We explore the possible ways modern cryptographic methodscan be applied to the field of medical data analysis. Current systems require large computational facilities owned by the data owners or excessive trust given to the researchers. We implement one possible solution inwhich researchers operate directly on homomorphically encrypted data and the data owner decrypts the results. We test our implementation on large datasets and show that it is sufficiently practical that it could be a helpful tool for modern researchers. We also perform a heuristic analysis of the security of our system.