Exploiting robust quadratic polynomial hyperchaotic map and pixel fusion strategy for efficient image encryption

Abstract

Recently, to offer better protection for images, new image encryption (IE) algorithms have been continuously proposed. However, these algorithms still exhibit some problems, such as poor chaotic performance, flawed key design, and low efficiency. To solve these problems, we first constructed a robust hyperchaotic map called 2D-SQPM. Then, we further developed an efficient IE algorithm based on 2D-SQPM and a pixel fusion strategy (IEASP). The robustness and superiority of 2D-SQPM were verified through several chaotic indicators. These indicators include the Lyapunov exponent, sample entropy, Kolmogorov entropy, and permutation entropy, with average values of 11.5129, 2.8861, 2.4262, and 0.99989, respectively. Several targeted measures were devised in IEASP. Specifically, the common keystream avoids the need to constantly change secret keys. Pixel fusion reduces the computational cost of encryption operations. Two rounds of vector-level image filtering, chaotic pixel superposition, and intra-vector quick scrambling speed up encryption while strengthening security. The security and superiority of IEASP were confirmed through extensive experiments. IEASP achieved excellent scores for correlation coefficients (<0.005), information entropy (7.9998), NPCR (99.6096), and UACI (33.4643). Notably, IEASP also achieved an impressive average encryption rate of 56.3358 Mbps. Due to our targeted designs, IEASP outperforms many recently reported leading IE algorithms in several aspects, particularly in encryption efficiency.