A most likely sequence of states corresponding to an observation sequence stored at a client is determined securely with respect to a HMM stored at a server. An encryption of a log-probability of the current element of the observation sequence is determined for each state of the HMM. A product of an encryption of the log-probability of the state for the current element, an encryption of a transition probability to the state, and the encryption of a log-probability of the current element of the observation sequence is determined iteratively, for each state of the HMM, to produce an encrypted matrix of indexes of the states; and the encrypted matrix is transmitted to the client.