Private Information Retrieval and Writing at the same time possible? Are there any (possibly multiserver) private information retrieval (PIR) schemes that support private reads and writes (so called PIR Writing) at the same time, while having sublinear (in the database size) communication overhead?
The most recent, very efficient, PIR scheme I could find is the one based on distributed point functions, but it seems to only support one operation at a time. That is, I can either outsource a database, where I have private reads or I can outsource a database, where I have private writes, but not both on one database. Preferably I am looking for something that is not based on heavy tools like FHE.
Here's a single-server one: https://link.springer.com/content/pdf/10.1007%2F978-3-642-13708-2_26.pdf

Obviously the data would need to be encrypted, otherwise it will be obvious what was changed, and the PIR-write protocol needs to somehow re-randomize the ciphertexts that were not modified.