using MATLAB R2018b, and was implemented in the Cyclone II EP2C35F672C6 device FPGA. On average, for a cipher image, the Peak Signal to Noise ratio (PSNR) was 9.09303 dB and the entropy was 7.9990 bits. For the cipher image, the Number of Pixels Change Rate (NPCR) and Unified Average Change Intensity (UACI) were 99.6039 and 33.4980, respectively. This proved that the algorithm could effectively mitigate the statistical and differential attacks. The key space was 2 (M ×N ×7 ×8), which was sufficiently high and mitigated the brute force attacks. The obtained results confirm that the cipher images resulting from the proposed ciphering scheme possess good cryptographic properties in terms of entropy, PSNR, UACI, NPCR, and keyspace analysis. Furthermore, the strength of the key is evaluated by the NIST test suite.