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.
Increasing concerns about graph privacy have been raised with the wide adoption of the cloud computing paradigm over the past decade. Chase and Kamara @cite_47 first introduced the notion of graph encryption, where they proposed several constructions for graph operations, such as adjacency queries and neighboring queries. @cite_53 defined and solved the problem of privacy-preserving query over encrypted graph data in cloud computing by utilizing the principle of filtering-and-verification''. They built the feature-based index of a graph in advance and then chose the efficient inner product to carry out the filtering procedure. Some approaches @cite_28 @cite_15 @cite_40 utilized the differential privacy technique to query graphs privately, which might suffer from weak security. These studies, however, introduced prohibitively great storage costs and were not practical for large-scale graphs. @cite_35 proposed three computationally efficient constructions that supported the approximate shortest distance querying with distance oracles, which were provably secure against a semi-honest cloud server.
@cite_35 @cite_15 @cite_28 @cite_53 @cite_40 @cite_47
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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. 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. As Cloud Computing becomes prevalent, sensitive information are being increasingly centralized into the cloud. For the protection of data privacy, sensitive data has to be encrypted before outsourcing, which makes effective data utilization a very challenging task. Although traditional searchable encryption schemes allow users to securely search over encrypted data through keywords, these techniques support only boolean search, without capturing any relevance of data files. This approach suffers from two main drawbacks when directly applied in the context of Cloud Computing. On the one hand, users, who do not necessarily have pre-knowledge of the encrypted cloud data, have to post process every retrieved file in order to find ones most matching their interest, On the other hand, invariably retrieving all files containing the queried keyword further incurs unnecessary network traffic, which is absolutely undesirable in today's pay-as-you-use cloud paradigm. In this paper, for the first time we define and solve the problem of effective yet secure ranked keyword search over encrypted cloud data. Ranked search greatly enhances system usability by returning the matching files in a ranked order regarding to certain relevance criteria (e.g., keyword frequency), thus making one step closer towards practical deployment of privacy-preserving data hosting services in Cloud Computing. We first give a straightforward yet ideal construction of ranked keyword search under the state-of-the-art searchable symmetric encryption (SSE) security definition, and demonstrate its inefficiency. To achieve more practical performance, we then propose a definition for ranked searchable symmetric encryption, and give an efficient design by properly utilizing the existing cryptographic primitive, order-preserving symmetric encryption (OPSE). Thorough analysis shows that our proposed solution enjoys as-strong-as-possible" security guarantee compared to previous SSE schemes, while correctly realizing the goal of ranked keyword search. Extensive experimental results demonstrate the efficiency of the proposed solution. Driven by the growing security demands of data outsourcing applications in sustainable smart cities, encrypting clients’ data has been widely accepted by academia and industry. Data encryptions should be done at the client side before outsourcing, because clouds and edges are not trusted. Therefore, how to properly encrypt data in a way that the encrypted and remotely stored data can still be queried has become a challenging issue. Though keyword searches over encrypted textual data have been extensively studied, approaches for encrypting graph-structured data with support for answering graph queries are still lacking in the literature. In this paper, we specially investigate graph encryption method for an important graph query type, called top-k Nearest Keyword (kNK) searches. We design several indexes to store necessary information for answering queries and guarantee that private information about the graph such as vertex identifiers, keywords and edges are encrypted or excluded. Security and efficiency of our graph encryption scheme are demonstrated by theoretical proofs and experiments on real-world datasets, respectively.