Fully Homomorphic Encryption Applications: The Strive Towards Practicality

PhD ThesisFully Homomorphic Encryption (FHE) schemes are becoming evermore prevalent in the cryptography domain. They allow computation on encrypted data without the necessity of decryption, thus opening a plethora of new applications relating to cloud computing and cryptography. FHE schemes have been viewed generally as being impractical in a real-world scenario, thus leading to a relatively slow uptake within industry despite the high level of interest in the topic. This has caused a lack of FHE applications and thus various practical questions have not been tackled due to such problems not arising or going unnoticed within research. This thesis explores three contrasting FHE applications, each of which contain new ideas and overcome challenges within FHE. Namely, we analyse applications that require signi cant levels of bootstrapping, alternative data representations as well as the possibility of using FHE in the anonymity domain. Proofs of concept have been developed for each application to display the feasibility of each idea. The aim of this research is to present the mathematics of FHE in a comprehensive manner to improve the accessibility of concepts within FHE. Furthermore we analyse the usability and versatility of FHE in various scenarios with the aim to demonstrate the practicality of using FHE in a real-world setting