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The procedure for extracting a cryptographic key from noisy sources, such as biometrics and physically uncloneable functions (PUFs), is known as fuzzy extractor (FE). Although FE constructions deal with discrete sources, most noisy sources are continuous. In the continuous case, it is required to transform the source to a discrete one. We introduce a 1) model-based uncoupling construction that directly deals with the continuous noisy source and produces helper data uncoupling the discrete representation from the noisy source, guaranteeing the diversity of the discrete representation, and making it more robust and a 2) strengthened uncoupled fuzzy extractor , suitable for privacy-preserving applications, which integrates an additional fixed authentication factor and obtains a key uncoupled to the noisy sources and unlinkable helper data. We present optimal model-based uncoupling constructions for Gaussian sources. Specifically, we show how to: 1) extract one or multiple bits from a single Gaussian source; 2) extract one bit from several unreliable Gaussian sources; and 3) provide a general procedure to obtain an optimal uncoupled FE from Gaussian source(s). Our experiments show that the proposed constructions achieve much higher security levels for wide operational scenarios, approximately doubling the obtained effective key length without affecting false rejection rates.