# Empirical Study of Fully Homomorphic Encryption Using Microsoft SEAL
## 2 Related Works
### Research Trends and Challenges  
Homomorphic encryption (HE) is a form of encryption that allows computations to be performed on ciphertexts, producing an output which, when decrypted, matches the result of operations applied to the plaintexts. This innovative approach to data security enables the analysis of sensitive information without exposing the underlying data, thus ensuring privacy and confidentiality in digital transactions. Homomorphic encryption can be broadly categorized into three types, each offering different levels of functionality and efficiency. Partially homomorphic encryption (PHE) is the simplest form of homomorphic encryption, supporting either addition or multiplication operations on encrypted data, but not both. PHE has been the basis for many early applications of homomorphic encryption due to its relatively straightforward implementation and lower computational requirements compared to more advanced forms. Somewhat homomorphic encryption (SHE) extends the capabilities of PHE by allowing a limited number of both additions and multiplications on encrypted data. However, the depth of these operations is constrained, as performing too many operations can degrade the integrity of the encryption, rendering the data unusable. Finally, fully homomorphic encryption (FHE) represents the most ad vanced form of homomorphic encryption, enabling an unlimited number of additions and multiplications on encrypted data without compromising the encryption's integrity. This level of functionality allows for complex computations on encrypted data, making FHE a highly sought-after solution for secure data processing in sensitive applications. Since the conception of fully homomorphic encryption by [PERSON] in 2009, presenting a lattice-based construction that proved the feasibility of FHE [8], the field has seen rapid advancements and an interesting range of applications. The authors in [11] introduce a secure and anonymous face verification scheme utilizing FHE and the SEAL Microsoft library. Their proposal contains a three-party architecture with a client, a data server, and an authentication server. The scheme ensures privacy by preventing the disclosure of facial data and indices to untrusted servers. They use the Brakerski-Fan-Vercauteren (BFV) homomorphic encryption scheme integrated with private information retrieval for efficient query processing that maintains user anonymity. It operates with a communication volume of 264 KB and completes verifications in 84.91 ms, making it suitable for devices with limited computational power. The rigorous security analysis confirms that the scheme robustly protects sensitive facial features and verification indices while ensuring minimal data exposure, even in untrusted cloud environments. Other novel works in related fields could benefit from the integration of FHE. For instance, integrating FHE with the Signal Noise Separation-Based Network (SNIS) for image forgery detection method proposed in [12] could enhance privacy-preserving image analysis. By adapting SNIS algorithms to process encrypted data using an optimized FHE scheme like Cheon-Kim-Kim-Song (CKKS), sensitive images could be analyzed without decryption, ensuring data confidentiality and compliance with data protection laws such as GDPR and HIPAA. From a different approach, a framework for employing FHE over neural network graphs, specifically applying it to vision-based tasks and agricultural yield forecasting using a privacy-preserving machine learning model on encrypted data, is introduced in [13]. Their framework utilizes the CKKS encryption scheme integrated within Microsoft SEAL. They focus on enhancing the usability of FHE in practical deep learning scenarios by automating cyphertext parameterization and optimizing graph traversal and computational graph configurations for neural networks.