Embodiments may provide distance computations on homomorphic and/or functional encrypted vectors while detecting whether the resulting distance has wrapped around due to the vectors having elements not in an allowed range. A method of user authentication processing may comprise receiving and storing enrollment information from a client computer system, the enrollment information comprising a template of authentication data and at least one additional encrypted vector, receiving an additional template to be used to authenticate the user from the client computer system, authenticating the user using the received additional template using the stored template and the stored at least one additional encrypted vector, and determining that authentication is successful when the received additional template matches the stored template and is valid based on the stored at least one additional encrypted vector.