Homomorphic Encryption (HE) is a fundamental Privacy-Enhancing Technology (PET) that enables computations on encrypted data without decryption. Despite its utility, designing an efficient and secure HE scheme is highly complex, requiring sophisticated cryptographic techniques. This paper introduces a novel approach to achieving homomorphic properties—supporting either one addition or one multiplication—within composite groups. While the proposed technique exhibits one-wayness, it has a good potential to serve as a foundational building block for constructing indistinguishable cryptosystems. This work contributes to the advancement of homomorphic encryption by providing a new perspective on secure computation within structured algebraic settings.