What protocol enhancements needs to be made to public blockchain to allow for enough privacy to allow for information about more privacy-sensitive transactions, like healthcare visits ( associated metadata)

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The most powerful technology that holds promise in direction is, of course, cryptographically secure obfuscation. In general, obfuscation is a way of turning any program into a “black box” equivalent of the program, in such a way that the program still has the same “internal logic”, and still gives the same outputs for the same inputs, but it’s impossible to determine any other details about how the program works. Apply this to blockchain technology and it becomes virtually impossible to breach or hack therefore protecting and safeguarding privacy-sensitive transactions and data like nothing else !
This is an issue where several projects for Digital or Electronic Health Records (EHR) failed. Imo the most advanced EHR now in use is the Personally Controlled Electronic Health Record (PCEHR) by the Australian Government.
From a privacy perspective, it should be ensured that any push, pull, and view requests are authorized by the patient and authorization may be revoked. For that to work, the patient needs to own his/her EHR and generate authorization via biometrics, e.g. fingerprint, and maybe 2FA. To protect the identity of the patient one could think about mixing personal data, that make a patient identifiable, before the record is stored on the blockchain. Think of it as address mixing as done by privacy coins like Monero/ XMR, or with an on/off feature like to be implemented with the Wraith protocol of Verge/ XVG. Another interesting project to look at could be Civic/ CVC with its identity authenication and protection features.