A method, system and computer program product for performing computations on sensitive data while guaranteeing privacy. A service provider receives a first and a second ciphertext from a medical provider that homomorphically encrypts matrices A and B, respectively, using an encryption key, where the matrices A and B include medical data encoded as vectors. The service provider performs a homomorphic matrix multiplication on the first and second ciphertexts without decrypting the first and second ciphertexts. An encrypted result from the performed homomorphic matrix multiplication on the first and second ciphertexts is generated and transmitted to the medical provider to decrypt which matches a result of performing a matrix multiplication on unencrypted matrices A and B thereby enabling computations to be performed on the medical data in a secure manner.