Optimalisaties en toepassingen van volledig homomorfe encryptie

In today's digital age, cloud storage and computing have become indispensable. Resource-constrained clients such as individuals and small organisations increasingly rely on powerful servers to store, manage and process their data. However, outsourcing data to external servers leads to significant privacy concerns, particularly when dealing with sensitive information such as medical records, financial transactions, or personal data. Fully homomorphic encryption (FHE) is a cryptographic technique that allows computation over encrypted data. In secure outsourcing with FHE, a client sends encrypted data to a server, which can perform requested computations without accessing the original data. The server returns the resulting ciphertexts, which the client can decrypt to obtain the final output. Despite its strong privacy guarantees, the practical adoption of FHE is limited by two main challenges: efficiency, which arises from the substantial performance overhead of FHE; and integrity, which stems from the lack of mechanisms to verify the correctness of the outsourced computation. In this thesis, we contribute to addressing these challenges in three aspects. First, we optimise oblivious algorithms for use in FHE, achieving improvements in key performance metrics and accelerating both bootstrapping and a range of applications. Second, we build efficient privacy-preserving information systems based on FHE. These include (i) two private machine learning protocols, the k-nearest neighbour algorithm and decision tree evaluation, (ii) SQUID, a secure system for storing and analysing genotype-phenotype data, and (iii) a protocol for securely delegating zero-knowledge proof generation. Third, we construct verifiable secure delegation of computation through FHE techniques. We provide the notion of blind proofs to provide integrity guarantees and demonstrate its practicality using blind zkSNARKs, a concrete instantiation of blind proofs.