# Efficient and Secure Outsourcing of Differentially Private Data Publication

## Abstract

While big data becomes a main impetus to the next generation of IT industry, big data privacy, as an unevadable topic in big data era, has received considerable attention in recent years. To deal with the privacy challenges, differential privacy has been widely discussed as one of the most popular privacy-enhancing techniques. However, with today’s differential privacy techniques, it is impossible to generate a sanitized dataset that can suit different algorithms or applications regardless of the privacy budget. In other words, in order to adapt to various applications and privacy budgets, different kinds of noises have to be added, which inevitably incur enormous costs for both communication and storage. To address the above challenges, in this paper, we propose a novel scheme for outsourcing differential privacy in cloud computing, where an additive homomorphic encryption (e.g., Paillier encryption) is employed to compute noise for differential privacy by cloud servers to boost efficiency. The proposed scheme allows data providers to outsource their dataset sanitization procedure to cloud service providers with a low communication cost. In addition, the data providers can go offline after uploading their datasets and noise parameters, which is one of the critical requirements for a practical system. We present a detailed theoretical analysis of our proposed scheme, including proofs of differential privacy and security. Moreover, we also report an experimental evaluation on real UCI datasets, which confirms the effectiveness of the proposed scheme.

## Notes

### Acknowledgement

This work was supported by Natural Science Foundation of Guangdong Province for Distinguished Young Scholars (2014A030306020), National Natural Science Foundation of China (No. 61472091) and National Natural Science Foundation for Outstanding Youth Foundation (No. 61722203). This work was also supported in part by US National Science Foundation under grants CNS-1446478 and CNS-1443889.

## References

- 1.Barak, B., Chaudhuri, K., Dwork, C., Kale, S., Mcsherry, F., Talwar, K.: Privacy, accuracy, and consistency too: a holistic solution to contingency table release, pp. 273–282 (2007)Google Scholar
- 2.Benjamin, D., Atallah, M.J.: Private and cheating-free outsourcing of algebraic computations, pp. 240–245 (2008)Google Scholar
- 3.Blum, A., Ligett, K., Roth, A.: A learning theory approach to non-interactive database privacy, pp. 609–618 (2008)Google Scholar
- 4.Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_7CrossRefGoogle Scholar
- 5.Chen, R., Mohammed, N., Fung, B.C.M., Desai, B.C., Xiong, L.: Publishing set-valued data via differential privacy. Proc. VLDB Endow.
**4**, 1087–1098 (2011)Google Scholar - 6.Chevallier-Mames, B., Coron, J.-S., McCullagh, N., Naccache, D., Scott, M.: Secure delegation of elliptic-curve pairing. In: Gollmann, D., Lanet, J.-L., Iguchi-Cartigny, J. (eds.) CARDIS 2010. LNCS, vol. 6035, pp. 24–35. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12510-2_3CrossRefGoogle Scholar
- 7.Cormode, G., Procopiuc, C.M., Srivastava, D., Shen, E., Yu, T.: Differentially private spatial decompositions, pp. 20–31 (2012)Google Scholar
- 8.Dwork, C., Lei, J.: Differential privacy and robust statistics, pp. 371–380 (2009)Google Scholar
- 9.Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_14CrossRefGoogle Scholar
- 10.Dwork, C., Naor, M., Reingold, O., Rothblum, G.N., Vadhan, S.: On the complexity of differentially private data release: efficient algorithms and hardness results, pp. 381–390 (2009)Google Scholar
- 11.Dwork, C., Naor, M., Vadhan, S.: The privacy of the analyst and the power of the state, pp. 400–409 (2012)Google Scholar
- 12.Dwork, C., Rothblum, G.N., Vadhan, S.: Boosting and differential privacy, pp. 51–60 (2010)Google Scholar
- 13.Gupta, S.K., Rana, S., Venkatesh, S.: Differentially private multi-task learning. In: Chau, M., Wang, G.A., Chen, H. (eds.) PAISI 2016. LNCS, vol. 9650, pp. 101–113. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31863-9_8CrossRefGoogle Scholar
- 14.Hardt, M., Rothblum, G.N., Servedio, R.A.: Private data release via learning thresholds, pp. 168–187 (2012)Google Scholar
- 15.Hay, M., Rastogi, V., Miklau, G., Suciu, D.: Boosting the accuracy of differentially private histograms through consistency. Proc. VLDB Endow.
**3**, 1021–1032 (2010)CrossRefGoogle Scholar - 16.Huang, Z., Liu, S., Mao, X., Chen, K., Li, J.: Insight of the protection for data security under selective opening attacks. Inf. Sci.
**412–413**, 223–241 (2017)CrossRefGoogle Scholar - 17.Jagadish, H.V., Koudas, N., Muthukrishnan, S., Poosala, V., Sevcik, K.C., Suel, T.: Optimal histograms with quality guarantees. Very Large Data Bases, 275–286 (2010)Google Scholar
- 18.Ji, Z., Jiang, X., Wang, S., Xiong, L., Ohnomachado, L.: Differentially private distributed logistic regression using private and public data. BMC Med. Genomics
**7**(1), 1–10 (2014)CrossRefGoogle Scholar - 19.Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately, pp. 531–540 (2008)Google Scholar
- 20.Kasiviswanathan, S.P., Rudelson, M., Smith, A., Ullman, J.: The price of privately releasing contingency tables and the spectra of random matrices with correlated rows, pp. 775–784 (2010)Google Scholar
- 21.Li, C., Hay, M., Rastogi, V., Miklau, G., Mcgregor, A.: Optimizing linear counting queries under differential privacy, pp. 123–134 (2010)Google Scholar
- 22.Li, P., Li, J., Huang, Z., Gao, C., Chen, W., Chen, K.: Privacy-preserving outsourced classification in cloud computing. Cluster Comput. 1–10 (2017)Google Scholar
- 23.Li, P., et al.: Multi-key privacy-preserving deep learning in cloud computing. Future Gener. Comput. Syst.
**74**, 76–85 (2017)CrossRefGoogle Scholar - 24.Mcsherry, F.: Privacy integrated queries: an extensible platform for privacy-preserving data analysis. Commun. ACM
**53**(9), 89–97 (2010)CrossRefGoogle Scholar - 25.Mcsherry, F., Talwar, K.: Mechanism design via differential privacy, pp. 94–103 (2007)Google Scholar
- 26.Mohammed, N., Chen, R., Fung, B.C.M., Yu, P.S.: Differentially private data release for data mining, pp. 493–501 (2011)Google Scholar
- 27.Pathak, M.A., Rane, S., Raj, B.: Multiparty differential privacy via aggregation of locally trained classifiers, pp. 1876–1884 (2010)Google Scholar
- 28.Qardaji, W., Yang, W., Li, N.: Differentially private grids for geospatial data, pp. 757–768 (2013)Google Scholar
- 29.Qardaji, W., Yang, W., Li, N.: Priview: practical differentially private release of marginal contingency tables, pp. 1435–1446 (2014)Google Scholar
- 30.Shokri, R., Shmatikov, V.: Privacy-preserving deep learning, pp. 1310–1321 (2015)Google Scholar
- 31.Su, S., Tang, P., Cheng, X., Chen, R., Wu, Z.: Differentially private multi-party high-dimensional data publishing, pp. 205–216 (2016)Google Scholar
- 32.Vaidya, J., Clifton, C.: Privacy preserving association rule mining in vertically partitioned data, pp. 639–644 (2002)Google Scholar
- 33.Vaidya, J., Clifton, C.: Privacy-preserving k-means clustering over vertically partitioned data, pp. 206–215 (2003)Google Scholar
- 34.Wang, B., Li, M., Chow, S.S.M., Li, H.: A tale of two clouds: computing on data encrypted under multiple keys. In: Communications and Network Security, pp. 337–345 (2014)Google Scholar
- 35.Xiao, X., Wang, G., Gehrke, J.: Differential privacy via wavelet transforms. IEEE Trans. Knowl. Data Eng.
**23**(8), 1200–1214 (2011)CrossRefGoogle Scholar - 36.Xiao, Y., Xiong, L., Yuan, C.: Differentially private data release through multidimensional partitioning. In: Jonker, W., Petković, M. (eds.) SDM 2010. LNCS, vol. 6358, pp. 150–168. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15546-8_11CrossRefGoogle Scholar
- 37.Xu, J., Zhang, Z., Xiao, X., Yang, Y., Yu, G., Winslett, M.: Differentially private histogram publication. Very Large Data Bases
**22**(6), 797–822 (2013)CrossRefGoogle Scholar - 38.Yuan, G., Zhang, Z., Winslett, M., Xiao, X., Yang, Y., Hao, Z.: Low-rank mechanism: optimizing batch queries under differential privacy. Proc. VLDB Endow.
**5**(11), 1352–1363 (2012)CrossRefGoogle Scholar