Data outsourcing aims to mitigate our concerns about data security and reliability by ensuring that the data is handled in a professional manner. Due to a lack of assurances regarding the reliability and security of data stored on servers, the increasing use of outsourcing is causing users concern. There have been some attempts to deal with these issues by implementing Secret Sharing-based Data Outsourcing (SSDO) schemes. The efficiency decline of SSDO schemes prompted researchers to use index trees. By releasing some secret information, index trees can be subject to frequency analysis. We propose a new type of index tree called Bucket-Chain $B^+Tree$ ($BCB^+Tree$) that thwarts frequency analysis by keeping indexes in a chain of buckets. Therefore, as opposed to $B^+Tree$, $BCB^+Tree$'s exposure will not provide any information to outsiders, increasing the security of the scheme. Leveraging $BCB^+Tree$, we have proposed an efficient and secure SSDO scheme. A number of implementations suggest that the proposed scheme performs better than the current schemes. Additionally, it has been shown that the adversary cannot recover the shared values by accessing $k-1$ data servers and the index tree.
