Advertisement

Secure Multiparty Linear Programming Using Fixed-Point Arithmetic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6345)

Abstract

Collaborative optimization problems can often be modeled as a linear program whose objective function and constraints combine data from several parties. However, important applications of this model (e.g., supply chain planning) involve private data that the parties cannot reveal to each other. Traditional linear programming methods cannot be used in this case. The problem can be solved using cryptographic protocols that compute with private data and preserve data privacy. We present a practical solution using multiparty computation based on secret sharing. The linear programming protocols use a variant of the simplex algorithm and secure computation with fixed-point rational numbers, optimized for this type of application. We present the main protocols as well as performance measurements for an implementation of our solution.

Keywords

Secure multiparty computation linear programming secure fixed-point arithmetic secret sharing 

References

  1. 1.
    Bednarz, A., Bean, N., Roughan, M.: Hiccups on the road to privacy-preserving linear programming. In: WPES 2009: Proc. of the 8th ACM Workshop on Privacy in the electronic society, pp. 117–120. ACM, New York (2009)CrossRefGoogle Scholar
  2. 2.
    Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization. Athena Scientific, Belmont (1997)Google Scholar
  3. 3.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13(1), 143–202 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Catrina, O., Saxena, A.: Secure computation with fixed-point numbers. In: Financial Cryptography and Data Security. LNCS, Springer, Heidelberg (2010)Google Scholar
  5. 5.
    Cramer, R., Damgård, I., Ishai, Y.: Share conversion, pseudorandom secret-sharing and applications to secure computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Cramer, R., Damgård, I., Maurer, U.: General Secure Multi-Party Computation from any Linear Secret-Sharing Scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Thorbek, R.: Non-interactive Proofs for Integer Multiplication. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 412–429. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Damgard, I., Thorbek, R.: Efficient conversion of secret-shared values between different fields. Cryptology ePrint Archive, Report 2008/221 (2008)Google Scholar
  10. 10.
    Ercegovac, M.D., Lang, T.: Digital Arithmetic. Morgan Kaufmann, San Francisco (2003)Google Scholar
  11. 11.
    Frati, F., Damiani, E., Ceravolo, P., Cimato, S., Fugazza, C., Gianini, G., Marrara, S., Scotti, O.: Hazards in full-disclosure supply chains. In: Proc. 8th Conference on Advanced Information Technologies for Management, AITM 2008 (2008)Google Scholar
  12. 12.
    Gennaro, R., Rabin, M., Rabin, T.: Simplified VSS and fast-track multi-party computations with applications to threshold cryptography. In: Proc. of ACM Symposium on Principles of Distributed Computing, PODC 1998 (1998)Google Scholar
  13. 13.
    Li, J., Atallah, M.: Secure and Private Collaborative Linear Programming. In: Proc. 2nd Int. Conference on Collaborative Computing: Networking, Applications and Worksharing (ColaborateCom 2006), Atlanta, USA, pp. 19–26 (2006)Google Scholar
  14. 14.
    Nishide, T., Ohta, K.: Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Rosenberg, G.: Enumeration of All Extreme Equilibria of Bimatrix Games with Integer Pivoting and Improved Degeneracy Check. Research Report LSE-CDAM-2005-18, London School of Economics and Political Science (2005)Google Scholar
  16. 16.
    SecureSCM. Security Analysis. Deliverable D9.2, EU FP7 Project Secure Supply Chain Management, SecureSCM (2009)Google Scholar
  17. 17.
    SecureSCM. Protocol Description V2. Deliverable D3.2, EU FP7 Project Secure Supply Chain Management, SecureSCM (2010)Google Scholar
  18. 18.
    Toft, T.: Primitives and Applications for Multi-party Computation. PhD dissertation, Univ. of Aarhus, Denmark, BRICS, Dep. of Computer Science (2007)Google Scholar
  19. 19.
    Toft, T.: Solving Linear Programs Using Multiparty Computation. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 90–107. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. of Computer ScienceUniversity of MannheimGermany
  2. 2.Dept. of Mathematics and Computer ScienceTU EindhovenThe Netherlands

Personalised recommendations