Securely Solving Simple Combinatorial Graph Problems

Aly, Abdelrahaman; Cuvelier, Édouard; Mawet, Sophie; Pereira, Olivier; Vyve, Mathieu Van

doi:10.1007/978-3-642-39884-1_21

Cited by 42 publications

(26 citation statements)

References 29 publications

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“…Aly et al [1] addressed the problem of transforming classical graph algorithms to a privacy preserving environment. More concretely, they considered different secure algorithms for the shortest path and the maximum flow in "honestbut-curious" model.…”

Section: Related Workmentioning

confidence: 99%

Privacy-Preserving Triangle Counting in Distributed Graphs

Giang

2016

2016 IEEE 30th International Conference on Advanced Information Networking and Applications (AINA)

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Together with the popularity of graph structure in real world data, graph analysis has become an attractive research topic. Triangle counting is one of typical graph mining tasks and plays a significant role in complex network analysis, with a wide range of applications in social network analysis, spam detection, and computer-aided design applications. Given the sensitive nature of graph data, the disclosure of graph content for the purpose of analysis may raise a major privacy concern to both individuals and organizations. In this paper, we propose a protocol for privacy-preserving triangle counting when the overall graph is distributed to different parties. We firstly present the solution in a two-party scenario and then extend the protocol to any number of participating parties. The graph structure is represented by an adjacency matrix, and cryptographic secure matrix computation is utilized to tackle the problem. A secure multi-party power of matrix sum protocol is proposed to serve as a building block for the solution. We have evaluated the computational complexity and scalability of the proposed protocols both analytically and empirically. The results show that the protocols are efficient and scalable for small and medium size data.

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Section: Related Workmentioning

confidence: 99%

Privacy-Preserving Triangle Counting in Distributed Graphs

Giang

2016

2016 IEEE 30th International Conference on Advanced Information Networking and Applications (AINA)

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“…However, we could also keep the topology private, which comes at an overhead of O(n 3 ), where n is the number of ASes [46]. For country-level ASes, especially when excluding stub-nodes, this overhead seems tolerable.…”

Section: Hiding the Network Topologymentioning

confidence: 99%

Privacy-Preserving Interdomain Routing at Internet Scale

Asharov

Demmler

Schapira

et al. 2017

Proceedings on Privacy Enhancing Technologies

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Abstract:The Border Gateway Protocol (BGP) computes routes between the organizational networks that make up today's Internet. Unfortunately, BGP suffers from deficiencies, including slow convergence, security problems, a lack of innovation, and the leakage of sensitive information about domains' routing preferences. To overcome some of these problems, we revisit the idea of centralizing and using secure multi-party computation (MPC) for interdomain routing which was proposed by Gupta et al. (ACM HotNets'12). We implement two algorithms for interdomain routing with state-of-the-art MPC protocols. On an empirically derived dataset that approximates the topology of today's Internet (55 809 nodes), our protocols take as little as 6 s of topologyindependent precomputation and only 3 s of online time. We show, moreover, that when our MPC approach is applied at country/region-level scale, runtimes can be as low as 0.17 s online time and 0.20 s pre-computation time. Our results motivate the MPC approach for interdomain routing and furthermore demonstrate that current MPC techniques are capable of efficiently tackling real-world problems at a large scale.

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“…In Section 5 we use our oblivious array to construct an oblivious priority queue, where secret shared items can be efficiently added and removed from the queue without revealing any information (even the type of operation being performed) and show how to use this to securely implement Dijkstra's shortest path algorithm in time O(|E| log 5 |E| + |V | log 4 |V |), when only the number of vertices and edges in the graph is public. The previous best known algorithm [2] for this takes time in O(|V | 3 ). In Appendix B we also show how to modify the underlying ORAM to implement a priority queue directly, where each priority queue operation essentially takes just one ORAM access (instead of log |V | accesses), but we have not implemented this variant.…”

Section: Our Contributionsmentioning

confidence: 99%

“…Secure variants of shortest path and maximum flow algorithms were presented for use in MPC by Aly et al [2]. They operate on a secret-shared adjacency matrix without using ORAM, which leads to an asymptotic complexity in O(|V | 3 ) for Dijkstra's algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…We chose it as a simple example of a graph with low degree. Figure 4 shows the timings of our implementation of the algorithm without ORAM techniques by Aly et al [2] as well as our implementation using the oblivious array in Section 3.1 and the SCSL ORAM in Section 4.2. In all cases, we used MPC over a finite field modulo a 128-bit prime to allow for integer arithmetic.…”

Section: Dijkstra's Algorithmmentioning

confidence: 99%

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Efficient, Oblivious Data Structures for MPC

Keller

Schöll

2014

Lecture Notes in Computer Science

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Abstract. We present oblivious implementations of several data structures for secure multiparty computation (MPC) such as arrays, dictionaries, and priority queues. The resulting oblivious data structures have only polylogarithmic overhead compared with their classical counterparts. To achieve this, we give secure multiparty protocols for the ORAM of Shi et al. (Asiacrypt '11) and the Path ORAM scheme of Stefanov et al. (CCS '13), and we compare the resulting implementations. We subsequently use our oblivious priority queue for secure computation of Dijkstra's shortest path algorithm on general graphs, where the graph structure is secret. To the best of our knowledge, this is the first implementation of a non-trivial graph algorithm in multiparty computation with polylogarithmic overhead. We implemented and benchmarked all of our protocols using the SPDZ protocol of Damgård et al. (Crypto '12), which works in the preprocessing model and ensures active security against an adversary corrupting all but one players. For two parties, the online access time for an oblivious array of size 1 million is under 250 ms.

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Securely Solving Simple Combinatorial Graph Problems

Cited by 42 publications

References 29 publications

Privacy-Preserving Triangle Counting in Distributed Graphs

Privacy-Preserving Triangle Counting in Distributed Graphs

Privacy-Preserving Interdomain Routing at Internet Scale

Efficient, Oblivious Data Structures for MPC

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