" three researchers have crafted a long-sought version of private information retrieval and extended it to build a more general privacy strategy. The work, which received a Best Paper Award in June 2023 at the annual Symposium on Theory of Computing, topples a major theoretical barrier on the way to a truly private search."
Actually, to make it with cryptographic guarantees is pretty hard… I know of at least one university professor in the PET (Privacy Enhancing Technologies)/cryptography space who spent quite some time on his startup to develop such a search engine. In the end it all fell apart because of one the mathematical assumptions being unprovable. This is just one example but I guess it illustrates pretty well why we’ve yet to see a cryptographically secure/private search engine as a product!