Constrained shortest distance (CSD) querying is one of the fundamental graph query primitives, which finds the shortest distance from an origin to a destination in a graph with a constraint that the total cost does not exceed a given threshold. CSD querying has a wide range of applications, such as routing in telecommunications and transportation. With an increasing prevalence of cloud computing paradigm, graph owners desire to outsource their graphs to cloud servers. In order to protect sensitive information, these graphs are usually encrypted before being outsourced to the cloud. This, however, imposes a great challenge to CSD querying over encrypted graphs. Since performing constraint filtering is an intractable task, existing work mainly focuses on unconstrained shortest distance queries. CSD querying over encrypted graphs remains an open research problem. In this paper, we propose Connor , a novel graph encryption scheme that enables approximate CSD querying. Connor is built based on an efficient, tree-based ciphertext comparison protocol, and makes use of symmetric-key primitives and the somewhat homomorphic encryption, making it computationally efficient. Using Connor , a graph owner can first encrypt privacy-sensitive graphs and then outsource them to the cloud server, achieving the necessary privacy without losing the ability of querying. Extensive experiments with real-world data sets demonstrate the effectiveness and efficiency of the proposed graph encryption scheme.
We propose graph encryption schemes that efficiently support approximate shortest distance queries on large-scale encrypted graphs. Shortest distance queries are one of the most fundamental graph operations and have a wide range of applications. Using such graph encryption schemes, a client can outsource large-scale privacy-sensitive graphs to an untrusted server without losing the ability to query it. Other applications include encrypted graph databases and controlled disclosure systems. We propose GRECS (stands for GRaph EnCryption for approximate Shortest distance queries) which includes three oracle encryption schemes that are provably secure against any semi-honest server. Our first construction makes use of only symmetric-key operations, resulting in a computationally-efficient construction. Our second scheme makes use of somewhat-homomorphic encryption and is less computationally-efficient but achieves optimal communication complexity (i.e. uses a minimal amount of bandwidth). Finally, our third scheme is both computationally-efficient and achieves optimal communication complexity at the cost of a small amount of additional leakage. We implemented and evaluated the efficiency of our constructions experimentally. The experiments demonstrate that our schemes are efficient and can be applied to graphs that scale up to 1.6 million nodes and 11 million edges.  We develop algorithms for the private analysis of network data that provide accurate analysis of realistic networks while satisfying stronger privacy guarantees than those of previous work. We present several techniques for designing node differentially private algorithms, that is, algorithms whose output distribution does not change significantly when a node and all its adjacent edges are added to a graph. We also develop methodology for analyzing the accuracy of such algorithms on realistic networks. The main idea behind our techniques is to 'project' (in one of several senses) the input graph onto the set of graphs with maximum degree below a certain threshold. We design projection operators, tailored to specific statistics that have low sensitivity and preserve information about the original statistic. These operators can be viewed as giving a fractional (low-degree) graph that is a solution to an optimization problem described as a maximum flow instance, linear program, or convex program. In addition, we derive a generic, efficient reduction that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph. This reduction is based on analyzing the smooth sensitivity of the 'naive' truncation that simply discards nodes of high degree. In the emerging cloud computing paradigm, data owners become increasingly motivated to outsource their complex data management systems from local sites to the commercial public cloud for great flexibility and economic savings. For the consideration of users' privacy, sensitive data have to be encrypted before outsourcing, which makes effective data utilization a very challenging task. In this paper, for the first time, we define and solve the problem of privacy-preserving query over encrypted graph-structured data in cloud computing (PPGQ), and establish a set of strict privacy requirements for such a secure cloud data utilization system to become a reality. Our work utilizes the principle of "filtering-and-verification". We prebuild a feature-based index to provide feature-related information about each encrypted data graph, and then choose the efficient inner product as the pruning tool to carry out the filtering procedure. To meet the challenge of supporting graph query without privacy breaches, we propose a secure inner product computation technique, and then improve it to achieve various privacy requirements under the known-background threat model.  We consider the problem of encrypting structured data (e.g., a web graph or a social network) in such a way that it can be efficiently and privately queried. For this purpose, we introduce the notion of structured encryption which generalizes previous work on symmetric searchable encryption (SSE) to the setting of arbitrarily-structured data.