A very simple PIR scheme on top of homomorphic encryption that supports multiplying with a plaintext and homomorphic addition, would look like this:
The client one-hot-encodes the query: Enc(0), Enc(1), Enc(0). The server has 3 values: x, y, z. Now the server computes: Enc(0) * x + Enc(1) * y + Enc(0) * z == Enc(y). Client can decrypt Enc(y) and get the value y. Server received three ciphertexts, but does not know which one of them was encryption of zero or one, because the multiplications and additions that the server did, never leak the underlying value.
This gives some intuition on how PIR works, actual schemes are more efficient.
[Disclosure: I work on the team responsible for the feature]
Does the server reads specific rows from spam numbers DB or the whole database?
In this PIR model the server has to read the whole database, otherwise it would be easy on the server to see, that these rows were not accessed and therefore they are not the one the client queried.
In this PIR model the server runtime is O(n) where n is the number of rows.
To keep it practical, we do support sharding the database. Client leaks a few bits of hashed query to pick the right shard, where we process the entire shard. There is a inherent privacy-performance tradeoff: less shards = less leakage vs more shards = better performance & less privacy.
Thanks for explanation. I will read the code to see how sharing works.
https://github.com/apple/swift-homomorphic-encryption/blob/3...
Run SHA256 on the keyword, truncate the hash and take the modulus with number of shards.