The ability to efficiently retrieve data in their encrypted form is important for the cloud to become a truly secure and practical data sharing platform. Although this field has attracted tremendous research attention in the past a few years, most existing solutions do not support efficient searches with complex query conditions. Also, there has been little work to explore various comparison methods to specify complex query conditions. In this paper, we propose a framework of multi-keyword secure data retrieval to meet the needs of secure data retrieval with complex query support by leveraging recent development in attribute-based encryptions. Moreover, we propose a novel cryptographic comparison method based on forward and backward deviation functions (FDF/BDF). This method supports dual range comparisons and tree-oriented keyword search, as well as almost constant complexity for large size of integer range. We also provide several authentication mechanisms for preventing unpermitted access and verifying validity of protocol output. We implement a prototype system and our experimental results demonstrate its efficiency for practical usage.
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