Encrypted search system design for email client-side encryption

A system comprising:

• data processing hardware of a user device associated with a user;
• and
• memory hardware in communication with the data processing hardware, the memory hardware storing instructions that when executed on the data processing
• receiving a search query for a keyword, the keyword appearing in one or more encrypted emails within a corpus of encrypted emails stored on an untrusted storage device;
• accessing a count table to obtain a count of unique emails within the corpus of encrypted emails that include the keyword;
• generating a delegatable pseudorandom function (DPRF) based on the keyword, a private cryptographic key, and the count of unique emails that include the keyword, and
• delegating at least a portion of the DPRF to the untrusted storage device, the delegated at least the portion of the DPRF when received by the untrusted storage device causing the untrusted storage device to:
• evaluate the delegated at least the portion of the DPRF;
• access an encrypted search index associated with the corpus of encrypted emails stored on the untrusted storage device;
• determine one or more encrypted emails within the corpus of encrypted emails associated with the delegated at least the portion of the DPRF based on the encrypted search index;
• and
• return, to the user device, an identifier for each encrypted email of at least a portion of the one or more encrypted emails associated with the delegated at least the portion of the DPRF.