Homomorphic Encryption (HE), Artificial Intelligence (AI): An Analysis, Significance and Applications with Coding in Python

Cryptography has changed dramatically, although in ancient times the use of simple ciphers was done manually. Cryptography is based on computationally infeasible problem structures to provide basic security objectives, including confidentiality, data integrity, authentication, and non-repudiation. In the past, cryptography mainly concerned methods of encryption such as substitution and transposition ciphers, as well as mechanical equipment used to hide message content from unauthorized parties. The invention of computers and contributions of researchers such as Claude Shannon transformed cryptography into a scientific and mathematical field of study. Conventional cryptographic algorithms such as AES, RSA, and Elliptic Curve Cryptography (ECC) have been very useful in providing data protection at rest and in transit, but not the confidentiality of data during computation. This limitation poses challenges for modern applications like cloud computing, artificial intelligence, and massive data analytics. Homomorphic Encryption (HE), particularly Fully Homomorphic Encryption (FHE), addresses this issue by enabling computation on encrypted data without decryption. This paper provides an overview of the development of cryptographic algorithms, beginning with classical encryption and extending to Partially Homomorphic Encryption (PHE), Somewhat Homomorphic Encryption (SWHE), and Fully Homomorphic Encryption. Special attention is given to encrypted intelligence systems, where AI models learn and infer on encrypted data while preserving privacy. The paper also analyzes the mathematics of FHE, prominent schemes such as BGV, BFV, and CKKS, and discusses challenges including computational overhead, noise growth, and implementation feasibility, along with future research directions.