Thumbnail-preserving encryption (TPE) schemes have been continuously proposed in recent years. It is well known that the thumbnail block size affects the usability and privacy of ciphertext images, but there is no definitive method for determining block size. In this paper, firstly, we propose a new chaotic model called the Delayed Logarithmic Logistic Chaotic Model (DLLM). The simulation experiments show that this model has excellent chaotic properties and can generate complex pseudo-random sequences. Then, we design a DLLM-based TPE scheme. It makes each ciphertext image achieve a good balance of usability and privacy by expanding the range of block size and using a face comparison algorithm to determine the optimal block size.
Deng et al. (2025) studied this question.