Encrypted search cloud service with cryptographic sharing

A method for sharing read access to a document stored on memory hardware. The method includes receiving a shared read access command from a sharor sharing read access to a sharee for a document stored on memory hardware in communication with the data processing hardware, and receiving a shared read access request from the sharee. The shared read access command includes an encrypted value and a first cryptographic share value based on a write key, a read key, a document identifier, and a sharee identifier. The method also includes multiplying the first and second cryptographic share values to determine a cryptographic read access value. The cryptographic read access value authorizes read access to the sharee for the document. The method also includes storing a read access token for the sharee including the cryptographic read access value and the encrypted value in a user read set of the memory hardware.