"Because searchable encryption can be used to solve the issue of search on encrypted data in cloud computing enviornment, it has been widely studied by researches recently. At present the research on searchable encryption focuses on a single-user setting, namely the user can only search its own encrypted data. But there are multiple users in the real world and some application scenarios need search on encrypted data in a multi-user setting, for example, keyword search on the encrypted E-mails of multiple users, or the join query on multiple users' ciphertexts for outsourced database. At present the study of searchable public key encryption in a multi-user setting is not mature. It is a meaningful and challenging topic. This project intends to provide a set of searchable public key encryption schemes in a multi-user setting. More specifically, it includes: public key encryption schemes supporting keyword search with various properties in a multi-user setting and public key encryption schemes supporting ciphertexts

comparison with various properties in a multi-user setting and its generic construction. Based on the existing works on searchable encryption in a

single-user setting, this project intends to solve these two key problems in a multi-user setting: security models of public key encryption with keyword search and efficient primitives of public key encryption supporting ciphertexts comparison, and thereby providing a new theoretical basis for further study of searchable encryption in a multi-user setting.

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