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Medical images contain sensitive information that will be shared with healthcare workers, patients, and researchers for diagnostic and research purposes. However, the security of these images during transmission is extremely important, especially after the COVID-19 pandemic. In diagnosis, MRI and CT images are two common medical images, and the two medical images complement each other to a certain extent. The fusion of these two images can help doctors diagnose more intuitively. This paper proposes a zero-watermarking encryption scheme with an authentication function based on multimodal medical image fusion. In addition, an improved three-dimensional Chebyshev and ICMIC closed-loop coupling mapping (3D-CICCM) is proposed and applied to the design of medical image encryption. This scheme mainly includes: medical image fusion based on bilateral filtering and local gradient energy, authentication based on the Fresnel transform, double random phase encryption based on the Fresnel transform and shuffle algorithm, and zero-watermark generation algorithm based on stationary wavelet transform. The experimental results prove the effectiveness of this scheme. [ABSTRACT FROM AUTHOR]