Image encryption based on 3D hyperchaotic mapping and its FPGA implementation

As information technology continues to evolve, the importance of ensuring data security has become paramount. Images, being a prevalent multimedia tool, are often vulnerable to unauthorized access. To counter this, numerous encryption schemes have been proposed, but traditional encryption schemes often grapple with issues related to efficiency and security. The field of cryptography urgently requires an encryption algorithm that is both efficient and secure. The advent of chaos theory provides a promising direction for new encryption methods. Owing to its ergodicity, randomness, and sensitivity to initial values, chaos theory has immense potential for image encryption. Consequently, the derived chaotic image encryption algorithm exhibits excellent security and robust interference resistance.

Against this background, this paper introduces an image encryption algorithm based on three-dimensional hyperchaotic mapping. Initially, a new type of memristor is designed using a triangular wave function, which is then cascaded using sine and cosine functions to construct a new three-dimensional memristive chaotic system. Then, based on this system, the parameter-dependent Lyapunov exponent and bifurcation diagram are studied, and the randomness of the generated sequence is validated through the NIST test. The results show that the system possesses a wide parameter range and a considerable chaotic region. Compared with the traditional chaotic system, the one presented here exhibits better chaotic characteristics. The sequences it generates possess stronger randomness. Such features elevate the security and reliability of the encryption process, rendering it ideal for image encryption. Then, the image is scrambled and diffused on the basis of this system. The scrambling stage involves indexing and sorting the original image pixels by a chaotic sequence, effectively disrupting the image structure and pixel distribution and thereby increasing the decryption difficulty. During the diffusion stage, the processed chaotic sequence performs a hierarchical XOR on the pixel values of the scrambled image, enhancing the image complexity and randomness and thus bolstering the security of the encryption algorithm.

The algorithm's effectiveness was validated through software simulations and performance analysis. Software simulations demonstrated that the algorithm could effectively hide the pixel information and restore the image. The performance analysis revealed that the algorithm possesses high security and robust interference resistance. In addition, the algorithm was applied to an FPGA hardware platform for image encryption, expanding the algorithm's application scope.

The algorithm, encompassing both software simulation and hardware implementation, can effectively enhance students' theoretical and practical skills. It enriches their understanding of nonlinear theory, rendering abstract theoretical teaching vivid and tangible. This approach offers new insights and methods for teaching nonlinear system theory, nonlinear circuit design, and other subjects. As technology continues to advance, the potential applications of this algorithm are expected to expand across diverse fields. It is poised to play a significant role in safeguarding people's privacy and enhancing information security with its effective protection measures.