Medical image security can be enhanced by using watermark (WM), which is formed using an identifier of the image (ID). Identifier may consist of doctor's digital signature or personal number. We propose a reversible WM secret system consisting of modulo addition of the mark into a cover image. This approach is only applicable to image storing formats, that utilize no transform domain compression techniques. There is also a restriction to the image format type, so that image compression should either be lossless or image should be compressed before the embedding. The referent pattern of WM is the secret key of the system, which can be generated randomly or evaluated from doctors' personal ID's. The use of modulo operations for WM embedding allows us to recover the exact original image. In order to avoid significant degradation of the WM detection efficiency, we propose an adaptive choice of WM detector and WM intensity combined with error-correcting codes. With this approach the watermarked images cannot be used as-is for medical applications because of visible distortion.