In distributed systems like the Internet of Things (IoT), wireless sensor networks, and cloud-based systems, secure data aggregation is essential as the integrity of data, its confidentiality, and efficiency have to be ensured at once. The mathematical framework of secure data aggregation as proposed in this paper is a semiring with the algebraic property of closure, associativity and distributives to enable robust aggregation mechanisms. The methodology translates semiring operations to additive and multiplicative aggregation functions, allowing an easy and secure way of computing with encrypted or partially masked data. The semiring structures are used to design a novel aggregation algorithm that guarantees consistency, scalability, and inference and tampering of data resistance. Experimental analysis shows a higher accuracy of aggregation of 96.8% and lower computation costs in comparison with traditional algorithms. The findings shed light on the usefulness of semiring-based models towards obtaining secure, efficient and scalable data aggregation in heterogeneous distributed environments.