Attribute Based Encryption (ABE) has become a potent concept of access control on a fine-grained basis in a distributed and cloud setting. The paper will delve into number theoretic underpinnings of the ABE schemes, and in particular the role of the Euler theorems and Fermat’s little theorems and modular arithmetic in the key generation and encryption processes. It also explores the pairing-based cryptographic constructions that can be used to expressive access policies along bilinear mappings. The most important processes of secret keys reconstruction in the form of a poly-nominal interpolation and Lagrange coefficients are discussed. In addition, the optimization techniques, such as pre-computation and batching are also examined in order to enhance the computational efficiency and scalability. The results show that the integration of such powerful number theoretic concepts and powerful implementation mechanisms have much to do in improving the security, flexibility and performance of ABE systems in the real world.