Fully Homomorphic Encryption and applications to Machine Learning

Fully Homomorphic Encryption (FHE) is a cryptographic technique that enables computations to be performed directly on encrypted data, without needing to decrypt it first. This capability has the potential to revolutionize how sensitive information is processed in a variety of fields, including Machine Learning (ML). In recent years, ML has been applied to numerous real-world problems, many of which rely on a client-server framework where sensitive data is sent to powerful servers for processing. Nevertheless, this structure poses significant privacy challenges, as client data must be shared with third parties for model training and inference, exposing it to potential breaches and misuse. FHE offers a promising solution, ensuring that sensitive information remains private throughout the process. However, encrypting data with FHE comes with a price: the computational effort can be high, and this can become a problem when considering complex tasks. This thesis explores the integration of FHE with ML algorithms, focusing on the tradeoff between safeguarding data confidentiality and keeping the model accurate and efficient. We discuss the theoretical foundations of FHE, presenting its origins and main employments, focusing on its role in preserving privacy in ML scenarios, and on the practical challenges of implementing FHE in real-world applications. In particular, we analyze three ML algorithms: K-Nearest Neighbors, Support Vector Machines, Decision Tree (and Random Forest), and we compare encrypted and unencrypted models, describing some of the proposed solutions in literature. Our goal is to give a general idea, showing how TFHE and CCKS, two of the main FHE schemes, are integrated with the aforementioned ML methods. Our work demonstrates the potential of FHE to enable secure ML safeguarding user privacy, so that the clients' data can be processed by servers without any information leakage.