A Polynomial-Root-Based Lightweight Homomorphic Encryption Scheme to preserve confidentiality in a Cloud Environment

Abstract

The computations can be carried out straightaway on the ciphertext while keeping the underlying plaintext confidential throughout the process with the help of Fully Homomorphic Encryption [FHE]. This study aimed to develop an enhanced FHE framework using polynomial structures and implant techniques to maintain mathematical accuracy with fewer processing requirements. The novel design incorporates three major components: secret key generation based on polynomial matrices, public key masking using numeric attributes, and a scaling mechanism to standardise and merge the hidden information. Together, these components offer a structured approach to perform operations on protected data while preserving its privacy. The algebraic structure of the polynomial is designed with security aspects that improve operational efficiency in the proposed techniques. By creating a direct linkage between polynomial structure and the encryption process, data confidentiality is maintained as the secret keys are generated from the defined polynomial relationships, which diminishes unnecessary transformation steps and provides a practical alternative to orthodox homomorphic encryption approaches. The accuracy of homomorphic computations is maintained by calculating the scaling factor from the ratio of the aggregated polynomial coefficients to the corresponding aggregated ciphertext results. This normalisation helps to regulate the increase in ciphertext values during computation and keeps the encrypted results reliable with the intended plaintext operations without adding substantial computational challenges.