Hybrid Model of Fixed and Floating Point Numbers in Secure Multiparty Computations

  • Toomas Krips
  • Jan Willemson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8783)


This paper develops a new hybrid model of floating point numbers suitable for operations in secure multi-party computations. The basic idea is to consider the significand of the floating point number as a fixed point number and implement elementary function applications separately of the significand. This gives the greatest performance gain for the power functions (e.g. inverse and square root), with computation speeds improving up to 18 times in certain configurations. Also other functions (like exponent and Gaussian error function) allow for the corresponding optimisation.

We have proposed new polynomials for approximation, and implemented and benchmarked all our algorithms on the Sharemind secure multi-party computation framework.


Hybrid Model Secret Sharing Chebyshev Polynomial Point Number Full Version 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aliasgari, M., Blanton, M., Zhang, Y., Steele, A.: Secure computation on floating point numbers. In: NDSS (2013)Google Scholar
  2. 2.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: A Framework for Fast Privacy-Preserving Computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Bogdanov, D., Niitsoo, M., Toft, T., Willemson, J.: High-performance secure multi-party computation for data mining applications. International Journal of Information Security 11(6), 403–418 (2012)CrossRefGoogle Scholar
  4. 4.
    Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Catrina, O., Dragulin, C.: Multiparty computation of fixed-point multiplication and reciprocal. In: 20th International Workshop on Database and Expert Systems Application, DEXA 2009, pp. 107–111 (2009)Google Scholar
  6. 6.
    Catrina, O., de Hoogh, S.: Secure multiparty linear programming using fixed-point arithmetic. In: Gritzalis, D., Preneel, B., Theoharidou, M. (eds.) ESORICS 2010. LNCS, vol. 6345, pp. 134–150. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Catrina, O., Saxena, A.: Secure computation with fixed-point numbers. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 35–50. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Dahl, M., Ning, C., Toft, T.: On secure two-party integer division. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 164–178. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169–178 (2009)Google Scholar
  10. 10.
    Gentry, C., Halevi, S.: Implementing gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Kamm, L., Willemson, J.: Secure floating-point arithmetic and private satellite collision analysis. Cryptology ePrint Archive, Report 2013/850 (2013),
  12. 12.
    Kerschbaum, F., Schroepfer, A., Zilli, A., Pibernik, R., Catrina, O., de Hoogh, S., Schoenmakers, B., Cimato, S., Damiani, E.: Secure collaborative supply-chain management. Computer 44(9), 38–43 (2011)CrossRefGoogle Scholar
  13. 13.
    Krips, T., Willemson, J.: Hybrid model of fixed and floating point numbers in secure multiparty computations. Cryptology ePrint Archive, Report 2014/221 (2014),
  14. 14.
    Laur, S., Willemson, J., Zhang, B.: Round-Efficient Oblivious Database Manipulation. In: Lai, X., Zhou, J., Li, H. (eds.) ISC 2011. LNCS, vol. 7001, pp. 262–277. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Liedel, M.: Secure distributed computation of the square root and applications. In: Ryan, M.D., Smyth, B., Wang, G. (eds.) ISPEC 2012. LNCS, vol. 7232, pp. 277–288. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Liu, Y.-C., Chiang, Y.-T., Hsu, T.S., Liau, C.-J., Wang, D.-W.: Floating point arithmetic protocols for constructing secure data analysis applicationGoogle Scholar
  17. 17.
    Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M.: L-diversity: Privacy Beyond K-anonymity. ACM Transactions on Knowledge Discovery from Data (TKDD) 1(1) (March 2007)Google Scholar
  18. 18.
    Samarati, P.: Protecting Respondents’ Identities in Microdata Release. IEEE Transactions on Knowledge and Data Engineering 13, 1010–1027 (2001)CrossRefGoogle Scholar
  19. 19.
    Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Sweeney, L.: K-anonymity: A Model for Protecting Privacy. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10(5), 557–570 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Zhang, Y., Steele, A., Blanton, M.: Picco: A general-purpose compiler for private distributed computation. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, CCS 2013, pp. 813–826. ACM, New York (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Toomas Krips
    • 2
    • 3
  • Jan Willemson
    • 1
    • 3
  1. 1.CyberneticaTartuEstonia
  2. 2.Institute of Computer ScienceUniversity of TartuTartuEstonia
  3. 3.STACCTartuEstonia

Personalised recommendations