Cloud-based data management systems should have strong data handling mechanisms that discourage unauthorized access and provide effective data recovery. The issue that the present paper will address is to construct efficient threshold secret sharing schemes on the basis of the combinatorial design theory. This is aimed at developing a mathematically-based structure using Balanced Incomplete Block Designs (BIBD) and Finite Field-based polynomial interpolation to enhance security and scalability. The proposed model encodes secrets in combinatorial structures and this enables them to be shared with subjects in controlled manner and only authorized subsets having the power to recreate the secret. The use of algorithms is focused on the effective encoding algorithms and the reconstruction algorithms that have a reduced computational load. Experiments have demonstrated resistance to collusion attack and 21.6 percent more reconstruction than traditional schemes.