To preserve the privacy of patients and service providers in biomedical signal processing applications, particular attention has been given to the use of secure multiparty computation techniques. This thesis focuses on the development of a privacy preserving automatic diagnosis system whereby a remote server classifies a biomedical signal provided by the patient without getting any information about the signal itself and the final result of the classification. Specifically, we present and compare two methods for the secure classification of electrocardiogram (ECG) signals: the former based on linear branching programs and the latter relying on neural networks. Moreover a protocol that performs a preliminary evaluation of the signal quality is proposed. The thesis deals with all the requirements and difficulties related to working with data that must stay encrypted during all the computation steps. The proposed systems prove that carrying out efficiently complex tasks, like ECG classification and quality evaluation, in the encrypted domain is indeed possible in the semihonest model, paving the way to interesting future applications wherein privacy of signal owners is protected by applying high security standards.