Data privacy is crucial when dealing with biometric data. Accounting for the latest European data privacy regulation and payment service directive, biometric template protection is essential for any commercial application. Ensuring unlinkability across biometric service operators, irreversibility of leaked encrypted templates, and renewability of e.g., voice models following the i-vector paradigm, biometric voice-based systems are prepared for the latest EU data privacy legislation. Employing Paillier cryptosystems, Euclidean and cosine comparators are known to ensure data privacy demands, without loss of discrimination nor calibration performance. Bridging gaps from template protection to speaker recognition, two architectures are proposed for the two-covariance comparator, serving as a generative model in this study. The first architecture preserves privacy of biometric data capture subjects. In the second architecture, model parameters of the comparator are encrypted as well, such that biometric service providers can supply the same comparison modules employing different key pairs to multiple biometric service operators. An experimental proof-of-concept and complexity analysis is carried out on the data from the 2013-2014 NIST i-vector machine learning challenge.