Many big data applications in industries such as research and healthcare thrive due to the widespread availability of large-scale processing capability and scalable storage via cloud computing. To enhance data management and facilitate easier mining, numerous data owners opt to outsource their data to cloud servers. However, significant privacy concerns arise when sensitive data, such as electronic health records, is shared in the cloud with partially untrusted third parties. A common approach to mitigate these risks is encrypting data before outsourcing, albeit this diminishes the data's value and renders traditional data analysis techniques, such as keyword-based top-k document retrieval, obsolete.This research addresses the challenges of multi-keyword top-k search for encrypted big data, aiming to safeguard against privacy intrusions. To provide a secure and efficient solution, we introduce a novel index structure based on trees and a random traversal method. This approach enhances query data privacy while maintaining query accuracy by ensuring that identical queries yield distinct traversal paths to the index. Additionally, we describe a group multi-keyword top-k search method that employs partitioning to construct multiple tree-based indexes for each dataset, thereby improving query efficiency. When integrated, these methods form a robust framework for handling the proposed top-k similarity search.Our methodology offers superior privacy protection, scalability, and query processing speed compared to state-of-the-art approaches. Extensive testing on real datasets has confirmed these advantages.