Abstract
This article proposes an image compression and encryption algorithm based on 3-D logistic-sine-memristor coupled map (3D-LSMCM), compressed sensing (CS), and the game-of-life scrambling with semi-tensor product (STP-GoL) to solve the problems of computational redundancy and security vulnerability in image transmission. First, the 3D-LSMCM is initialized by using a hash function to generate a random chaotic sequence iteratively, and it improves key unpredictability. Second, the semi-tensor product (STP) measurement matrix constructed from these sequences significantly reduces storage requirements in CS while supporting lossless compression through arithmetic coding. STP technology enables flexible matrix dimension design, effectively lowering computational costs. Finally, STP is used to convert logical operations into matrix operations in the entire encryption process. The cryptographic technique consists of the STP-GoL scrambling, chaotic global scrambling with STP (STP-CG), and the chain XOR diffusion based on STP (STP-CXOR). Furthermore, theoretical analysis indicates that the computational complexity of this algorithm is expected to be reduced by approximately 28% compared with recent studies, while the average information entropy of the ciphertext reaches 7.9987. Overall, this study proposes a novel, secure, and efficient image compression and encryption method, with its source code publicly available at https://github.com/Ssshou7/STP-GoL