Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption

Abstract

Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaotic system and a 2D sinusoidally constrained polynomial hyper-chaotic map (2D-SCPM). Then, we elaborately developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM (MIEA-FCSM). The introduction of the fractional-order 3D Lorenz chaotic system with the fourth parameter not only enables MIEA-FCSM to have a significantly large key space but also enhances its overall security. Compared with recent alternatives, the structure of 2D-SCPM is simpler and more conducive to application implementation. In our proposed MIEA-FCSM, multi-channel fusion initially reduces the number of pixels to one-sixth of the original. Next, after two rounds of plaintext-related chaotic random substitution, dynamic diffusion, and fast scrambling, the fused 2D pixel matrix is eventually encrypted into the ciphertext one. According to numerous experiments and analyses, MIEA-FCSM obtained excellent scores for key space (2541), correlation coefficients (<0.004), information entropy (7.9994), NPCR (99.6098%), and UACI (33.4659%). Significantly, MIEA-FCSM also attained an average encryption rate as high as 168.5608 Mbps. Due to the superiority of the new fractional-order chaotic system, 2D-SCPM, and targeted designs, MIEA-FCSM outperforms many recently reported leading image encryption algorithms.

Optical Encryption Using Attention-Inserted Physics-Driven Single-Pixel Imaging

“…In the proposed cryptosystem, the encrypted ciphertext comes from the output of the attention module. The key space [41,42,45] can be infinite because either the two sequences of single-pixel measurements or the input cryptographic key sequence are random with unlimited dynamic range.…”

“…Therefore, the forward propagation process of this module can also be regarded as the encryption of these three input vectors. Based on this concept, this paper proposes a physically driven neural network SPI encryption scheme using the above attention module to deal with multi-image encryption tasks [39][40][41][42]. We let the two vectors of the attention module be taken from single-pixel measurements that correspond to two different object images and set the sequence of cryptographic keys as the third vector.…”

Real-Time Synchronisation of Multiple Fractional-Order Chaotic Systems: An Application Study in Secure Communication

“…In [20], an innovative approach to the encryption of colour images was proposed, where the algorithm was based on extended DNA coding, the Zig-Zag transform, and a fractional-order laser system [21]. Other notable works in this area include "Achieving Superior Multi-Image Encryption Through the Use of Recently Conceived Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map" [22] and "Fragmentary Fractional Order Systems: Modeling and Initialization Using the Infinite State Representation" [23].…”

Frequency-domain image encryption based on IWT and 3D S-box

“…Chaos is widely used and highly respected in the field of image encryption due to its unpredictability, pseudorandomness, and high sensitivity to initial values. At present, a variety of encryption methods have been proposed, including quantum cipher [13][14][15], bit-level encryption [16][17][18], discrete wavelet transform [19][20][21], thumbnail-preserving encryption [22][23][24], biological coding [25][26][27], discrete cosine transform [28][29][30], Fourier transform [31][32][33], chaos theory [34][35][36][37][38][39][40] and so on [41][42][43][44][45].…”