The transition from paper-based information to Electronic-Health-Records (EHRs) has driven various advancements in the modern healthcare-industry. In many cases, patients need to share their EHR with healthcare professionals. Given the sensitive and security-critical nature of EHRs, it is essential to consider the security and privacy issues of storing and sharing EHR. However, existing security solutions excessively encrypt the whole database, thus requiring the entire database to be decrypted for each access request, which is a time-consuming process. On the other hand, the use of EHR for medical research (e.g., development of precision-medicine, diagnostics-techniques), as well as optimisation of practices in healthcare organisations, requires the EHR to be analysed, and for that, they should be easily accessible without compromising the privacy of the patient. In this paper, we propose an efficient technique called E-Tenon that not only securely keeps all EHR publicly accessible but also provides the desirable security features. To the best of our knowledge, this is the first work in which an Open Database is used for protecting EHR. The proposed E-Tenon empowers patients to securely share their EHR under multi-level, fine-grained access policies defined by themselves. Analyses show that our system outperforms existing solutions in terms of computational-complexity.