OblivGM: Oblivious Attributed Subgraph Matching as a Cloud Service

Abstract

In recent years there has been growing popularity of leveraging cloud computing for storing and querying attributed graphs, which have been widely used to model complex structured data in various applications. Such trend of outsourced graph analytics, however, is accompanied with critical privacy concerns regarding the information-rich and proprietary attributed graph data. In light of this, we design, implement, and evaluate OblivGM, a new system aimed at oblivious graph analytics services outsourced to the cloud. OblivGM focuses on the support for attributed subgraph matching, one popular and fundamental graph query functionality aiming to retrieve from a large attributed graph subgraphs isomorphic to a small query graph. Built from a delicate synergy of insights from attributed graph modelling and advanced lightweight cryptography, OblivGM protects the confidentiality of data content associated with attributed graphs and queries, conceals the connections among vertices in attributed graphs, and hides search access patterns. Meanwhile, OblivGM flexibly supports oblivious evaluation of varying subgraph queries, which may contain equality and/or range predicates. Extensive experiments over a real-world attributed graph dataset demonstrate that while providing strong security guarantees, OblivGM achieves practically affordable performance (with query latency on the order of a few seconds).

A Secure Multi-Party Computation Protocol for Graph Editing Distance against Malicious Attacks

“…Reference [15] uses a depth-first search code as a canonical tagging system, and on the basis of this code, a new graph similarity measure algorithm is proposed in combination with Levenshtein distance (i.e., string editing distance), which has a complexity of n 3 modulo exponential operation. Reference [16] designed secure graph isomorphism and similarity determination algorithms based on hash functions, which measure computational complexity by comparing the number of hash operations, and it has a complexity of 6h (h is the number of operations to perform one hash operation).…”

“…Communication complexity is usually measured in terms of communication rounds. Reference [15] requires six rounds of interaction to complete the computation, Reference [16] requires four rounds, Algorithm 1 in this paper requires one round of communication, and Algorithm 2 requires three rounds of communication to complete the computation. Table 1 shows a comparison of the performance.…”

“…In order to have a visual comparison of the computational complexity of each algorithm, the algorithms in References [15,16] and Algorithm 2 in this paper are experimentally simulated. The experimental environment is processor Intel(R) Core(TM) i5-8300 H @ 2.30 GHz, 12 GB of RAM, Windows 10 (64-bit) operating system, in PyCharm 2020.3.2 using the Python language.…”

“…The algorithms of both References [15,16] use a homomorphic encryption algorithm when calculating the graphs' editing distance, so the time used by References [15,16] and Algorithm 2 is tested through simulated experiments to compare the efficiency by comparing the time taken for the algorithm to execute. In the experiment, all other things being equal, the graph G A is transformed into G B by the add and delete operations, for example, by first randomly generating two undirected graphs with vertex number m. For the vertex m, the graphs are taken in order 5, 10, .…”

“…Graphs can visually represent the connection between things, and make the messy information orderly, intuitive, and clear, so almost everything can be expressed by graphs. Secure multi-party computation for graph theory focuses on the secure computation of graph intersection and union [9][10][11][12][13], the secure query of subgraphs [14][15][16][17][18], the secure query of graph edit distances [19][20][21][22][23][24], and the secure query of graph paths [25][26][27].…”