The spread of encrypted scientific information archives has posed an urgent need of retrieval systems that can maintain privacy of data and at the same time provide a pragmatic query efficiency. Traditional encryption algorithms ensure privacy, but come with extremely high-performance costs-making even large scientific databases computationally infeasible. This paper proposes a new Cryptographic Indexing Scheme (CIS) that is specifically designed to work with encrypted scientific database, it combines searchable symmetric encryption (SSE), secure hash-based multi-level indexing and lightweight partial homomorphic operations to facilitate complex structured and key-word querying. It has a hierarchical, leakage-resistant index, which is resistant to both access-pattern and inference attacks with a sub-linear search complexity. Assessment of large scale simulated genomic, climate and astrophysical data sets reveals that the proposed CIS is able to deliver 79.9 percent reduction in query response time, 73.1 percent less storage overhead, 97.3 percent retrieval precision and a security robustness score of 9.35/10 in comparison to current state of the art techniques. These findings support the idea that the proposed framework can be implemented in a real world secure scientific information management system.