Security Analysis of Schemes for k-NN Computation over Encrypted Databases

Sensitive applications running on the cloud often require data to be stored in encrypted form. To run data mining algorithms on such data, encryption schemes that are partially homomorphic (allowing certain operations in the ciphertext domain) have been devised. One such scheme for secure k nearest neighbours computation was designed to provide both, Data Privacy and Query Privacy. An enhancement to this scheme further ensures that the data owner approves each query issued by a user before it is processed by the cloud server. In this work, we describe an attack that invalidates the Data Privacy claim for these schemes. We show that a query user can tailor a query in a special manner to extract information about the secret key that is used to encrypt the data points. Furthermore, if the cloud service provider colludes with a malicious query user, it can use this secret information to derive all the plaintext data points. We then suggest a modification to these encryption schemes that makes such attacks on data privacy impossible while incurring very low additional costs in performance.