> In previous private search systems, for each client query, the server must perform at least one expensive cryptographic operation per database entry.
Exactly. (I had only looked at the homomorphic encryption post, not the Wally post.) Wally tries to work around this limitation by only using homomorphic encryption for a subset of the database, and reducing the resulting information leakage by using an anonymous network to hide which client is querying which subset. They say this network is operated by a third party, but ultimately you still have to trust that the network operator isn't colluding with the server operator to deanonymize your queries. That's a weaker privacy guarantee, but at least it's not painfully slow.
Exactly. (I had only looked at the homomorphic encryption post, not the Wally post.) Wally tries to work around this limitation by only using homomorphic encryption for a subset of the database, and reducing the resulting information leakage by using an anonymous network to hide which client is querying which subset. They say this network is operated by a third party, but ultimately you still have to trust that the network operator isn't colluding with the server operator to deanonymize your queries. That's a weaker privacy guarantee, but at least it's not painfully slow.