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Recent years have seen the rapid spread of biometric technologies for automatic people recognition. However, security and privacy issues still represent the main obstacles for the deployment of biometric-based authentication systems. In this paper, we propose an approach, which we refer to as BioConvolving, that is able to guarantee security and renewability to biometric templates. Specifically, we introduce a set of noninvertible transformations, which can be applied to any biometrics whose template can be represented by a set of sequences, in order to generate multiple transformed versions of the template. Once the transformation is performed, retrieving the original data from the transformed template is computationally as hard as random guessing. As a proof of concept, the proposed approach is applied to an on-line signature recognition system, where a hidden Markov model-based matching strategy is employed. The performance of a protected on-line signature recognition system employing the proposed BioConvolving approach is evaluated, both in terms of authentication rates and renewability capacity, using the MCYT signature database. The reported extensive set of experiments shows that protected and renewable biometric templates can be properly generated and used for recognition, at the expense of a slight degradation in authentication performance.