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
