The use of distributed systems in various fields, which has grown up, including cloud computing, IoT, and decentralized networks, has compounded the necessity to have an effective and robust security mechanism. Although traditional cryptographic designs are good, they can be characterized by large computation overhead and poor scalability in dynamic distributed system. In this work, we tackle these issues by coming up with a discrete algebraic security model, which makes use of finite field arithmetic and encoding with the help of polynomials to perform secure distributed computation. The main goal is to come up with a scalable and effective model that will provide data confidentiality, integrity, and antagonism with adversarial attacks. The key generation methodology combines algebra-based and encryption key generation techniques, and distributed computation of encrypted data, which is backed by a layered system architecture. The metrics that are used to evaluate performance include encryption/decryption time, throughput, latency, security strength and fault tolerance. The resulting experimentation proves the suggested framework to decrease the computational latency by about 25-40% and enhance the throughput up to 1.8 times compared to traditional RSA/ECC algorithms and be highly resistant to attacks. These results suggest that the suggested solution is a reasonable trade-off between security and efficiency, thus it is extremely applicable to distributed systems in the real world.