An inference–proof approach to privacy-preserving horizontally partitioned linear programs

Mangasarian (Optim. Lett., 6(3), 431–436, 2012) proposed a constraints transformation based approach to securely solving the horizontally partitioned linear programs among multiple entities—every entity holds its own private equality constraints. More recently, Li et al. (Optim. Lett., doi:10.1007/s11590-011-0403-2, 2012) extended the transformation approach to horizontally partitioned linear programs with inequality constraints. However, such transformation approach is not sufficiently secure – occasionally, the privately owned constraints are still under high risk of inference. In this paper, we present an inference–proof algorithm to enhance the security for privacy-preserving horizontally partitioned linear program with arbitrary number of equality and inequality constraints. Our approach reveals significantly less information than the prior work and resolves the potential inference attack.

[1]  Florian Kerschbaum,et al.  Practical Privacy-Preserving Multiparty Linear Programming Based on Problem Transformation , 2011, 2011 IEEE Third Int'l Conference on Privacy, Security, Risk and Trust and 2011 IEEE Third Int'l Conference on Social Computing.

[2]  Wenliang Du,et al.  A study of several specific secure two-party computation problems , 2001 .

[3]  Zhinan Zhang,et al.  The rank of a random matrix , 2007, Appl. Math. Comput..

[4]  Jaideep Vaidya.  A Secure Revised Simplex Algorithm for Privacy-Preserving Linear Programming , 2009, 2009 International Conference on Advanced Information Networking and Applications.

[5]  Olvi L. Mangasarian.  Privacy-preserving horizontally partitioned linear programs , 2012, Optim. Lett..

[6]  Jaideep Vaidya,et al.  Secure and efficient distributed linear programming , 2012, J. Comput. Secur..

[7]  Shigenobu Kobayashi,et al.  A genetic algorithm for privacy preserving combinatorial optimization , 2007, GECCO '07.

[8]  Matthew Roughan,et al.  Hiccups on the road to privacy-preserving linear programming , 2009, WPES '09.

[9]  Basit Shafiq,et al.  Privacy-Preserving Tabu Search for Distributed Graph Coloring , 2011, 2011 IEEE Third Int'l Conference on Privacy, Security, Risk and Trust and 2011 IEEE Third Int'l Conference on Social Computing.

[10]  Jaideep Vaidya,et al.  Privacy-preserving linear programming , 2009, SAC '09.

[11]  Mikhail J. Atallah,et al.  Secure and Private Collaborative Linear Programming , 2006, 2006 International Conference on Collaborative Computing: Networking, Applications and Worksharing.

[12]  Wei Li,et al.  Privacy-preserving horizontally partitioned linear programs with inequality constraints , 2013, Optim. Lett..

[13]  Jaideep Vaidya,et al.  Efficient Distributed Linear Programming with Limited Disclosure , 2011, DBSec.