Homomorphic cryptography: Challenges and perspectives

The study proposes practical recommendations and future directions to improve HE’s relevance in the real world, especially in healthcare, digital forensics, Machine Learning (ML), and smart infrastructure. The primary product of this study is a cohesive framework that unifies mathematical foundations with real-world applications to direct the implementation and development of Homomorphic Cryptography (HC) in privacy-preserving computing. Homomorphic Encryption (HE), which is an innovative cryptographic technique, protects confidentiality, integrity, and authenticity in untrusted computing environments such as cloud infrastructure and Internet of Things (IoT) ecosystems by allowing computations on encrypted data without the need for decryption. The present study provides an in-depth investigation of HC, identifying symmetric and asymmetric methods and assigning them to the appropriate security services. The mathematical complexities of well-known HE algorithms like BGV, BFV, DGHV, and CKKS are further explained, and experimental performance evaluations are provided using the Python-SEAL and Microsoft SEAL libraries. The paper examines contemporary attacks and defences while highlighting significant drawbacks, such as computational cost and security flaws.