Methods, systems, and apparatus, including a system that includes a secure hardware unit; and a database system including one or more processors; and a computer-readable medium having stored instructions that, when executed by the one or more processors, cause the one or more processors to perform operations including: receiving a client request to perform a database operation using first encrypted data as an encrypted value of a field to be operated on by the database operation, where the first encrypted data has been encrypted by a database client using a first encryption key; providing, to the secure hardware unit, a system request for performing one or more data processing operations, the system request including (i) the first encrypted data and (ii) data identifying the first encryption key; and receiving, from the secure hardware unit, output data representing an output of the one or more data processing operations.