Hiding Alice in Wonderland: A Case for the Use of Signal Processing Techniques in Differential Privacy

  • Maurizio NaldiEmail author
  • Alessandro Mazzoccoli
  • Giuseppe D’Acquisto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11079)


A transformation of data in statistical databases is proposed to hide the presence of an individual. The transformation employs a cascade of spectral whitening and colouring (named recolouring for brevity) that preserves the first- and second-order statistical properties of the true data (i.e. mean and correlation). A measure of practical indistinguishability is introduced for the presence of the individual to be hidden (the Impact Factor), and the transformation is applied to a toy model for the case of correlated data following a Gaussian copula model. It is shown that the Impact Factor is a multiple of what would be achieved with noise addition: the proposed recolouring transformation significantly enlarges the range of attribute values for which the presence of the individual of interest cannot be reliably inferred.


Privacy Statistical databases Differential privacy Noise addition Correlation 


  1. 1.
    Björck, Å., Hammarling, S.: A schur method for the square root of a matrix. Linear Algebra Appl. 52, 127–140 (1983)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brand, R.: Microdata protection through noise addition. In: Domingo-Ferrer, J. (ed.) Inference Control in Statistical Databases. LNCS, vol. 2316, pp. 97–116. Springer, Heidelberg (2002). Scholar
  3. 3.
    Ciriani, V., De Capitani di Vimercati, S., Foresti, S., Samarati, P.: Microdata protection. In: Yu, T., Jajodia, S. (eds.) Secure Data Management in Decentralized Systems, pp. 291–321. Springer, Boston (2007). Scholar
  4. 4.
    Domingo-Ferrer, J., Sebé, F., Castellà-Roca, J.: On the security of noise addition for privacy in statistical databases. In: Domingo-Ferrer, J., Torra, V. (eds.) PSD 2004. LNCS, vol. 3050, pp. 149–161. Springer, Heidelberg (2004). Scholar
  5. 5.
    Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006). Scholar
  6. 6.
    Dwork, C.: Differential privacy: a survey of results. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008). Scholar
  7. 7.
    Dwork, C.: A firm foundation for private data analysis. Commun. ACM 54(1), 86–95 (2011)CrossRefGoogle Scholar
  8. 8.
    Galati, G. (ed.): Advanced Radar Techniques and Systems. Peter Peregrinus Ltd., London (1993)Google Scholar
  9. 9.
    Glasserman, P., Kang, W., Shahabuddin, P.: Large deviations in multifactor portfolio credit risk. Math. Financ. 17(3), 345–379 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Heffetz, O., Ligett, K.: Privacy and data-based research. J. Econ. Perspect. 28(2), 75–98 (2014)CrossRefGoogle Scholar
  11. 11.
    Kim, J.J.: A method for limiting disclosure in microdata based on random noise and transformation, pp. 303–308. American Statistical Association (1986)Google Scholar
  12. 12.
    Li, C., Hay, M., Rastogi, V., Miklau, G., McGregor, A.: Optimizing linear counting queries under differential privacy. In: Proceedings of the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2010, pp. 123–134. ACM, New York (2010)Google Scholar
  13. 13.
    Liu, C., Chakraborty, S., Mittal, P.: Dependence makes you vulnerable: differential privacy under dependent tuples. In: Proceedings of Network and Distributed System Security Symposium (NDSS 2016) (2016)Google Scholar
  14. 14.
    McClure, D., Reiter, J.P.: Differential privacy and statistical disclosure risk measures: an investigation with binary synthetic data. Trans. Data Privacy 5(3), 535–552 (2012)MathSciNetGoogle Scholar
  15. 15.
    Mivule, K.: Utilizing noise addition for data privacy, an overview. arXiv preprint arXiv:1309.3958 (2013)
  16. 16.
    Naldi, M., D’Acquisto, G.: Differential privacy for counting queries: can Bayes estimation help uncover the true value? arXiv preprint arXiv:1407.0116 (2014)
  17. 17.
    Naldi, M., D’Acquisto, G.: Differential privacy: an estimation theory-based method for choosing epsilon. arXiv preprint arXiv:1510.00917 (2015)
  18. 18.
    Naldi, M., D’Acquisto, G.: Mr X vs. Mr Y: the emergence of externalities in differential privacy. In: Schweighofer, E., Leitold, H., Mitrakas, A., Rannenberg, K. (eds.) APF 2017. LNCS, vol. 10518, pp. 120–140. Springer, Cham (2017). Scholar
  19. 19.
    Sarathy, R., Muralidhar, K.: Evaluating laplace noise addition to satisfy differential privacy for numeric data. Trans. Data Priv. 4(1), 1–17 (2011)MathSciNetGoogle Scholar
  20. 20.
    Spruill, N.L.: The confidentiality and analytic usefulness of masked business microdata. Rev. Public Data Use 12(4), 307–314 (1984)MathSciNetGoogle Scholar
  21. 21.
    Sullivan, G.R.: The use of added error to avoid disclosure in microdata releases. Ph.D. thesis, Iowa State University (1989)Google Scholar
  22. 22.
    Tendick, P.: Optimal noise addition for preserving confidentiality in multivariate data. J. Stat. Plan. Infer. 27(3), 341–353 (1991)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Tendick, P., Matloff, N.: A modified random perturbation method for database security. ACM Trans. Database Syst. (TODS) 19(1), 47–63 (1994)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Maurizio Naldi
    • 1
    Email author
  • Alessandro Mazzoccoli
    • 1
  • Giuseppe D’Acquisto
    • 1
  1. 1.Department of Civil Engineering and Computer ScienceUniversity of Rome Tor VergataRomeItaly

Personalised recommendations