A logistic sine-cosine random-delay chaotic map and its application to robust multi-image compression and encryption

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Abstract In practical image transmission, limited bandwidth and unreliable channels are common challenges. Moreover, multiple images are often transmitted in batches, such as groups of portrait or landscape images. To address these issues in a unified manner, this paper proposes a robust multi-image compression and encryption scheme for channel-impaired environments. First, a logistic sine-cosine random-delay chaotic map is designed. The results of various dynamical system tests demonstrate its strong chaotic characteristics. The proposed chaotic map is used to generate column-dependent measurement matrices for compressed sensing, thereby increasing the diversity and unpredictability of the sensing process. In addition, chaotic sequences are incorporated into the image encryption process to enhance the randomness of the ciphertext. Second, to improve the encryption performance of the overall scheme, a spiral ternary-tree diffusion strategy is designed. This strategy strengthens the interaction among non-adjacent pixels and improves plaintext sensitivity. Finally, to cope with unreliable channels, threshold secret sharing is combined with Reed–Solomon (RS) coding to generate robust share images. As a result, the proposed scheme achieves not only robustness among shares, but also internal robustness within each share. Experimental results show that the proposed scheme maintains high reconstruction quality under different compression ratios, produces near-uniform share images, and supports image recovery from partially corrupted shares when the RS decoding condition is satisfied.

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