RLHMBC: A novel lightweight symmetric cipher supporting multiplicative homomorphism

Homomorphic Encryption (HE), which enables computations to be done directly on encrypted data without sacrificing privacy, has become a key technology for safe data processing in recent years. Thus, the creation of a novel multiplicative block cipher scheme is the primary goal of this work. The suggested technique intends to increase the efficiency and security of homomorphic operations, particularly in applications needing safe outsourced computations, such as healthcare and financial ones. The RLHMBC (Robust and Lightweight Homomorphic Multiplicative Block Cipher) relies on four fundamental homomorphic operations that form the core of each encryption round: a homomorphic substitution box (S-box), a homomorphic permutation box (P-box), a homomorphic diffusion matrix multiplication, and a homomorphic multiplication with a round key. An important contribution of this work is the development of a homomorphic multiplicative Sbox based on non-linear operations. A series of security tests and theoretical crypt-analysis are carried out to assess the security properties of the proposed scheme. The efficiency of the proposed scheme for real-world applications is also demonstrated by benchmarking its performance against the state-of-the-art methods in homomorphic encryption. With potential applications in secure cloud computing, and other domains where data privacy is crucial, this work advances the area of cryptography by offering a novel method for enhancing homomorphic encryption’s effectiveness.