Popular service providers, such as Google and Amazon, have turned their vast resources into a cloud computing model and enforced their businesses to run applications on the servers of such new model. To ensure security and privacy in this environments, customers have to encrypt their data before uploading them into the cloud servers. Unfortunately, modern unbreakable encryption methods are inadequate because they do not have the ability to execute database queries on the encrypted data. In this paper, we address the problem of how to calculate the geographical distance over an encrypted dataset. Specifically, the data owner, Alice, sends her encrypted dataset of geographical locations into the cloud server. At any time, Bob would like to check the proximity of his submitted query from the locations of Alice. Our proposed scheme enables the untrusted server to perform such task without compromising the privacy of either the dataset of Alice or the query of Bob. Among various distance metrics, we employ the efficient principle of approximate matching to obtain the proximity between query and data locations. Furthermore, we use the inner product similarity to formalize such principle for similarity measurement. Several experiments have been conducted to investigate the overhead and the efficiency of the proposed scheme.
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