> The main threat to encrypting health information is actually dishonest cryptographers.
Wow, okay, you have me hooked.
> instead of searching for user Michael Knight in a database of cancer patients, you hash the name, use a bloom filter to determine if the hash exists in the protected data set or not
The protocol you loosely described here could be either totally fine or horrendously broken depending on the implementation details and architecture of the application. Not to mention the universal cryptography concerns; i.e., key management.
> and then tell your regulators and the public that the foreign jurisdiction research assistants hired from fiverr don't have access to your health information because everything is encrypted and we only compare hashes.
You've said "hashes" twice now, so I have to ask:
1. Are they only hashing, or are they using a keyed hash (e.g., HMAC)?
2. Are they doing something ridiculous like using MD5?
If you're familiar with cryptography at all, passing around MD5(data) is vastly different from truncating HMAC-SHA384(data, staticKey) to a few bits and protecting staticKey with an HSM.
Without more detail, I can't tell if your assertion that cryptographers are being dishonest is warranted. It's sort of like simplifying RSA encryption to "multiplying integers". Yes, that's what's happening on some level, but some essential information was omitted.