Lossless Frequency-Domain Image Encryption via 3D Exponential Hyper-Chaotic Map and Integer Lifting Wavelet Transform

To resolve the inherent conflict between high robustness and strict reversibility in frequency-domain image encryption, as well as to eliminate data expansion caused by floating-point errors, this paper presents a novel lossless frequency-domain image encryption scheme via 3D exponential hyper-chaos and integer lifting wavelet transform (ILWT). Firstly, a 3D hyper-chaotic exponential sine map (3D-HESM) is constructed by introducing nonlinear exponential coupling, providing a high-entropy keystream source with wider chaotic ranges than traditional maps. Secondly, to guarantee lossless reconstruction, the ILWT is employed to diffuse image coefficients in the frequency domain. By integrating modular arithmetic into the lifting steps, this transform confines coefficients within the finite integer ring, effectively solving the data expansion problem while maintaining perfect mathematical reversibility. Thirdly, an adaptive key generation protocol is designed by fusing SHA-512 with Singular Value Decomposition (SVD). Leveraging the geometric stability of singular values, this mechanism establishes a balance between extreme sensitivity to plaintext alterations and tolerance to channel noise. Experimental results and security analyses demonstrate that the proposed scheme achieves a vast key space and resists differential attacks. Furthermore, it exhibits superior robustness against data cropping and noise interference compared to state-of-the-art methods, validating its suitability for secure and lossless image transmission.