Medical images are transmitted via the Internet or the hospital intranet which include many important information about the patient's personal information. Medical image encryption is a technology that can effectively protect the information contained in these medical images. In this paper, we give a secure and trusty Combined Cellular Automata (CoCA) based medical image encryption algorithm. CoCA is made up of a nonlinear CA and a linear 90/150 maximum length CA, and three dimensional generalized chaotic map. The proposed algorithm consists of two phases. The first phase encryption process that changes pixel values of a given image using two CoCAs. The second phase is to change the position of each pixel in the image encrypted using the three dimensional generalized chaotic cat map that can change with effect the position of pixels not only in two dimensions horizontally and vertically but also in color plane three colored channels simultaneously. We show the stability and high reliability of the given color medical image cryptosystem through detailed analysis and various statistical experimental tests.