As the advent of cloud computing and cloud storage systems, more and more people andorganizations chose to outsource their data to the cloud servers. Since the cloud serversare not fully trustable, to protect data privacy, people usually encrypt the data beforeoutsourcing it to the cloud. As search has become a most primary way for users toretrieve the data they want, but it is extremely difficult to do search on encrypted datain the cloud. The existing works on searchable encryption can be classified into twocategories: exact keyword search and similarity keyword search. Both types of searchlimit the power of search for users. The principal goal of this project is to develop ascheme that facilitates Generalized Pattern-matching String-search on Encrypted data(GPSE for short). GPSE is a powerful search function, which can support SQL-likequeries and give users great flexibility to specify targeted search. The project consists ofthree major tasks:1) Design a framework for GPSE. We will design a general framework for GPSE, suchthat a wide range of search operations defined by various pattern matching rules can berealized in it.2) Design algorithms to support commonly used pattern matching rules in GPSE. We willfocus on the commonly used matching rules for search, such as substring matching,prefix matching, suffix matching, and design algorithms to realize them in theframework of GPSE.3) Design schemes to support joint queries in GPSE. We will design schemes in GPSE tosupport search by joint queries that consist of multiple subqueries joint by logicaloperations, such as AND, OR, or NOT.?