Accessing private data always requires a complex negotiation process. This process becomes even more challenging under privacy regulations such as the General Data Protection Regulation and the California Consumer Privacy Act. However, in most cases, the availability of greater amounts of data leads to significant technological breakthroughs. The perfect example is the ImageNet classification challenge, which leads to significant improvements in the image recognition area. The combination of these concerns raises the question of performing computations on data that cannot be seen, and a whole new research field that consolidates privacy-preserving concepts and modern data mining techniques comes into place. This is also the purpose of the work presented in this paper, the discovery of Secure Multi-Party Computation (SMPC) capabilities on protecting privacy during the machine learning process. The main attention is paid towards the combination of SMPC and image classification approach based on the convolutional neural network, especially the secure inference process on the encrypted magnetic resonance images.