Block-based perceptual encryption (PE) algorithms are becoming popular for multimedia data protection because of their low computational demands and format-compliancy with the JPEG standard. In conventional methods, a colored image as an input is a prerequisite to enable smaller block size for better security. However, in domains such as medical image processing, unavailability of color images makes PE methods inadequate for their secure transmission and storage. Therefore, this study proposes a PE method that is applicable for both color and grayscale images. In the proposed method, efficiency is achieved by considering smaller block size in encryption steps that have negligible effect on the compressibility of an image. The analyses have shown that the proposed system offers better security with only 12% more bitrate requirement as opposed to 113% in conventional methods. As an application of the proposed method, we have considered a smart hospital that avails healthcare cloud services to outsource their deep learning (DL) computations and storage needs. The EfficientNetV2-based model is implemented for automatic tuberculosis (TB) diagnosis in chest X-ray images. In addition, we have proposed noise-based data augmentation method to address data deficiency in medical image analysis. As a result, the model accuracy was improved by 10%.