Fully Homomorphic Encryption (FHE) is a form of encryption that allows arbitrary computations to be performed on encrypted data, without ever decrypting the data. The real-world practicality of FHE is yet limited, and for several reasons, such as the huge computational cost it induces, the lack of implementation support and the immaturity of available libraries and tools. Nevertheless, FHE can be made practical for concrete applications. We intend to apply the homomorphic approach to unlock the technological potential of two specific applications:(1) Privacy-preserving (biometric) authentication. Privacy remains an intricate issue in our era of social networking and online life sharing, in particular when we need to authenticate ourselves. Privacy-preserving technologies are much in demand in more than one context and homomorphic encryption is one of the most promising techniques that underlies these technologies, but it currently lacks user-friendliness, efficiency and concrete implementations. There is no systematic understanding either of how HE can be securely used in this context; some privacy-preserving biometric authentication techniques based on HE have been shown to be vulnerable to some attacks. We intend to solve all these issues.(2) Statistical aggregation of sensitive data. This a key application of homomorphic encryption, one most prominent example being for medical data. A lot remains to be done in that area too before HE can be perceived as a truly transformative technology. Data protection regulations restrict the processing of personal data, in particular with the entering into force of the new GDPR next May. Still, statistical data aggregation might be possible by processing directly on encrypted data.With this project, we plan to conceive and implement new lattice-based FHE schemes specifically optimized for these two targeted applications and invent new ways to overcome the underlying challenges.