Abstract
A chaotic system refers to a deterministic system with seemingly random irregular motion, and its behavior is uncertain, unrepeatable, and unpredictable. In recent years, researchers have proposed various image encryption schemes based on a single low-dimensional or high-dimensional chaotic system, but many algorithms have problems such as low security. Therefore, designing a good chaotic system and encryption scheme is very important for encryption algorithms. This paper constructs a new double chaotic system based on tent mapping and logistic mapping. In order to verify the practicability and feasibility of the new chaotic system, a displacement image encryption algorithm based on the new chaotic system was subsequently proposed. This paper proposes a displacement image encryption algorithm based on the new chaotic system. The algorithm uses an improved new nonlinear feedback function to generate two random sequences, one of which is used to generate the index sequence, the other is used to generate the encryption matrix, and the index sequence is used to control the generation of the encryption matrix required for encryption. Then, the encryption matrix and the scrambling matrix are XORed to obtain the first encryption image. Finally, a bit-shift encryption method is adopted to prevent the harm caused by key leakage and to improve the security of the algorithm. Numerical experiments show that the key space of the algorithm is not only large, but also the key sensitivity is relatively high, and it has good resistance to various attacks. The analysis shows that this algorithm has certain competitive advantages compared with other encryption algorithms.