One example is a private OCSP. Every time you open a TLS-secured webpage, your browser has to check whether or not the TLS certificate has been revoked (I'm leaving out some complications but bear with me). In order to do that, you browser has to contact the certificate authority (CA) and ask "has anyone revoked this cert?". But in doing that, the browser is revealing your browsing patterns to the CA!
It would be nice, instead, to use Private Information Retrieval to ask the CA "please process this encrypted query and return the result". Then the CA knows nothing about your browsing patterns, and you still get your data. Well, (computational) Private Information Retrieval is super inefficient today, and the best asymptotic solution we have is based on FHE (https://eprint.iacr.org/2017/1142). So getting efficient FHE would hopefully make something like this a lot more reasonable for moderately sized databases.
For the record, this is only a toy example. We actually have really good solutions for private OCSP that don't require FHE. We can side-step the difficult of Private Information Retrieval in this case because OCSP databases are small enough for anyone to download. If this interests you, check out CRLite https://blog.mozilla.org/security/2020/01/09/crlite-part-1-a...
that kind of thing.
It also won't know the size of the result, only seeing a fixed-size buffer.
You could run statistics on data or do a grid-based simulation.
Running a neural net would be almost trivial.
General purpose code is extremely difficult to adapt, since it loves to branch based on data.
Hell, I’m not an ML practitioner and I almost never use python, and yet it took me maybe a day or two learn enough about covnet training to detect my dog on a home security camera.
All you have to do is multiply each weight and add up each node.
Pure bulk arithmetic is both simple and a perfect match for FHE.
If you mean is it useless as a replacement for the mysql backend of your php app, the answer is yes.
Because simply querying the database a billion times and replacing SSN with 1, 2 etc. is never going to work in any reasonably secure environment. Queries are logged and people will know if you're trying to brute force a table.
Especially for data lakes where the act of manipulating data can sometimes involve moving actual files around a distributed cluster in a potentially insecure environment e.g. cloud.