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Efficient Verification of Shortest Path Search Via Authenticated Hints Man Lung YIU Hong Kong Polytechnic University

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Efficient Verification of Shortest Path Search Via Authenticated Hints Man Lung YIU Hong Kong Polytechnic University View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Knowledge at Singapore Management University Singapore Management University Institutional Knowledge at Singapore Management University Research Collection School Of Information Systems School of Information Systems 3-2010 Efficient Verification of Shortest Path Search Via Authenticated Hints Man Lung YIU Hong Kong Polytechnic University Yimin LIN Singapore Management University, [email protected] Kyriakos MOURATIDIS Singapore Management University, [email protected] DOI: https://doi.org/10.1109/ICDE.2010.5447914 Follow this and additional works at: https://ink.library.smu.edu.sg/sis_research Part of the Databases and Information Systems Commons, and the Numerical Analysis and Scientific omputC ing Commons Citation YIU, Man Lung; LIN, Yimin; and MOURATIDIS, Kyriakos. Efficient Verification of Shortest Path Search Via Authenticated Hints. (2010). ICDE 2010: IEEE 26th International Conference on Data Engineering: Long Beach, California, USA, 1 - 6 March 2010. 237-248. Research Collection School Of Information Systems. Available at: https://ink.library.smu.edu.sg/sis_research/507 This Conference Proceeding Article is brought to you for free and open access by the School of Information Systems at Institutional Knowledge at Singapore Management University. It has been accepted for inclusion in Research Collection School Of Information Systems by an authorized administrator of Institutional Knowledge at Singapore Management University. For more information, please email [email protected]. Efficient Verification of Shortest Path Search via Authenticated Hints Man Lung Yiu #1, Yimin Lin ∗2, Kyriakos Mouratidis ∗3 #Department of Computing, Hong Kong Polytechnic University Hung Hom, Hong Kong [email protected] ∗School of Information Systems, Singapore Management University 80 Stamford Road, Singapore 178902 [email protected] [email protected] Abstract— Shortest path search in transportation networks is (target vt) unarguably one of the most important online search services v4 nowadays (e.g., Google Maps, MapQuest, etc), with applications 9 1 v2 spanning logistics, spatial optimization, or everyday driving (source v ) decisions. Often times, the owner of the road network data s 1 shortest v v 6 (e.g., a transport authority) provides its database to third-party 1 path 2 query services, which are responsible for answering shortest path v queries posed by their clients. The issue arising here is that 2 5 v v a query service might be returning sub-optimal paths either 3 3 2 7 purposely (in order to serve its own purposes like computational savings or commercial reasons) or because it has been compro- mised by Internet attackers who falsify the results. Therefore, Fig. 1. Shortest path example for the above applications to succeed, it is essential that each reported path is accompanied by a proof, which allows clients to Query (vs,vt) Data Graph G Service verify the path’s correctness. Client owner ADS, Hints provider This is the first study on shortest path verification in out- Path P, sourced network databases. We propose the concept of authen- Graph G, Graph G, Proof Owner’s ticated hints, which is used to reduce the size of the proofs. Private key ADS, Hints public key We develop several authentication techniques and quantify their tradeoffs with respect to offline construction cost and proof Fig. 2. Outsourcing architecture size. Experiments on real road networks demonstrate that our solutions are indeed efficient and lead to compact query proofs. path computation also finds many applications for personal I. INTRODUCTION use. Prior to a hiking trip or a bike tour, a group of people A road network is modeled as a graph G, whose nodes wish to find the shortest path from their gathering point to a represent road junctions and whose edges correspond to road particular target location. segments. The weight of an edge typically reflects the travel Usually, the road network data belong to and are maintained distance, the driving time, or the toll fee of the respective by a commonly trusted government or transport authority, road segment. Given a source node vs and a target node vt referred to as the data owner. On the other hand, the afore- on such a graph G, the shortest path query returns the path mentioned business and personal needs are attended to by between vs and vt, along which the sum of edge weights is third-party online service providers (such as Google Maps, minimal. Figure 1 shows an example of a graph where the MapQuest, etc), who download the network information from weight of each edge corresponds to its length and is indicated the owner and use it to compute shortest paths on demand. by a number next to the edge. Suppose that the source node is The issue here is that returned paths may be incorrect for v1 and the target node is v4. The shortest path between them a variety of reasons. Firstly, the service provider may be is v1 → v3 → v5 → v6 → v4 with total cost (i.e., total length) returning sub-optimal paths for profit purposes (e.g., favorably 2+3+2+1=8. selecting paths that pass by the gas stations of a certain chain), Shortest path search is crucial to a wide range of ap- or in order to save computational resources (e.g., employing plications. For example, taxi drivers want to find shortest directional heuristics that report fast but approximate results). paths to the target locations specified by passengers. Logistics Furthermore, even if the provider is legitimate, its servers may companies need to find shortest paths (in a transportation be infiltrated by attackers via the Internet; recent studies show network) for quickly delivering packages from senders to that multi-step intrusions into online servers are becoming receivers. Besides the above daily business operations, shortest increasingly common [1]. Should an attacker take over a server, he may be falsifying the results to serve his own II. RELATED WORK purposes or to simply be a nuisance to the clients and the In this section we review the cryptographic primitives that service provider (e.g., sending clients to non-existing roads or underlie our approach, and survey related work in the areas of damaging the service provider’s reputation). This risk becomes database authentication and shortest path computation. more severe as the service providers are gradually using the low-cost cloud computing environment, where many security A. Cryptographic Primitives concerns remain unresolved. One-way hash function: Such a function H maps a message The aforementioned reasons necessitate the development of m of arbitrary length into a fixed-length output H(m), which mechanisms that will allow clients to verify the correctness is called message digest. It is fast to compute H(m), but it of the returned paths. Specifically, a client should be able to is computationally infeasible to find a message that maps to verify that: (i) the returned path P is possible, i.e., P is an a given digest. SHA-1 [9] is a commonly used one-way hash existing path in the original graph G of the data owner, and (ii) function. P is the shortest among all possible paths in G between the Cryptographic signature: A message owner creates a pair source and target nodes. To enable this, we take the following of a private and a public key; the former is kept secret and approach. The data owner constructs an authenticated data the latter is publicly distributed. A message can be signed by structure (ADS) on top of the network data and uploads them its owner using his private key. The integrity and ownership together to the provider. The provider returns parts of this of the message can then be verified by any recipient using the authentication information to the clients in the form of a signature and the owner’s public key. The most widely used correctness proof, along with each shortest path reported. This public-key signature algorithm is RSA [10]. process is depicted in Figure 2. Merkle Hash Tree (MHT): The MHT [11] is a structure Interestingly, the definition of the shortest path itself makes used for set membership verification. It is a binary tree, its verification a challenging problem. A na¨ıve solution would where each node is the digest of the concatenation of its be to generate all possible paths between the source node and two children; the leaf level contains the hashes of the set’s the target node, and show that none of them can be shorter elements (messages). The MHT root is signed by the set’s than the server’s reported path. Unfortunately, this approach owner. The integrity and ownership of an element (message) incurs a prohibitively high communication overhead between can be verified using the element itself and a proof. The proof the service provider and the client. In this paper, our challenge contains the signed root and the sibling nodes (hashes) of is to minimize the size of the proof, while it is still sufficient the path from the root down to the element. The message is for verification. To achieve this, we propose that the data owner deemed authentic if its digest combined with the proof hashes pre-computes and authenticates some auxiliary information leads to an MHT root that matches the owner’s root signature. called authenticated hints from the network. The hints are The MHT idea can be applied to arbitrary DAGs [12]. collected during query processing and inserted into the proof. B. Query Result Verification We develop a spectrum of authenticated hints with different The outsourced database model [13] includes three entities: tradeoffs in terms of offline construction cost and proof size. data owner, service provider and clients.
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