With the many benefits of cloud computing, an entity may want to outsource its data and their related analytics tasks to a cloud. When data are sensitive, it is in the interest of the entity to outsource encrypted data to the cloud; however, this limits the types of operations that can be performed on the cloud side. Especially, evaluating queries over the encrypted data stored on the cloud without the entity performing any computation and without ever decrypting the data become a very challenging problem. In this paper, we propose solutions to conduct range queries over outsourced encrypted data. The existing methods leak valuable information to the cloud which can violate the security guarantee of the underlying encryption schemes. In general, the main security primitive used to evaluate range queries is secure comparison (SC) of encrypted integers. However, we observe that the existing SC protocols are not very efficient. To this end, we first propose a novel SC scheme that takes encrypted integers and outputs encrypted comparison result. We empirically show its practical advantage over the current state-of-the-art. We then utilize the proposed SC scheme to construct two new secure range query protocols. Our protocols protect data confidentiality, privacy of user's query, and also preserve the semantic security of the encrypted data; therefore, they are more secure than the existing protocols. Furthermore, our second protocol is lightweight at the user end, and it can allow an authorized user to use any device with limited storage and computing capability to perform the range queries over outsourced encrypted data.
We design an encryption scheme called multi-dimensional range query over encrypted data (MRQED), to address the privacy concerns related to the sharing of network audit logs and various other applications. Our scheme allows a network gateway to encrypt summaries of network flows before submitting them to an untrusted repository. When network intrusions are suspected, an authority can release a key to an auditor, allowing the auditor to decrypt flows whose attributes (e.g., source and destination addresses, port numbers, etc.) fall within specific ranges. However, the privacy of all irrelevant flows are still preserved. We formally define the security for MRQED and prove the security of our construction under the decision bilinear Diffie-Hellman and decision linear assumptions in certain bilinear groups. We study the practical performance of our construction in the context of network audit logs. Apart from network audit logs, our scheme also has interesting applications for financial audit logs, medical privacy, untrusted remote storage, etc. In particular, we show that MRQED implies a solution to its dual problem, which enables investors to trade stocks through a broker in a privacy-preserving manner. We construct public-key systems that support comparison queries (x ≥ a) on encrypted data as well as more general queries such as subset queries (x∈ S). Furthermore, these systems support arbitrary conjunctive queries (P1 ∧ ... ∧ Pl) without leaking information on individual conjuncts. We present a general framework for constructing and analyzing public-key systems supporting queries on encrypted data. In this paper, we study the problem of supporting multidimensional range queries on encrypted data. The problem is motivated by secure data outsourcing applications where a client may store his her data on a remote server in encrypted form and want to execute queries using server's computational capabilities. The solution approach is to compute a secure indexing tag of the data by applying bucketization (a generic form of data partitioning) which prevents the server from learning exact values but still allows it to check if a record satisfies the query predicate. Queries are evaluated in an approximate manner where the returned set of records may contain some false positives. These records then need to be weeded out by the client which comprises the computational overhead of our scheme. We develop a bucketization procedure for answering multidimensional range queries on multidimensional data. For a given bucketization scheme, we derive cost and disclosure-risk metrics that estimate client's computational overhead and disclosure risk respectively. Given a multidimensional dataset, its bucketization is posed as an optimization problem where the goal is to minimize the risk of disclosure while keeping query cost (client's computational overhead) below a certain user-specified threshold value. We provide a tunable data bucketization algorithm that allows the data owner to control the trade-off between disclosure risk and cost. We also study the trade-off characteristics through an extensive set of experiments on real and synthetic data.