Spatial queries like range queries, nearest neighbor, circular range queries etc. are the most widely used queries in the location-based applications. Building secure and efficient solutions for these queries in the cloud computing framework is critical and has been an area of active research. This paper focuses on the problem of Secure Circular Range Queries (SCRQ), where client submits an encrypted query (consisting of a center point and radius of the circle) and the cloud (storing encrypted data points) has to return the points lying inside the circle. The existing solutions for this problem suffer from various disadvantages such as high processing time which is proportional to square of the query radius, query generation phase which is directly proportional to the number of points covered by the query etc. This paper presents solution for the above problem which is much more efficient than the existing solutions. Three protocols are proposed with varying characteristics. It is shown that all the three protocols are secure. The proposed protocols can be extended to multiple dimensions and thus are able to handle Secure Hypersphere Range Queries (SHRQ) as well. Internally the proposed protocols use pairing-based cryptography and a concept of lookup table. To enable the efficient use of limited size lookup table, a new storage scheme is presented. The proposed storage scheme enables the protocols to handle query with much larger radius values. Using the SHRQ protocols, we also propose a mechanism to answer the Secure range Queries. Extensive performance evaluation has been done to evaluate the efficiency of the proposed protocols
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