I'm doing a project at my university (HU Berlin) involving homomorphic encrypted searches on data bases. Does PostgreSQL support homomorphic encryption-based searches?
Not natively, as far as I know anyway.
I don't think pgcrypto offers any facilities you could use for useful homomorphic encryption, except for the obvious degenerate case of comparison by equality of unsalted encrypted data.
PostgreSQL is very extensible and you could definitely add data types for homomorphic encryption + the required index access method implementations etc. A quick Google search for "postgres homomorphic" finds various information on the topic.