Access-Private Outsourcing of Markov Chain and RandomWalk based Data Analysis Applications

Random walk graph and Markov chain based models are used heavily in many data and system analysis domains, including web, bioinformatics, and queueing. These models enable the description and analysis of various behaviors of stochastic systems. If the system being modelled has certain properties, such as if it is irreducible and aperiodic, close form formulations corresponding to its stationary behavior can be used to analyze its behavior. However, if the system does not have these properties or if the user is not interested in the stationary behavior, then an iterative approach needs to be used to determine potential outcomes based on the initial probability distribution inputs to the model. In this paper, we focus on access-privacy enabled outsourced Markov chain based data analysis applications, where a non-trusted service provider takes (hidden) user queries that are described in terms of initial state distributions, and evaluates them iteratively in an oblivious manner. We show that this iterative process can leak information regarding the possible values of the hidden input if the server has a priori knowledge about the underlying Markovian process. Hence as opposed to simple obfuscation mechanisms, we develop an algorithm based on methodical addition of extra states, which guarantees unbounded feasible regions for the inputs, thus preventing a malicious host from having an informed guess regarding the inputs.

[1]  Hakan Hacigümüs,et al.  Executing SQL over encrypted data in the database-service-provider model , 2002, SIGMOD '02.

[2]  Christian F. Tschudin,et al.  Protecting Mobile Agents Against Malicious Hosts , 1998, Mobile Agents and Security.

[3]  Chris Clifton,et al.  Tools for privacy preserving distributed data mining , 2002, SKDD.

[4]  Feng Shao,et al.  XRANK: ranked keyword search over XML documents , 2003, SIGMOD '03.

[5]  P. Diaconis,et al.  Random walks and hyperplane arrangements , 1998 .

[6]  Jon M. Kleinberg,et al.  Inferring Web communities from link topology , 1998, HYPERTEXT '98.

[7]  Martín Abadi,et al.  On hiding information from an oracle , 1987, STOC '87.

[8]  Gene Tsudik,et al.  A Privacy-Preserving Index for Range Queries , 2004, VLDB.

[9]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[10]  Luc Moreau,et al.  Certificates for mobile code security , 2002, SAC '02.

[11]  Martín Abadi,et al.  On Hiding Information from an Oracle , 1987, Proceeding Structure in Complexity Theory.

[12]  Wei Wu,et al.  Numerical Experiments with Iteration and Aggregation for Markov Chains , 1992, INFORMS J. Comput..

[13]  K. Candan,et al.  Data and Application Secutiry for Distributed Application Hosting Services , 2004 .

[14]  Jeroen Doumen,et al.  Using Secret Sharing for Searching in Encrypted Data , 2004, Secure Data Management.

[15]  David J. DeWitt,et al.  Limiting Disclosure in Hippocratic Databases , 2004, VLDB.

[16]  Ramakrishnan Srikant,et al.  Hippocratic Databases , 2002, VLDB.

[17]  Jim Alves-Foss,et al.  The use of encrypted functions for mobile agent security , 2004, 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the.

[18]  Jon M. Kleinberg,et al.  Clustering categorical data: an approach based on dynamical systems , 2000, The VLDB Journal.

[19]  K. Selçuk Candan,et al.  Hiding Tree Structured Data and Queries from Untrusted Data Stores , 2005, Inf. Secur. J. A Glob. Perspect..

[20]  Christian F. Tschudin,et al.  Towards mobile cryptography , 1998, Proceedings. 1998 IEEE Symposium on Security and Privacy (Cat. No.98CB36186).

[21]  Ehud Gudes,et al.  A Structure Preserving Database Encryption Scheme , 2004, Secure Data Management.

[22]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[23]  Vagelis Hristidis,et al.  ObjectRank: Authority-Based Keyword Search in Databases , 2004, VLDB.

[24]  K. Selçuk Candan,et al.  Secure and Privacy Preserving Outsourcing of Tree Structured Data , 2004, Secure Data Management.

[25]  Luc Bouganim,et al.  Chip-Secured Data Access: Reconciling Access Rights with Data Encryption , 2003, VLDB.

[26]  Giovanni Vigna,et al.  Cryptographic Traces for Mobile Agents , 1998, Mobile Agents and Security.

[27]  Rida A. Bazzi,et al.  Provably secure data hiding and tamper resistance for a simple loop program , 2003, SPIE Defense + Commercial Sensing.

[28]  Chris Clifton,et al.  Privacy-Enhanced Data Management for Next-Generation e-Commerce , 2003, VLDB.

[29]  Roger Barga,et al.  Proceedings of the 22nd International Conference on Data Engineering Workshops, ICDE 2006, 3-7 April 2006, Atlanta, GA, USA , 2006, ICDE Workshops.

[30]  Luc Bouganim,et al.  Chip-Secured Data Access: Confidential Data on Untrusted Servers , 2002, VLDB.

[31]  Chris Clifton,et al.  Privacy-preserving distributed mining of association rules on horizontally partitioned data , 2004, IEEE Transactions on Knowledge and Data Engineering.