A modular arithmetic structure of homomorphic encryption enables the capability to perform computation on encrypted data without revealing any information on plaintext, and hence it is highly suitable in privacy-sensitive applications in clouds and distributed systems. A systematic design that is founded on number-theoretic ideas like Euler, Fermat little theorem and Chinese Remainder Theorem (CRT) has been proposed in this paper to support efficient homomorphic functions. The model proposed uses algebraic structures such as modular rings, and classes of residues to allow the addition and multiplication of values on cipher texts directly. The encryption and evaluation will be made to run on a modular arithmetic based transformation mechanism and be correct and computationally viable. Key generation, encrypting, homomorphic evaluation and decryption, which provide privacy of data in processing will be implemented in the system architecture. Empirical evidence demonstrates that the model is more efficient and scalable in computations, and indicates that the model is relevant in secure data analytics, financial systems and privacy-conscious machine learning systems.