Example systems and methods for biometric authentication that can bridge fuzzy extractors with deep learning and achieve the goals of preserving privacy and providing recoverability from zero are disclosed. Embeddings comprising a face or speaker embedding in a non-Hamming distance space can be processed to create a personal reliable bit map and a reliable locality-sensitive hash (LSH) for mapping the non-Hamming distance space to a Hamming distance space. A fuzzy extractor can be applied to create metadata that can be stored on a computing device. A secret can be recovered from the metadata and can be used for identification.